import warnings
from copy import deepcopy
from functools import reduce
import json
from operator import and_
from pathlib import Path
import re
from typing import Any, Union
import numpy as np
import pandas as pd
from hikari.resources import (point_groups_json, space_groups_json,
point_groups_dataframe, space_groups_dataframe)
from hikari.symmetry.operations import BoundedOperation
from hikari.utility.typing import PathLike
from hikari.symmetry.group import Group
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CATALOG KEYS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
class GroupCatalogKey:
"""Base Class for every following `GroupCatalogKey`. Each named
`GroupCatalogKey` represents a single column in the `GroupCatalog` table."""
name: str = '' # if not empty, how key will be registered
accessor_priority: float = 0. # if > 0 used to access groups (inc. order)
dtype: Union[str, Any] = 'str' # used for type-casting at column creation
dependencies: list = [] # other keys needed to construct this key
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
"""Abstract method to implement only if key might have to be constructed"""
[docs]
class GroupCatalogKeyCompulsory(GroupCatalogKey):
"""Subclass of `GroupCatalogKey`, specifies key must exist in input table"""
[docs]
@classmethod
def construct(cls, table: pd.DataFrame):
if cls.name not in table:
raise KeyError('Compulsory `GroupCatalogKey` missing: ' + cls.name)
[docs]
class GroupCatalogKeyNC(GroupCatalogKeyCompulsory):
"""Unique group identification string composed of group number:setting"""
name = 'n_c'
[docs]
class GroupCatalogKeyNumber(GroupCatalogKey):
"""Integer assigned to each groups in ITC A, shared by all settings of a group"""
name = 'number'
accessor_priority = 350.
dependencies = [GroupCatalogKeyNC]
dtype = 'int16'
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
return (table['n_c'] + ':').str.split(':', expand=True).iloc[:, 0].astype(int)
[docs]
class GroupCatalogKeySetting(GroupCatalogKey):
"""Unique setting symbol (typically axis dir.) distinguishes same-number groups"""
name = 'setting'
dependencies = [GroupCatalogKeyNC]
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
return table['n_c'].str.split(':', expand=True).iloc[:, -1].fillna('').astype(str)
[docs]
class GroupCatalogKeyHM(GroupCatalogKeyCompulsory):
"""Full international Hermann-Mauguin name split with `_` with :setting"""
name = 'HM'
accessor_priority = 150.
[docs]
class GroupCatalogKeyHall(GroupCatalogKeyCompulsory):
"""Full Hall symbol of given group used to recreate it"""
name = 'Hall'
accessor_priority = 250.
[docs]
class GroupCatalogKeyGroup(GroupCatalogKey):
"""Creates and names `hikari.symmetry.Group` object based on Hall symbol"""
name = 'group'
dtype = Group
dependencies = [GroupCatalogKeyNumber, GroupCatalogKeyHM, GroupCatalogKeyHall]
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
groups = []
for n, name, symbol in zip(table['number'], table['HM'], table['Hall']):
group = Group.from_hall_symbol(symbol)
group.name = name
group.number = n
groups.append(group)
return pd.Series(groups)
[docs]
class GroupCatalogKeyHMShort(GroupCatalogKey):
"""Shortened `HM` symbol where all underscores were simply removed"""
name = 'HM_short'
accessor_priority = 140.
dependencies = [GroupCatalogKeyHM]
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
return table['HM'].str.replace('_', '')
[docs]
class GroupCatalogKeyHMSimple(GroupCatalogKey):
"""`HM_short` without setting and with `1` removed for monoclinic system"""
name = 'HM_simple'
accessor_priority = 130.
dependencies = [GroupCatalogKeyHM, GroupCatalogKeyHMShort, GroupCatalogKeyGroup]
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
has_colon = table['HM'].str.contains(':')
gsm = Group.System.monoclinic
monoclinic = np.array([g.system == gsm for g in table['group']])
simple = table['HM_short'].copy()
simple.loc[has_colon] = simple.loc[has_colon].str.replace(r'\:.', '', regex=True)
simple.loc[monoclinic] = '_' + table.loc[monoclinic, 'HM'] # needed for PG
simple.loc[monoclinic] = simple.loc[monoclinic].str.replace('_1', '')
return simple.str.replace('_', '')
[docs]
class GroupCatalogKeyHMNumbered(GroupCatalogKey):
"""Nicely-formatted name with `number: HM_short` to be used in GUIs"""
name = 'HM_numbered'
dependencies = [GroupCatalogKeyNumber, GroupCatalogKeyHMShort]
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
return table['number'].astype(str).str.cat(table['HM_short'], sep=': ')
[docs]
class GroupCatalogKeyStandard(GroupCatalogKey):
"""Boolean column with True if setting is standard (first with given number)"""
name = 'standard'
dependencies = [GroupCatalogKeyNumber]
dtype = bool
[docs]
@classmethod
def construct(cls, table: pd.DataFrame) -> pd.Series:
return table['number'].rolling(2).var().ne(0)
# ~~~~~~~~~~~~~~~~~~~~~~~~~ CATALOG HELPER FUNCTIONS ~~~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
def _resolve_construct_order(keys: list[GroupCatalogKey]) -> list[GroupCatalogKey]:
"""
Return `GroupCatalogKey`s in an order that warrants that
key's dependencies are constructed before it
"""
unordered = deepcopy(keys)
ordered = []
def find_constructable(unordered_: list[GroupCatalogKey]) -> GroupCatalogKey:
for key_i, key in enumerate(unordered_):
if all(any(issubclass(o, d) for o in ordered) for d in key.dependencies):
return unordered_.pop(key_i)
raise RuntimeError('Circular dependency when creating `GroupCatalog`')
while len(ordered) < len(keys):
ordered.append(find_constructable(unordered))
return ordered
# ~~~~~~~~~~~~~~~~~~~~~~~ CATALOG JSON ENCODER/DECODER ~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
class GroupCatalogJSONEncoder(json.JSONEncoder):
"""Handles serialization of `GroupCatalog` to a `.json` file"""
[docs]
def default(self, gc: 'GroupCatalog') -> dict:
if not isinstance(gc, GroupCatalog):
return super().default(gc) # raises TypeError for other input
records = []
for row in gc.table.itertuples(index=False):
record = dict(row._asdict()) # noqa - It should be protected
record['group'] = {
'generators': [g.code for g in record['group'].generators],
'operations': [o.code for o in record['group'].operations],
}
records.append(record)
return {'_type': gc.__class__.__name__, 'table': records}
[docs]
class GroupCatalogJSONDecoder(json.JSONDecoder):
"""Handles deserialization of `GroupCatalog` from a `.json` file"""
def __init__(self, *args, **kwargs) -> None:
json.JSONDecoder.__init__(self, object_hook=self.object_hook, *args, **kwargs)
[docs]
def object_hook(self, obj) -> Any: # noqa - signature must match
if '_type' not in obj:
return obj
_type = obj['_type']
if _type == 'GroupCatalog':
records = []
for record in obj['table']:
group = record['group']
group = Group.from_generators_operations(
generators=[BoundedOperation.from_code(c) for c in group['generators']],
operations=[BoundedOperation.from_code(c) for c in group['operations']])
group.name = record['HM']
group.number = record['number']
record.update({'group': group})
records.append(record)
return GroupCatalog(table=pd.DataFrame.from_records(records))
return obj
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CATALOG WARNING ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
class AmbiguousGroupAccessorWarning(UserWarning):
"""Raised if the accessors provided to get the `Group` match >1 `Group`"""
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CATALOG CLASS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
class GroupCatalog:
"""
Manage generating and mappings of point and space groups.
Relies on a built-in pandas DataFrame `table` to store all the information.
Individual columns are named & generated based on `GroupCatalogKey` data.
For
Some notes on the uniqueness of columns pairwise for accessing:
- Column `Hall` has 3 groups appear twice due to inconsistency of HM names:
`c_2_2_-1ac`, `a_2_2_-1ab`, and `b_2_2_-1ab`.
- There are no overlaps between `HM` and `Hall` column names
- There are no overlaps between `HM_short` and `Hall` column names
- There are no overlaps between `HM_simple` and `Hall` column names
- There are no overlaps between `HM_simple` and `HM` column names
- There are 345 overlaps between `HM_simple` and `HM_short` column names
"""
KEYS: list[GroupCatalogKey] = [
GroupCatalogKeyNC,
GroupCatalogKeyNumber,
GroupCatalogKeySetting,
GroupCatalogKeyHM,
GroupCatalogKeyHall,
GroupCatalogKeyGroup,
GroupCatalogKeyHMShort,
GroupCatalogKeyHMSimple,
GroupCatalogKeyHMNumbered,
GroupCatalogKeyStandard,
]
REST_COL_FORMAT = {
'n_c': '7.7s',
'Hall': '16.16s', # 14 is the longest
'HM': '16.16s', # 12 is the longest
'HM_short': '11.11s', # 9 is the longest
'HM_simple': '11.11s', # 7 is the longest
}
def __init__(self, table: pd.DataFrame) -> None:
if 'n_c' not in table and table.index.name == 'n_c':
table.reset_index(inplace=True)
for key in _resolve_construct_order(self.KEYS):
if key.name not in table:
table[key.name] = key.construct(table)
gck = {k.name: k for k in self.KEYS}[key.name]
if not (table[key.name].dtype == gck.dtype or (
isinstance(gck.dtype, type) and
all(isinstance(v, gck.dtype) for v in table[key.name]))):
table[key.name] = table[key.name].astype(gck.dtype)
self.table: pd.DataFrame = table
[docs]
def __eq__(self, other):
if isinstance(other, self.__class__):
return self.table.equals(other.table)
return NotImplemented
[docs]
def __len__(self) -> int:
return len(self.table)
[docs]
@classmethod
def from_json(cls, text: str) -> 'GroupCatalog':
"""Load from a json-formatted string"""
return json.loads(text, cls=GroupCatalogJSONDecoder)
[docs]
def to_json(self, json_path: PathLike) -> None:
with open(json_path, 'w') as json_file:
# noinspection PyTypeChecker
json.dump(obj=self, fp=json_file, cls=GroupCatalogJSONEncoder,
ensure_ascii=False, indent=4)
[docs]
def to_rest_table(self, txt_path: PathLike) -> None:
"""Generate a .txt file with ReST table containing `GroupCatalog` elements."""
r = self.REST_COL_FORMAT
field_len_re = re.compile(r'^(\d*)(?:\.\d+)?[a-z]*$')
field_lens = [int(field_len_re.match(v).group(1)) for v in r.values()]
sep = '+-' + '-+-'.join(['-' * f for f in field_lens]) + '-+'
fmt = '| ' + ' | '.join([f'{{:{f}.{f}s}}' for f in field_lens]) + ' |'
lines = [fmt.format(*r.keys())]
underscore_escape = re.compile(r'_(?=[-(])')
for t in self.table[list(r.keys())].itertuples(index=False):
t = [underscore_escape.sub(repl=r'\_', string=tt) for tt in t]
lines.append(fmt.format(*t))
rest = sep + '\n' + ('\n' + sep + '\n').join(lines) + '\n' + sep
with open(txt_path, 'w') as txt_file:
txt_file.write(rest)
@property
def accessors(self) -> list['GroupCatalogKey']:
"""Lists `cls.KEYS whose accessor priority is not 0 in decreasing order"""
accessors = [k for k in self.KEYS if k.accessor_priority]
return sorted(accessors, key=lambda a: a.accessor_priority, reverse=True)
@property
def standard(self) -> 'GroupCatalog':
"""A subset of current catalog with standard-setting groups only"""
standard = deepcopy(self.table[self.table['standard']]).reset_index(drop=True)
return self.__class__(standard)
# ~~~~~~~~~~~~~~~~~~~~ DUCK-TYPING DICT-LIKE INTERFACE ~~~~~~~~~~~~~~~~~~~ #
[docs]
def keys(self) -> list[str]:
return list(self.table['n_c'])
[docs]
def values(self) -> list[Group]:
return list(self.table['group'])
[docs]
def items(self) -> list[tuple[Union[int, str], Group]]:
return [(k, v) for k, v in zip(self.table['n_c'], self.table['group'])]
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SMART GETTERS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #
[docs]
def _get_by_key(self, key: Union[str, int]) -> pd.DataFrame:
"""Iterate over accessors; whenever key is in accessor, return matching group"""
matching = []
for accessor in self.accessors:
matching.append(self.table[self.table.loc[:, accessor.name] == key])
return pd.concat(matching, axis=0)
[docs]
def _get_by_kwargs(self, **kwargs) -> pd.DataFrame:
"""Return the first group that matches all queries specified in kwargs"""
masks = []
for key, value in kwargs.items():
masks.append(self.table[key].eq(value))
return self.table[reduce(and_, masks)]
[docs]
def get(self, key: Union[str, int] = None, **kwargs) -> Union[Group, None]:
"""Get first `Group` matching provided anonymous&known accessors or None"""
got1 = deepcopy(self._get_by_key(key)) if key else pd.DataFrame()
got2 = deepcopy(self._get_by_kwargs(**kwargs)) if kwargs else pd.DataFrame()
if len(got1) == 0 and len(got2) == 0:
return
elif len(got1) > 0 and len(got2) == 0:
got = got1
elif len(got1) == 0 and len(got2) > 0:
got = got2
else:
got = got1.merge(got2, how='inner', on=['n_c'])
got.drop_duplicates(subset='n_c', inplace=True, ignore_index=True)
got.sort_values(by='standard', kind='stable', ascending=False, inplace=True)
first_got = got['group'].iloc[0] if len(got) else None
if len(got) > 1:
matches = list(got['HM_numbered'])
msg = (f'get(key={key}, kwargs={kwargs}) yielded multiple matches: '
f'{matches}. Returning first in standard setting, '
f'if possible: {first_got.name}')
warnings.warn(msg, AmbiguousGroupAccessorWarning)
return deepcopy(first_got)
[docs]
def __getitem__(self, item: Union[str, int]) -> Group:
"""Get first `Group` matching provided anonymous accessor or raise"""
got = self.get(key=item)
if not got:
raise KeyError(f'Unknown key: {item}')
return got
[docs]
def regenerate_group_catalog_jsons():
r"""
This function regenerates current `resources/*_group.json`s from `.wsv`s.
It should be run from hikari's parent directory with hikari imported
as module whenever any changes to `GroupCatalog` class are made.
"""
pg = GroupCatalog(point_groups_dataframe)
sg = GroupCatalog(space_groups_dataframe)
pg.to_json(Path('hikari/resources/point_groups.json'))
sg.to_json(Path('hikari/resources/space_groups.json'))
# ~~~~~~~~~~~~~~~~~~~~~~~~ PRE-DEFINED GROUPS CATALOGS ~~~~~~~~~~~~~~~~~~~~~~~~ #
PG = GroupCatalog.from_json(point_groups_json)
r"""
Since hikari's groups do not carry information about lattice translations,
hikari does not differentiate between point groups and space groups.
As a result, all groups are instances of the same class `Group`,
and are stored in almost identical `GroupCatalog`s.
This pre-defined `GroupCatalog` `PG` holds and provides access
to all pre-defined point groups available in hikari.
The point groups are named and generated based on a wsv file in resources.
Individual groups can be accessed in two different ways:
- using a dict-like anonymous accessor: `PG[32]`, `PG['m-3m']`;
- using `get()` method: `PG.get(number=32)`, `PG.get(HM_short='m-3m')`;
The `get()` method can use a combination of various keywords to unambiguously
localize the correct space group. The following keyword arguments can be used:
- `n_c` - unique "number:setting" string identifying each group
- `number` - index of the point group as given in ICT A (integer)\*
- `setting` - arbitrary string declaring group setting
- `HM` - Full underscore-delimited Hermann-Mauguin symbol\*
- `HM_short` - Hermann-Mauguin symbol with underscores removed\*
- `HM_simple` - Short Hermann-Mauguin symbol without setting information\*
- `HM_numbered` - "number: Short Hermann-Mauguin symbol" string
- `Hall` - Full Hall symbol\*
- `standard` - True for groups in standard setting only
The keywords marked with "*" are called "accessors" and can be used to `get`
the group using bracket notation `get[accessor]`. If `get` finds ambiguity,
If `get` finds ambiguity, for example `PG['2/m']` matches all settings
of point group #5: `1_2/m_1` (std), `1_1_2/m`, and `2/m_1_1`,
the user is warned and the first group in std setting, if possible, is returned.
The following table lists all possible values of selected point `Group`
keywords. Please mind that in the raw docstring all `\` should be ignored.
+---------+------------------+------------------+-------------+-------------+
| n_c | Hall | HM | HM_short | HM_simple |
+---------+------------------+------------------+-------------+-------------+
| 1 | 1 | 1 | 1 | 1 |
+---------+------------------+------------------+-------------+-------------+
| 2 | -1 | -1 | -1 | -1 |
+---------+------------------+------------------+-------------+-------------+
| 3:b | 2y | 1_2_1 | 121 | 2 |
+---------+------------------+------------------+-------------+-------------+
| 3:c | 2 | 1_1_2 | 112 | 2 |
+---------+------------------+------------------+-------------+-------------+
| 3:a | 2x | 2_1_1 | 211 | 2 |
+---------+------------------+------------------+-------------+-------------+
| 4:b | -2y | 1_m_1 | 1m1 | m |
+---------+------------------+------------------+-------------+-------------+
| 4:c | -2 | 1_1_m | 11m | m |
+---------+------------------+------------------+-------------+-------------+
| 4:a | -2x | m_1_1 | m11 | m |
+---------+------------------+------------------+-------------+-------------+
| 5:b | -2y | 1_2/m_1 | 12/m1 | 2/m |
+---------+------------------+------------------+-------------+-------------+
| 5:c | -2 | 1_1_2/m | 112/m | 2/m |
+---------+------------------+------------------+-------------+-------------+
| 5:a | -2x | 2/m_1_1 | 2/m11 | 2/m |
+---------+------------------+------------------+-------------+-------------+
| 6 | 2_2 | 2_2_2 | 222 | 222 |
+---------+------------------+------------------+-------------+-------------+
| 7 | 2\_-2 | m_m_2 | mm2 | mm2 |
+---------+------------------+------------------+-------------+-------------+
| 8 | -2_2 | m_m_m | mmm | mmm |
+---------+------------------+------------------+-------------+-------------+
| 9 | 4 | 4 | 4 | 4 |
+---------+------------------+------------------+-------------+-------------+
| 10 | -4 | -4 | -4 | -4 |
+---------+------------------+------------------+-------------+-------------+
| 11 | -4 | 4/m | 4/m | 4/m |
+---------+------------------+------------------+-------------+-------------+
| 12 | 4_2 | 4_2_2 | 422 | 422 |
+---------+------------------+------------------+-------------+-------------+
| 13 | 4\_-2 | 4_m_m | 4mm | 4mm |
+---------+------------------+------------------+-------------+-------------+
| 14 | -4_2 | -4_2_m | -42m | -42m |
+---------+------------------+------------------+-------------+-------------+
| 15 | -4_2 | 4/m_m_m | 4/mmm | 4/mmm |
+---------+------------------+------------------+-------------+-------------+
| 16 | 3 | 3 | 3 | 3 |
+---------+------------------+------------------+-------------+-------------+
| 17 | -3 | -3 | -3 | -3 |
+---------+------------------+------------------+-------------+-------------+
| 18 | 3_2 | 3_1_2 | 312 | 312 |
+---------+------------------+------------------+-------------+-------------+
| 19 | 3\_-2" | 3_m_1 | 3m1 | 3m1 |
+---------+------------------+------------------+-------------+-------------+
| 20 | -3_2 | -3_1_m | -31m | -31m |
+---------+------------------+------------------+-------------+-------------+
| 21 | 6 | 6 | 6 | 6 |
+---------+------------------+------------------+-------------+-------------+
| 22 | -6 | -6 | -6 | -6 |
+---------+------------------+------------------+-------------+-------------+
| 23 | -6 | 6/m | 6/m | 6/m |
+---------+------------------+------------------+-------------+-------------+
| 24 | 6_2 | 6_2_2 | 622 | 622 |
+---------+------------------+------------------+-------------+-------------+
| 25 | 6\_-2 | 6_m_m | 6mm | 6mm |
+---------+------------------+------------------+-------------+-------------+
| 26 | -6_2 | -6_m_2 | -6m2 | -6m2 |
+---------+------------------+------------------+-------------+-------------+
| 27 | -6_2 | 6/m_m_m | 6/mmm | 6/mmm |
+---------+------------------+------------------+-------------+-------------+
| 28 | 2_2_3 | 2_3 | 23 | 23 |
+---------+------------------+------------------+-------------+-------------+
| 29 | -2_2_3 | m\_-3 | m-3 | m-3 |
+---------+------------------+------------------+-------------+-------------+
| 30 | 4_2_3 | 4_3_2 | 432 | 432 |
+---------+------------------+------------------+-------------+-------------+
| 31 | -4_2_3 | -4_3_m | -43m | -43m |
+---------+------------------+------------------+-------------+-------------+
| 32 | -4_2_3 | m\_-3_m | m-3m | m-3m |
+---------+------------------+------------------+-------------+-------------+
"""
SG = GroupCatalog.from_json(space_groups_json)
r"""
Since hikari's groups do not carry information about lattice translations,
hikari does not differentiate between point groups and space groups.
As a result, all groups are instances of the same class `Group`,
and are stored in almost identical `GroupCatalog`s.
This pre-defined `SpaceGroupCatalog` `SG` holds and provides access
to all pre-defined space groups available in hikari.
The space groups are named and generated based on a wsv file in resources.
Individual groups can be accessed in two different ways:
- using a dict-like anonymous accessor: `PG[62]`, `PG['Pnma']`;
- using `get()` method: `PG.get(number=62)`, `PG.get(HM_short='Pnma')`;
The `get()` method can use a combination of various keywords to unambiguously
localize the correct space group. The following keyword arguments can be used:
- `n_c` - unique "number:setting" string identifying each group
- `number` - index of the point group as given in ICT A (integer)\*
- `setting` - arbitrary string declaring group setting
- `HM` - Full underscore-delimited Hermann-Mauguin symbol\*
- `HM_short` - Hermann-Mauguin symbol with underscores removed\*
- `HM_simple` - Short Hermann-Mauguin symbol without setting information\*
- `HM_numbered` - "number: Short Hermann-Mauguin symbol" string
- `Hall` - Full Hall symbol\*
- `standard` - True for groups in standard setting only
The keywords marked with "*" are called "accessors" and can be used to `get`
the group using bracket notation `get[accessor]`.
If `get` finds ambiguity, for example `SG['P2/m']` matches all settings
of space group #10: `P_1_2/m_1` (std), `P_1_1_2/m`, and `P_2/m_1_1`,
the user is warned and the first group in std setting, if possible, is returned.
The following table lists all possible values of selected space `Group`
keywords. Please mind that in the raw docstring all `\` should be ignored.
+---------+-----------------+-----------------+--------------+--------------+
| n_c | Hall | HM | HM_short | HM_simple |
+---------+-----------------+-----------------+--------------+--------------+
| 1 | p_1 | P_1 | P1 | P1 |
+---------+-----------------+-----------------+--------------+--------------+
| 2 | -p_1 | P\_-1 | P-1 | P-1 |
+---------+-----------------+-----------------+--------------+--------------+
| 3:b | p_2y | P_1_2_1 | P121 | P2 |
+---------+-----------------+-----------------+--------------+--------------+
| 3:c | p_2 | P_1_1_2 | P112 | P2 |
+---------+-----------------+-----------------+--------------+--------------+
| 3:a | p_2x | P_2_1_1 | P211 | P2 |
+---------+-----------------+-----------------+--------------+--------------+
| 4:b | p_2yb | P_1_21_1 | P1211 | P21 |
+---------+-----------------+-----------------+--------------+--------------+
| 4:c | p_2c | P_1_1_21 | P1121 | P21 |
+---------+-----------------+-----------------+--------------+--------------+
| 4:a | p_2xa | P_21_1_1 | P2111 | P21 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:b1 | c_2y | C_1_2_1 | C121 | C2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:b2 | a_2y | A_1_2_1 | A121 | A2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:b3 | i_2y | I_1_2_1 | I121 | I2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:c1 | a_2 | A_1_1_2 | A112 | A2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:c2 | b_2 | B_1_1_2 | B112 | B2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:c3 | i_2 | I_1_1_2 | I112 | I2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:a1 | b_2x | B_2_1_1 | B211 | B2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:a2 | c_2x | C_2_1_1 | C211 | C2 |
+---------+-----------------+-----------------+--------------+--------------+
| 5:a3 | i_2x | I_2_1_1 | I211 | I2 |
+---------+-----------------+-----------------+--------------+--------------+
| 6:b | p\_-2y | P_1_m_1 | P1m1 | Pm |
+---------+-----------------+-----------------+--------------+--------------+
| 6:c | p\_-2 | P_1_1_m | P11m | Pm |
+---------+-----------------+-----------------+--------------+--------------+
| 6:a | p\_-2x | P_m_1_1 | Pm11 | Pm |
+---------+-----------------+-----------------+--------------+--------------+
| 7:b1 | p\_-2yc | P_1_c_1 | P1c1 | Pc |
+---------+-----------------+-----------------+--------------+--------------+
| 7:b2 | p\_-2yac | P_1_n_1 | P1n1 | Pn |
+---------+-----------------+-----------------+--------------+--------------+
| 7:b3 | p\_-2ya | P_1_a_1 | P1a1 | Pa |
+---------+-----------------+-----------------+--------------+--------------+
| 7:c1 | p\_-2a | P_1_1_a | P11a | Pa |
+---------+-----------------+-----------------+--------------+--------------+
| 7:c2 | p\_-2ab | P_1_1_n | P11n | Pn |
+---------+-----------------+-----------------+--------------+--------------+
| 7:c3 | p\_-2b | P_1_1_b | P11b | Pb |
+---------+-----------------+-----------------+--------------+--------------+
| 7:a1 | p\_-2xb | P_b_1_1 | Pb11 | Pb |
+---------+-----------------+-----------------+--------------+--------------+
| 7:a2 | p\_-2xbc | P_n_1_1 | Pn11 | Pn |
+---------+-----------------+-----------------+--------------+--------------+
| 7:a3 | p\_-2xc | P_c_1_1 | Pc11 | Pc |
+---------+-----------------+-----------------+--------------+--------------+
| 8:b1 | c\_-2y | C_1_m_1 | C1m1 | Cm |
+---------+-----------------+-----------------+--------------+--------------+
| 8:b2 | a\_-2y | A_1_m_1 | A1m1 | Am |
+---------+-----------------+-----------------+--------------+--------------+
| 8:b3 | i\_-2y | I_1_m_1 | I1m1 | Im |
+---------+-----------------+-----------------+--------------+--------------+
| 8:c1 | a\_-2 | A_1_1_m | A11m | Am |
+---------+-----------------+-----------------+--------------+--------------+
| 8:c2 | b\_-2 | B_1_1_m | B11m | Bm |
+---------+-----------------+-----------------+--------------+--------------+
| 8:c3 | i\_-2 | I_1_1_m | I11m | Im |
+---------+-----------------+-----------------+--------------+--------------+
| 8:a1 | b\_-2x | B_m_1_1 | Bm11 | Bm |
+---------+-----------------+-----------------+--------------+--------------+
| 8:a2 | c\_-2x | C_m_1_1 | Cm11 | Cm |
+---------+-----------------+-----------------+--------------+--------------+
| 8:a3 | i\_-2x | I_m_1_1 | Im11 | Im |
+---------+-----------------+-----------------+--------------+--------------+
| 9:b1 | c\_-2yc | C_1_c_1 | C1c1 | Cc |
+---------+-----------------+-----------------+--------------+--------------+
| 9:b2 | a\_-2yab | A_1_n_1 | A1n1 | An |
+---------+-----------------+-----------------+--------------+--------------+
| 9:b3 | i\_-2ya | I_1_a_1 | I1a1 | Ia |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-b1 | a\_-2ya | A_1_a_1 | A1a1 | Aa |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-b2 | c\_-2yac | C_1_n_1 | C1n1 | Cn |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-b3 | i\_-2yc | I_1_c_1 | I1c1 | Ic |
+---------+-----------------+-----------------+--------------+--------------+
| 9:c1 | a\_-2a | A_1_1_a | A11a | Aa |
+---------+-----------------+-----------------+--------------+--------------+
| 9:c2 | b\_-2ab | B_1_1_n | B11n | Bn |
+---------+-----------------+-----------------+--------------+--------------+
| 9:c3 | i\_-2b | I_1_1_b | I11b | Ib |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-c1 | b\_-2b | B_1_1_b | B11b | Bb |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-c2 | a\_-2ab | A_1_1_n | A11n | An |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-c3 | i\_-2a | I_1_1_a | I11a | Ia |
+---------+-----------------+-----------------+--------------+--------------+
| 9:a1 | b\_-2xb | B_b_1_1 | Bb11 | Bb |
+---------+-----------------+-----------------+--------------+--------------+
| 9:a2 | c\_-2xac | C_n_1_1 | Cn11 | Cn |
+---------+-----------------+-----------------+--------------+--------------+
| 9:a3 | i\_-2xc | I_c_1_1 | Ic11 | Ic |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-a1 | c\_-2xc | C_c_1_1 | Cc11 | Cc |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-a2 | b\_-2xab | B_n_1_1 | Bn11 | Bn |
+---------+-----------------+-----------------+--------------+--------------+
| 9:-a3 | i\_-2xb | I_b_1_1 | Ib11 | Ib |
+---------+-----------------+-----------------+--------------+--------------+
| 10:b | -p_2y | P_1_2/m_1 | P12/m1 | P2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 10:c | -p_2 | P_1_1_2/m | P112/m | P2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 10:a | -p_2x | P_2/m_1_1 | P2/m11 | P2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 11:b | -p_2yb | P_1_21/m_1 | P121/m1 | P21/m |
+---------+-----------------+-----------------+--------------+--------------+
| 11:c | -p_2c | P_1_1_21/m | P1121/m | P21/m |
+---------+-----------------+-----------------+--------------+--------------+
| 11:a | -p_2xa | P_21/m_1_1 | P21/m11 | P21/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:b1 | -c_2y | C_1_2/m_1 | C12/m1 | C2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:b2 | -a_2y | A_1_2/m_1 | A12/m1 | A2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:b3 | -i_2y | I_1_2/m_1 | I12/m1 | I2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:c1 | -a_2 | A_1_1_2/m | A112/m | A2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:c2 | -b_2 | B_1_1_2/m | B112/m | B2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:c3 | -i_2 | I_1_1_2/m | I112/m | I2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:a1 | -b_2x | B_2/m_1_1 | B2/m11 | B2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:a2 | -c_2x | C_2/m_1_1 | C2/m11 | C2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 12:a3 | -i_2x | I_2/m_1_1 | I2/m11 | I2/m |
+---------+-----------------+-----------------+--------------+--------------+
| 13:b1 | -p_2yc | P_1_2/c_1 | P12/c1 | P2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 13:b2 | -p_2yac | P_1_2/n_1 | P12/n1 | P2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 13:b3 | -p_2ya | P_1_2/a_1 | P12/a1 | P2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 13:c1 | -p_2a | P_1_1_2/a | P112/a | P2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 13:c2 | -p_2ab | P_1_1_2/n | P112/n | P2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 13:c3 | -p_2b | P_1_1_2/b | P112/b | P2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 13:a1 | -p_2xb | P_2/b_1_1 | P2/b11 | P2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 13:a2 | -p_2xbc | P_2/n_1_1 | P2/n11 | P2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 13:a3 | -p_2xc | P_2/c_1_1 | P2/c11 | P2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 14:b1 | -p_2ybc | P_1_21/c_1 | P121/c1 | P21/c |
+---------+-----------------+-----------------+--------------+--------------+
| 14:b2 | -p_2yn | P_1_21/n_1 | P121/n1 | P21/n |
+---------+-----------------+-----------------+--------------+--------------+
| 14:b3 | -p_2yab | P_1_21/a_1 | P121/a1 | P21/a |
+---------+-----------------+-----------------+--------------+--------------+
| 14:c1 | -p_2ac | P_1_1_21/a | P1121/a | P21/a |
+---------+-----------------+-----------------+--------------+--------------+
| 14:c2 | -p_2n | P_1_1_21/n | P1121/n | P21/n |
+---------+-----------------+-----------------+--------------+--------------+
| 14:c3 | -p_2bc | P_1_1_21/b | P1121/b | P21/b |
+---------+-----------------+-----------------+--------------+--------------+
| 14:a1 | -p_2xab | P_21/b_1_1 | P21/b11 | P21/b |
+---------+-----------------+-----------------+--------------+--------------+
| 14:a2 | -p_2xn | P_21/n_1_1 | P21/n11 | P21/n |
+---------+-----------------+-----------------+--------------+--------------+
| 14:a3 | -p_2xac | P_21/c_1_1 | P21/c11 | P21/c |
+---------+-----------------+-----------------+--------------+--------------+
| 15:b1 | -c_2yc | C_1_2/c_1 | C12/c1 | C2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 15:b2 | -a_2yab | A_1_2/n_1 | A12/n1 | A2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:b3 | -i_2ya | I_1_2/a_1 | I12/a1 | I2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-b1 | -a_2ya | A_1_2/a_1 | A12/a1 | A2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-b2 | -c_2yac | C_1_2/n_1 | C12/n1 | C2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-b3 | -i_2yc | I_1_2/c_1 | I12/c1 | I2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 15:c1 | -a_2a | A_1_1_2/a | A112/a | A2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 15:c2 | -b_2ab | B_1_1_2/n | B112/n | B2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:c3 | -i_2b | I_1_1_2/b | I112/b | I2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-c1 | -b_2b | B_1_1_2/b | B112/b | B2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-c2 | -a_2ab | A_1_1_2/n | A112/n | A2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-c3 | -i_2a | I_1_1_2/a | I112/a | I2/a |
+---------+-----------------+-----------------+--------------+--------------+
| 15:a1 | -b_2xb | B_2/b_1_1 | B2/b11 | B2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 15:a2 | -c_2xac | C_2/n_1_1 | C2/n11 | C2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:a3 | -i_2xc | I_2/c_1_1 | I2/c11 | I2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-a1 | -c_2xc | C_2/c_1_1 | C2/c11 | C2/c |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-a2 | -b_2xab | B_2/n_1_1 | B2/n11 | B2/n |
+---------+-----------------+-----------------+--------------+--------------+
| 15:-a3 | -i_2xb | I_2/b_1_1 | I2/b11 | I2/b |
+---------+-----------------+-----------------+--------------+--------------+
| 16 | p_2_2 | P_2_2_2 | P222 | P222 |
+---------+-----------------+-----------------+--------------+--------------+
| 17 | p_2c_2 | P_2_2_21 | P2221 | P2221 |
+---------+-----------------+-----------------+--------------+--------------+
| 17:cab | p_2a_2a | P_21_2_2 | P2122 | P2122 |
+---------+-----------------+-----------------+--------------+--------------+
| 17:bca | p_2_2b | P_2_21_2 | P2212 | P2212 |
+---------+-----------------+-----------------+--------------+--------------+
| 18 | p_2_2ab | P_21_21_2 | P21212 | P21212 |
+---------+-----------------+-----------------+--------------+--------------+
| 18:cab | p_2bc_2 | P_2_21_21 | P22121 | P22121 |
+---------+-----------------+-----------------+--------------+--------------+
| 18:bca | p_2ac_2ac | P_21_2_21 | P21221 | P21221 |
+---------+-----------------+-----------------+--------------+--------------+
| 19 | p_2ac_2ab | P_21_21_21 | P212121 | P212121 |
+---------+-----------------+-----------------+--------------+--------------+
| 20 | c_2c_2 | C_2_2_21 | C2221 | C2221 |
+---------+-----------------+-----------------+--------------+--------------+
| 20:cab | a_2a_2a | A_21_2_2 | A2122 | A2122 |
+---------+-----------------+-----------------+--------------+--------------+
| 20:bca | b_2_2b | B_2_21_2 | B2212 | B2212 |
+---------+-----------------+-----------------+--------------+--------------+
| 21 | c_2_2 | C_2_2_2 | C222 | C222 |
+---------+-----------------+-----------------+--------------+--------------+
| 21:cab | a_2_2 | A_2_2_2 | A222 | A222 |
+---------+-----------------+-----------------+--------------+--------------+
| 21:bca | b_2_2 | B_2_2_2 | B222 | B222 |
+---------+-----------------+-----------------+--------------+--------------+
| 22 | f_2_2 | F_2_2_2 | F222 | F222 |
+---------+-----------------+-----------------+--------------+--------------+
| 23 | i_2_2 | I_2_2_2 | I222 | I222 |
+---------+-----------------+-----------------+--------------+--------------+
| 24 | i_2b_2c | I_21_21_21 | I212121 | I212121 |
+---------+-----------------+-----------------+--------------+--------------+
| 25 | p_2\_-2 | P_m_m_2 | Pmm2 | Pmm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 25:cab | p\_-2_2 | P_2_m_m | P2mm | P2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 25:bca | p\_-2\_-2 | P_m_2_m | Pm2m | Pm2m |
+---------+-----------------+-----------------+--------------+--------------+
| 26 | p_2c\_-2 | P_m_c_21 | Pmc21 | Pmc21 |
+---------+-----------------+-----------------+--------------+--------------+
| 26:ba-c | p_2c\_-2c | P_c_m_21 | Pcm21 | Pcm21 |
+---------+-----------------+-----------------+--------------+--------------+
| 26:cab | p\_-2a_2a | P_21_m_a | P21ma | P21ma |
+---------+-----------------+-----------------+--------------+--------------+
| 26:-cba | p\_-2_2a | P_21_a_m | P21am | P21am |
+---------+-----------------+-----------------+--------------+--------------+
| 26:bca | p\_-2\_-2b | P_b_21_m | Pb21m | Pb21m |
+---------+-----------------+-----------------+--------------+--------------+
| 26:a-cb | p\_-2b\_-2 | P_m_21_b | Pm21b | Pm21b |
+---------+-----------------+-----------------+--------------+--------------+
| 27 | p_2\_-2c | P_c_c_2 | Pcc2 | Pcc2 |
+---------+-----------------+-----------------+--------------+--------------+
| 27:cab | p\_-2a_2 | P_2_a_a | P2aa | P2aa |
+---------+-----------------+-----------------+--------------+--------------+
| 27:bca | p\_-2b\_-2b | P_b_2_b | Pb2b | Pb2b |
+---------+-----------------+-----------------+--------------+--------------+
| 28 | p_2\_-2a | P_m_a_2 | Pma2 | Pma2 |
+---------+-----------------+-----------------+--------------+--------------+
| 28:ba-c | p_2\_-2b | P_b_m_2 | Pbm2 | Pbm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 28:cab | p\_-2b_2 | P_2_m_b | P2mb | P2mb |
+---------+-----------------+-----------------+--------------+--------------+
| 28:-cba | p\_-2c_2 | P_2_c_m | P2cm | P2cm |
+---------+-----------------+-----------------+--------------+--------------+
| 28:bca | p\_-2c\_-2c | P_c_2_m | Pc2m | Pc2m |
+---------+-----------------+-----------------+--------------+--------------+
| 28:a-cb | p\_-2a\_-2a | P_m_2_a | Pm2a | Pm2a |
+---------+-----------------+-----------------+--------------+--------------+
| 29 | p_2c\_-2ac | P_c_a_21 | Pca21 | Pca21 |
+---------+-----------------+-----------------+--------------+--------------+
| 29:ba-c | p_2c\_-2b | P_b_c_21 | Pbc21 | Pbc21 |
+---------+-----------------+-----------------+--------------+--------------+
| 29:cab | p\_-2b_2a | P_21_a_b | P21ab | P21ab |
+---------+-----------------+-----------------+--------------+--------------+
| 29:-cba | p\_-2ac_2a | P_21_c_a | P21ca | P21ca |
+---------+-----------------+-----------------+--------------+--------------+
| 29:bca | p\_-2bc\_-2c | P_c_21_b | Pc21b | Pc21b |
+---------+-----------------+-----------------+--------------+--------------+
| 29:a-cb | p\_-2a\_-2ab | P_b_21_a | Pb21a | Pb21a |
+---------+-----------------+-----------------+--------------+--------------+
| 30 | p_2\_-2bc | P_n_c_2 | Pnc2 | Pnc2 |
+---------+-----------------+-----------------+--------------+--------------+
| 30:ba-c | p_2\_-2ac | P_c_n_2 | Pcn2 | Pcn2 |
+---------+-----------------+-----------------+--------------+--------------+
| 30:cab | p\_-2ac_2 | P_2_n_a | P2na | P2na |
+---------+-----------------+-----------------+--------------+--------------+
| 30:-cba | p\_-2ab_2 | P_2_a_n | P2an | P2an |
+---------+-----------------+-----------------+--------------+--------------+
| 30:bca | p\_-2ab\_-2ab | P_b_2_n | Pb2n | Pb2n |
+---------+-----------------+-----------------+--------------+--------------+
| 30:a-cb | p\_-2bc\_-2bc | P_n_2_b | Pn2b | Pn2b |
+---------+-----------------+-----------------+--------------+--------------+
| 31 | p_2ac\_-2 | P_m_n_21 | Pmn21 | Pmn21 |
+---------+-----------------+-----------------+--------------+--------------+
| 31:ba-c | p_2bc\_-2bc | P_n_m_21 | Pnm21 | Pnm21 |
+---------+-----------------+-----------------+--------------+--------------+
| 31:cab | p\_-2ab_2ab | P_21_m_n | P21mn | P21mn |
+---------+-----------------+-----------------+--------------+--------------+
| 31:-cba | p\_-2_2ac | P_21_n_m | P21nm | P21nm |
+---------+-----------------+-----------------+--------------+--------------+
| 31:bca | p\_-2\_-2bc | P_n_21_m | Pn21m | Pn21m |
+---------+-----------------+-----------------+--------------+--------------+
| 31:a-cb | p\_-2ab\_-2 | P_m_21_n | Pm21n | Pm21n |
+---------+-----------------+-----------------+--------------+--------------+
| 32 | p_2\_-2ab | P_b_a_2 | Pba2 | Pba2 |
+---------+-----------------+-----------------+--------------+--------------+
| 32:cab | p\_-2bc_2 | P_2_c_b | P2cb | P2cb |
+---------+-----------------+-----------------+--------------+--------------+
| 32:bca | p\_-2ac\_-2ac | P_c_2_a | Pc2a | Pc2a |
+---------+-----------------+-----------------+--------------+--------------+
| 33 | p_2c\_-2n | P_n_a_21 | Pna21 | Pna21 |
+---------+-----------------+-----------------+--------------+--------------+
| 33:ba-c | p_2c\_-2ab | P_b_n_21 | Pbn21 | Pbn21 |
+---------+-----------------+-----------------+--------------+--------------+
| 33:cab | p\_-2bc_2a | P_21_n_b | P21nb | P21nb |
+---------+-----------------+-----------------+--------------+--------------+
| 33:-cba | p\_-2n_2a | P_21_c_n | P21cn | P21cn |
+---------+-----------------+-----------------+--------------+--------------+
| 33:bca | p\_-2n\_-2ac | P_c_21_n | Pc21n | Pc21n |
+---------+-----------------+-----------------+--------------+--------------+
| 33:a-cb | p\_-2ac\_-2n | P_n_21_a | Pn21a | Pn21a |
+---------+-----------------+-----------------+--------------+--------------+
| 34 | p_2\_-2n | P_n_n_2 | Pnn2 | Pnn2 |
+---------+-----------------+-----------------+--------------+--------------+
| 34:cab | p\_-2n_2 | P_2_n_n | P2nn | P2nn |
+---------+-----------------+-----------------+--------------+--------------+
| 34:bca | p\_-2n\_-2n | P_n_2_n | Pn2n | Pn2n |
+---------+-----------------+-----------------+--------------+--------------+
| 35 | c_2\_-2 | C_m_m_2 | Cmm2 | Cmm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 35:cab | a\_-2_2 | A_2_m_m | A2mm | A2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 35:bca | b\_-2\_-2 | B_m_2_m | Bm2m | Bm2m |
+---------+-----------------+-----------------+--------------+--------------+
| 36 | c_2c\_-2 | C_m_c_21 | Cmc21 | Cmc21 |
+---------+-----------------+-----------------+--------------+--------------+
| 36:ba-c | c_2c\_-2c | C_c_m_21 | Ccm21 | Ccm21 |
+---------+-----------------+-----------------+--------------+--------------+
| 36:cab | a\_-2a_2a | A_21_m_a | A21ma | A21ma |
+---------+-----------------+-----------------+--------------+--------------+
| 36:-cba | a\_-2_2a | A_21_a_m | A21am | A21am |
+---------+-----------------+-----------------+--------------+--------------+
| 36:bca | b\_-2\_-2b | B_b_21_m | Bb21m | Bb21m |
+---------+-----------------+-----------------+--------------+--------------+
| 36:a-cb | b\_-2b\_-2 | B_m_21_b | Bm21b | Bm21b |
+---------+-----------------+-----------------+--------------+--------------+
| 37 | c_2\_-2c | C_c_c_2 | Ccc2 | Ccc2 |
+---------+-----------------+-----------------+--------------+--------------+
| 37:cab | a\_-2a_2 | A_2_a_a | A2aa | A2aa |
+---------+-----------------+-----------------+--------------+--------------+
| 37:bca | b\_-2b\_-2b | B_b_2_b | Bb2b | Bb2b |
+---------+-----------------+-----------------+--------------+--------------+
| 38 | a_2\_-2 | A_m_m_2 | Amm2 | Amm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 38:ba-c | b_2\_-2 | B_m_m_2 | Bmm2 | Bmm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 38:cab | b\_-2_2 | B_2_m_m | B2mm | B2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 38:-cba | c\_-2_2 | C_2_m_m | C2mm | C2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 38:bca | c\_-2\_-2 | C_m_2_m | Cm2m | Cm2m |
+---------+-----------------+-----------------+--------------+--------------+
| 38:a-cb | a\_-2\_-2 | A_m_2_m | Am2m | Am2m |
+---------+-----------------+-----------------+--------------+--------------+
| 39 | a_2\_-2b | A_e_m_2 | Aem2 | Aem2 |
+---------+-----------------+-----------------+--------------+--------------+
| 39:ba-c | b_2\_-2a | B_m_a_2 | Bma2 | Bma2 |
+---------+-----------------+-----------------+--------------+--------------+
| 39:cab | b\_-2a_2 | B_2_c_m | B2cm | B2cm |
+---------+-----------------+-----------------+--------------+--------------+
| 39:-cba | c\_-2a_2 | C_2_m_b | C2mb | C2mb |
+---------+-----------------+-----------------+--------------+--------------+
| 39:bca | c\_-2a\_-2a | C_m_2_a | Cm2a | Cm2a |
+---------+-----------------+-----------------+--------------+--------------+
| 39:a-cb | a\_-2b\_-2b | A_c_2_m | Ac2m | Ac2m |
+---------+-----------------+-----------------+--------------+--------------+
| 40 | a_2\_-2a | A_m_a_2 | Ama2 | Ama2 |
+---------+-----------------+-----------------+--------------+--------------+
| 40:ba-c | b_2\_-2b | B_b_m_2 | Bbm2 | Bbm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 40:cab | b\_-2b_2 | B_2_m_b | B2mb | B2mb |
+---------+-----------------+-----------------+--------------+--------------+
| 40:-cba | c\_-2c_2 | C_2_c_m | C2cm | C2cm |
+---------+-----------------+-----------------+--------------+--------------+
| 40:bca | c\_-2c\_-2c | C_c_2_m | Cc2m | Cc2m |
+---------+-----------------+-----------------+--------------+--------------+
| 40:a-cb | a\_-2a\_-2a | A_m_2_a | Am2a | Am2a |
+---------+-----------------+-----------------+--------------+--------------+
| 41 | a_2\_-2ab | A_e_a_2 | Aea2 | Aea2 |
+---------+-----------------+-----------------+--------------+--------------+
| 41:ba-c | b_2\_-2ab | B_b_a_2 | Bba2 | Bba2 |
+---------+-----------------+-----------------+--------------+--------------+
| 41:cab | b\_-2ab_2 | B_2_c_b | B2cb | B2cb |
+---------+-----------------+-----------------+--------------+--------------+
| 41:-cba | c\_-2ac_2 | C_2_c_b | C2cb | C2cb |
+---------+-----------------+-----------------+--------------+--------------+
| 41:bca | c\_-2ac\_-2ac | C_c_2_a | Cc2a | Cc2a |
+---------+-----------------+-----------------+--------------+--------------+
| 41:a-cb | a\_-2ab\_-2ab | A_c_2_a | Ac2a | Ac2a |
+---------+-----------------+-----------------+--------------+--------------+
| 42 | f_2\_-2 | F_m_m_2 | Fmm2 | Fmm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 42:cab | f\_-2_2 | F_2_m_m | F2mm | F2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 42:bca | f\_-2\_-2 | F_m_2_m | Fm2m | Fm2m |
+---------+-----------------+-----------------+--------------+--------------+
| 43 | f_2\_-2d | F_d_d_2 | Fdd2 | Fdd2 |
+---------+-----------------+-----------------+--------------+--------------+
| 43:cab | f\_-2d_2 | F_2_d_d | F2dd | F2dd |
+---------+-----------------+-----------------+--------------+--------------+
| 43:bca | f\_-2d\_-2d | F_d_2_d | Fd2d | Fd2d |
+---------+-----------------+-----------------+--------------+--------------+
| 44 | i_2\_-2 | I_m_m_2 | Imm2 | Imm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 44:cab | i\_-2_2 | I_2_m_m | I2mm | I2mm |
+---------+-----------------+-----------------+--------------+--------------+
| 44:bca | i\_-2\_-2 | I_m_2_m | Im2m | Im2m |
+---------+-----------------+-----------------+--------------+--------------+
| 45 | i_2\_-2c | I_b_a_2 | Iba2 | Iba2 |
+---------+-----------------+-----------------+--------------+--------------+
| 45:cab | i\_-2a_2 | I_2_c_b | I2cb | I2cb |
+---------+-----------------+-----------------+--------------+--------------+
| 45:bca | i\_-2b\_-2b | I_c_2_a | Ic2a | Ic2a |
+---------+-----------------+-----------------+--------------+--------------+
| 46 | i_2\_-2a | I_m_a_2 | Ima2 | Ima2 |
+---------+-----------------+-----------------+--------------+--------------+
| 46:ba-c | i_2\_-2b | I_b_m_2 | Ibm2 | Ibm2 |
+---------+-----------------+-----------------+--------------+--------------+
| 46:cab | i\_-2b_2 | I_2_m_b | I2mb | I2mb |
+---------+-----------------+-----------------+--------------+--------------+
| 46:-cba | i\_-2c_2 | I_2_c_m | I2cm | I2cm |
+---------+-----------------+-----------------+--------------+--------------+
| 46:bca | i\_-2c\_-2c | I_c_2_m | Ic2m | Ic2m |
+---------+-----------------+-----------------+--------------+--------------+
| 46:a-cb | i\_-2a\_-2a | I_m_2_a | Im2a | Im2a |
+---------+-----------------+-----------------+--------------+--------------+
| 47 | -p_2_2 | P_m_m_m | Pmmm | Pmmm |
+---------+-----------------+-----------------+--------------+--------------+
| 48:1 | p_2_2\_-1n | P_n_n_n:1 | Pnnn:1 | Pnnn |
+---------+-----------------+-----------------+--------------+--------------+
| 48:2 | -p_2ab_2bc | P_n_n_n:2 | Pnnn:2 | Pnnn |
+---------+-----------------+-----------------+--------------+--------------+
| 49 | -p_2_2c | P_c_c_m | Pccm | Pccm |
+---------+-----------------+-----------------+--------------+--------------+
| 49:cab | -p_2a_2 | P_m_a_a | Pmaa | Pmaa |
+---------+-----------------+-----------------+--------------+--------------+
| 49:bca | -p_2b_2b | P_b_m_b | Pbmb | Pbmb |
+---------+-----------------+-----------------+--------------+--------------+
| 50:1 | p_2_2\_-1ab | P_b_a_n:1 | Pban:1 | Pban |
+---------+-----------------+-----------------+--------------+--------------+
| 50:2 | -p_2ab_2b | P_b_a_n:2 | Pban:2 | Pban |
+---------+-----------------+-----------------+--------------+--------------+
| 50:1cab | p_2_2\_-1bc | P_n_c_b:1 | Pncb:1 | Pncb |
+---------+-----------------+-----------------+--------------+--------------+
| 50:2cab | -p_2b_2bc | P_n_c_b:2 | Pncb:2 | Pncb |
+---------+-----------------+-----------------+--------------+--------------+
| 50:1bca | p_2_2\_-1ac | P_c_n_a:1 | Pcna:1 | Pcna |
+---------+-----------------+-----------------+--------------+--------------+
| 50:2bca | -p_2a_2c | P_c_n_a:2 | Pcna:2 | Pcna |
+---------+-----------------+-----------------+--------------+--------------+
| 51 | -p_2a_2a | P_m_m_a | Pmma | Pmma |
+---------+-----------------+-----------------+--------------+--------------+
| 51:ba-c | -p_2b_2 | P_m_m_b | Pmmb | Pmmb |
+---------+-----------------+-----------------+--------------+--------------+
| 51:cab | -p_2_2b | P_b_m_m | Pbmm | Pbmm |
+---------+-----------------+-----------------+--------------+--------------+
| 51:-cba | -p_2c_2c | P_c_m_m | Pcmm | Pcmm |
+---------+-----------------+-----------------+--------------+--------------+
| 51:bca | -p_2c_2 | P_m_c_m | Pmcm | Pmcm |
+---------+-----------------+-----------------+--------------+--------------+
| 51:a-cb | -p_2_2a | P_m_a_m | Pmam | Pmam |
+---------+-----------------+-----------------+--------------+--------------+
| 52 | -p_2a_2bc | P_n_n_a | Pnna | Pnna |
+---------+-----------------+-----------------+--------------+--------------+
| 52:ba-c | -p_2b_2n | P_n_n_b | Pnnb | Pnnb |
+---------+-----------------+-----------------+--------------+--------------+
| 52:cab | -p_2n_2b | P_b_n_n | Pbnn | Pbnn |
+---------+-----------------+-----------------+--------------+--------------+
| 52:-cba | -p_2ab_2c | P_c_n_n | Pcnn | Pcnn |
+---------+-----------------+-----------------+--------------+--------------+
| 52:bca | -p_2ab_2n | P_n_c_n | Pncn | Pncn |
+---------+-----------------+-----------------+--------------+--------------+
| 52:a-cb | -p_2n_2bc | P_n_a_n | Pnan | Pnan |
+---------+-----------------+-----------------+--------------+--------------+
| 53 | -p_2ac_2 | P_m_n_a | Pmna | Pmna |
+---------+-----------------+-----------------+--------------+--------------+
| 53:ba-c | -p_2bc_2bc | P_n_m_b | Pnmb | Pnmb |
+---------+-----------------+-----------------+--------------+--------------+
| 53:cab | -p_2ab_2ab | P_b_m_n | Pbmn | Pbmn |
+---------+-----------------+-----------------+--------------+--------------+
| 53:-cba | -p_2_2ac | P_c_n_m | Pcnm | Pcnm |
+---------+-----------------+-----------------+--------------+--------------+
| 53:bca | -p_2_2bc | P_n_c_m | Pncm | Pncm |
+---------+-----------------+-----------------+--------------+--------------+
| 53:a-cb | -p_2ab_2 | P_m_a_n | Pman | Pman |
+---------+-----------------+-----------------+--------------+--------------+
| 54 | -p_2a_2ac | P_c_c_a | Pcca | Pcca |
+---------+-----------------+-----------------+--------------+--------------+
| 54:ba-c | -p_2b_2c | P_c_c_b | Pccb | Pccb |
+---------+-----------------+-----------------+--------------+--------------+
| 54:cab | -p_2a_2b | P_b_a_a | Pbaa | Pbaa |
+---------+-----------------+-----------------+--------------+--------------+
| 54:-cba | -p_2ac_2c | P_c_a_a | Pcaa | Pcaa |
+---------+-----------------+-----------------+--------------+--------------+
| 54:bca | -p_2bc_2b | P_b_c_b | Pbcb | Pbcb |
+---------+-----------------+-----------------+--------------+--------------+
| 54:a-cb | -p_2b_2ab | P_b_a_b | Pbab | Pbab |
+---------+-----------------+-----------------+--------------+--------------+
| 55 | -p_2_2ab | P_b_a_m | Pbam | Pbam |
+---------+-----------------+-----------------+--------------+--------------+
| 55:cab | -p_2bc_2 | P_m_c_b | Pmcb | Pmcb |
+---------+-----------------+-----------------+--------------+--------------+
| 55:bca | -p_2ac_2ac | P_c_m_a | Pcma | Pcma |
+---------+-----------------+-----------------+--------------+--------------+
| 56 | -p_2ab_2ac | P_c_c_n | Pccn | Pccn |
+---------+-----------------+-----------------+--------------+--------------+
| 56:cab | -p_2ac_2bc | P_n_a_a | Pnaa | Pnaa |
+---------+-----------------+-----------------+--------------+--------------+
| 56:bca | -p_2bc_2ab | P_b_n_b | Pbnb | Pbnb |
+---------+-----------------+-----------------+--------------+--------------+
| 57 | -p_2c_2b | P_b_c_m | Pbcm | Pbcm |
+---------+-----------------+-----------------+--------------+--------------+
| 57:ba-c | -p_2c_2ac | P_c_a_m | Pcam | Pcam |
+---------+-----------------+-----------------+--------------+--------------+
| 57:cab | -p_2ac_2a | P_m_c_a | Pmca | Pmca |
+---------+-----------------+-----------------+--------------+--------------+
| 57:-cba | -p_2b_2a | P_m_a_b | Pmab | Pmab |
+---------+-----------------+-----------------+--------------+--------------+
| 57:bca | -p_2a_2ab | P_b_m_a | Pbma | Pbma |
+---------+-----------------+-----------------+--------------+--------------+
| 57:a-cb | -p_2bc_2c | P_c_m_b | Pcmb | Pcmb |
+---------+-----------------+-----------------+--------------+--------------+
| 58 | -p_2_2n | P_n_n_m | Pnnm | Pnnm |
+---------+-----------------+-----------------+--------------+--------------+
| 58:cab | -p_2n_2 | P_m_n_n | Pmnn | Pmnn |
+---------+-----------------+-----------------+--------------+--------------+
| 58:bca | -p_2n_2n | P_n_m_n | Pnmn | Pnmn |
+---------+-----------------+-----------------+--------------+--------------+
| 59:1 | p_2_2ab\_-1ab | P_m_m_n:1 | Pmmn:1 | Pmmn |
+---------+-----------------+-----------------+--------------+--------------+
| 59:2 | -p_2ab_2a | P_m_m_n:2 | Pmmn:2 | Pmmn |
+---------+-----------------+-----------------+--------------+--------------+
| 59:1cab | p_2bc_2\_-1bc | P_n_m_m:1 | Pnmm:1 | Pnmm |
+---------+-----------------+-----------------+--------------+--------------+
| 59:2cab | -p_2c_2bc | P_n_m_m:2 | Pnmm:2 | Pnmm |
+---------+-----------------+-----------------+--------------+--------------+
| 59:1bca | p_2ac_2ac\_-1ac | P_m_n_m:1 | Pmnm:1 | Pmnm |
+---------+-----------------+-----------------+--------------+--------------+
| 59:2bca | -p_2c_2a | P_m_n_m:2 | Pmnm:2 | Pmnm |
+---------+-----------------+-----------------+--------------+--------------+
| 60 | -p_2n_2ab | P_b_c_n | Pbcn | Pbcn |
+---------+-----------------+-----------------+--------------+--------------+
| 60:ba-c | -p_2n_2c | P_c_a_n | Pcan | Pcan |
+---------+-----------------+-----------------+--------------+--------------+
| 60:cab | -p_2a_2n | P_n_c_a | Pnca | Pnca |
+---------+-----------------+-----------------+--------------+--------------+
| 60:-cba | -p_2bc_2n | P_n_a_b | Pnab | Pnab |
+---------+-----------------+-----------------+--------------+--------------+
| 60:bca | -p_2ac_2b | P_b_n_a | Pbna | Pbna |
+---------+-----------------+-----------------+--------------+--------------+
| 60:a-cb | -p_2b_2ac | P_c_n_b | Pcnb | Pcnb |
+---------+-----------------+-----------------+--------------+--------------+
| 61 | -p_2ac_2ab | P_b_c_a | Pbca | Pbca |
+---------+-----------------+-----------------+--------------+--------------+
| 61:ba-c | -p_2bc_2ac | P_c_a_b | Pcab | Pcab |
+---------+-----------------+-----------------+--------------+--------------+
| 62 | -p_2ac_2n | P_n_m_a | Pnma | Pnma |
+---------+-----------------+-----------------+--------------+--------------+
| 62:ba-c | -p_2bc_2a | P_m_n_b | Pmnb | Pmnb |
+---------+-----------------+-----------------+--------------+--------------+
| 62:cab | -p_2c_2ab | P_b_n_m | Pbnm | Pbnm |
+---------+-----------------+-----------------+--------------+--------------+
| 62:-cba | -p_2n_2ac | P_c_m_n | Pcmn | Pcmn |
+---------+-----------------+-----------------+--------------+--------------+
| 62:bca | -p_2n_2a | P_m_c_n | Pmcn | Pmcn |
+---------+-----------------+-----------------+--------------+--------------+
| 62:a-cb | -p_2c_2n | P_n_a_m | Pnam | Pnam |
+---------+-----------------+-----------------+--------------+--------------+
| 63 | -c_2c_2 | C_m_c_m | Cmcm | Cmcm |
+---------+-----------------+-----------------+--------------+--------------+
| 63:ba-c | -c_2c_2c | C_c_m_m | Ccmm | Ccmm |
+---------+-----------------+-----------------+--------------+--------------+
| 63:cab | -a_2a_2a | A_m_m_a | Amma | Amma |
+---------+-----------------+-----------------+--------------+--------------+
| 63:-cba | -a_2_2a | A_m_a_m | Amam | Amam |
+---------+-----------------+-----------------+--------------+--------------+
| 63:bca | -b_2_2b | B_b_m_m | Bbmm | Bbmm |
+---------+-----------------+-----------------+--------------+--------------+
| 63:a-cb | -b_2b_2 | B_m_m_b | Bmmb | Bmmb |
+---------+-----------------+-----------------+--------------+--------------+
| 64 | -c_2ac_2 | C_m_c_e | Cmce | Cmce |
+---------+-----------------+-----------------+--------------+--------------+
| 64:ba-c | -c_2ac_2ac | C_c_m_b | Ccmb | Ccmb |
+---------+-----------------+-----------------+--------------+--------------+
| 64:cab | -a_2ab_2ab | A_b_m_a | Abma | Abma |
+---------+-----------------+-----------------+--------------+--------------+
| 64:-cba | -a_2_2ab | A_c_a_m | Acam | Acam |
+---------+-----------------+-----------------+--------------+--------------+
| 64:bca | -b_2_2ab | B_b_c_m | Bbcm | Bbcm |
+---------+-----------------+-----------------+--------------+--------------+
| 64:a-cb | -b_2ab_2 | B_m_a_b | Bmab | Bmab |
+---------+-----------------+-----------------+--------------+--------------+
| 65 | -c_2_2 | C_m_m_m | Cmmm | Cmmm |
+---------+-----------------+-----------------+--------------+--------------+
| 65:cab | -a_2_2 | A_m_m_m | Ammm | Ammm |
+---------+-----------------+-----------------+--------------+--------------+
| 65:bca | -b_2_2 | B_m_m_m | Bmmm | Bmmm |
+---------+-----------------+-----------------+--------------+--------------+
| 66 | -c_2_2c | C_c_c_m | Cccm | Cccm |
+---------+-----------------+-----------------+--------------+--------------+
| 66:cab | -a_2a_2 | A_m_a_a | Amaa | Amaa |
+---------+-----------------+-----------------+--------------+--------------+
| 66:bca | -b_2b_2b | B_b_m_b | Bbmb | Bbmb |
+---------+-----------------+-----------------+--------------+--------------+
| 67 | -c_2a_2 | C_m_m_e | Cmme | Cmme |
+---------+-----------------+-----------------+--------------+--------------+
| 67:ba-c | -c_2a_2a | C_m_m_b | Cmmb | Cmmb |
+---------+-----------------+-----------------+--------------+--------------+
| 67:cab | -a_2b_2b | A_b_m_m | Abmm | Abmm |
+---------+-----------------+-----------------+--------------+--------------+
| 67:-cba | -a_2_2b | A_c_m_m | Acmm | Acmm |
+---------+-----------------+-----------------+--------------+--------------+
| 67:bca | -b_2_2a | B_m_c_m | Bmcm | Bmcm |
+---------+-----------------+-----------------+--------------+--------------+
| 67:a-cb | -b_2a_2 | B_m_a_m | Bmam | Bmam |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1 | c_2_2\_-1ac | C_c_c_e:1 | Ccce:1 | Ccce |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2 | -c_2a_2ac | C_c_c_e:2 | Ccce:2 | Ccce |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1ba- | c_2_2\_-1ac | C_c_c_b:1 | Cccb:1 | Cccb |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2ba- | -c_2a_2c | C_c_c_b:2 | Cccb:2 | Cccb |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1cab | a_2_2\_-1ab | A_b_a_a:1 | Abaa:1 | Abaa |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2cab | -a_2a_2b | A_b_a_a:2 | Abaa:2 | Abaa |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1-cb | a_2_2\_-1ab | A_c_a_a:1 | Acaa:1 | Acaa |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2-cb | -a_2ab_2b | A_c_a_a:2 | Acaa:2 | Acaa |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1bca | b_2_2\_-1ab | B_b_c_b:1 | Bbcb:1 | Bbcb |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2bca | -b_2ab_2b | B_b_c_b:2 | Bbcb:2 | Bbcb |
+---------+-----------------+-----------------+--------------+--------------+
| 68:1a-c | b_2_2\_-1ab | B_b_a_b:1 | Bbab:1 | Bbab |
+---------+-----------------+-----------------+--------------+--------------+
| 68:2a-c | -b_2b_2ab | B_b_a_b:2 | Bbab:2 | Bbab |
+---------+-----------------+-----------------+--------------+--------------+
| 69 | -f_2_2 | F_m_m_m | Fmmm | Fmmm |
+---------+-----------------+-----------------+--------------+--------------+
| 70:1 | f_2_2\_-1d | F_d_d_d:1 | Fddd:1 | Fddd |
+---------+-----------------+-----------------+--------------+--------------+
| 70:2 | -f_2uv_2vw | F_d_d_d:2 | Fddd:2 | Fddd |
+---------+-----------------+-----------------+--------------+--------------+
| 71 | -i_2_2 | I_m_m_m | Immm | Immm |
+---------+-----------------+-----------------+--------------+--------------+
| 72 | -i_2_2c | I_b_a_m | Ibam | Ibam |
+---------+-----------------+-----------------+--------------+--------------+
| 72:cab | -i_2a_2 | I_m_c_b | Imcb | Imcb |
+---------+-----------------+-----------------+--------------+--------------+
| 72:bca | -i_2b_2b | I_c_m_a | Icma | Icma |
+---------+-----------------+-----------------+--------------+--------------+
| 73 | -i_2b_2c | I_b_c_a | Ibca | Ibca |
+---------+-----------------+-----------------+--------------+--------------+
| 73:ba-c | -i_2a_2b | I_c_a_b | Icab | Icab |
+---------+-----------------+-----------------+--------------+--------------+
| 74 | -i_2b_2 | I_m_m_a | Imma | Imma |
+---------+-----------------+-----------------+--------------+--------------+
| 74:ba-c | -i_2a_2a | I_m_m_b | Immb | Immb |
+---------+-----------------+-----------------+--------------+--------------+
| 74:cab | -i_2c_2c | I_b_m_m | Ibmm | Ibmm |
+---------+-----------------+-----------------+--------------+--------------+
| 74:-cba | -i_2_2b | I_c_m_m | Icmm | Icmm |
+---------+-----------------+-----------------+--------------+--------------+
| 74:bca | -i_2_2a | I_m_c_m | Imcm | Imcm |
+---------+-----------------+-----------------+--------------+--------------+
| 74:a-cb | -i_2c_2 | I_m_a_m | Imam | Imam |
+---------+-----------------+-----------------+--------------+--------------+
| 75 | p_4 | P_4 | P4 | P4 |
+---------+-----------------+-----------------+--------------+--------------+
| 76 | p_4w | P_41 | P41 | P41 |
+---------+-----------------+-----------------+--------------+--------------+
| 77 | p_4c | P_42 | P42 | P42 |
+---------+-----------------+-----------------+--------------+--------------+
| 78 | p_4cw | P_43 | P43 | P43 |
+---------+-----------------+-----------------+--------------+--------------+
| 79 | i_4 | I_4 | I4 | I4 |
+---------+-----------------+-----------------+--------------+--------------+
| 80 | i_4bw | I_41 | I41 | I41 |
+---------+-----------------+-----------------+--------------+--------------+
| 81 | p\_-4 | P\_-4 | P-4 | P-4 |
+---------+-----------------+-----------------+--------------+--------------+
| 82 | i\_-4 | I\_-4 | I-4 | I-4 |
+---------+-----------------+-----------------+--------------+--------------+
| 83 | -p_4 | P_4/m | P4/m | P4/m |
+---------+-----------------+-----------------+--------------+--------------+
| 84 | -p_4c | P_42/m | P42/m | P42/m |
+---------+-----------------+-----------------+--------------+--------------+
| 85:1 | p_4ab\_-1ab | P_4/n:1 | P4/n:1 | P4/n |
+---------+-----------------+-----------------+--------------+--------------+
| 85:2 | -p_4a | P_4/n:2 | P4/n:2 | P4/n |
+---------+-----------------+-----------------+--------------+--------------+
| 86:1 | p_4n\_-1n | P_42/n:1 | P42/n:1 | P42/n |
+---------+-----------------+-----------------+--------------+--------------+
| 86:2 | -p_4bc | P_42/n:2 | P42/n:2 | P42/n |
+---------+-----------------+-----------------+--------------+--------------+
| 87 | -i_4 | I_4/m | I4/m | I4/m |
+---------+-----------------+-----------------+--------------+--------------+
| 88:1 | i_4bw\_-1bw | I_41/a:1 | I41/a:1 | I41/a |
+---------+-----------------+-----------------+--------------+--------------+
| 88:2 | -i_4ad | I_41/a:2 | I41/a:2 | I41/a |
+---------+-----------------+-----------------+--------------+--------------+
| 89 | p_4_2 | P_4_2_2 | P422 | P422 |
+---------+-----------------+-----------------+--------------+--------------+
| 90 | p_4ab_2ab | P_4_21_2 | P4212 | P4212 |
+---------+-----------------+-----------------+--------------+--------------+
| 91 | p_4w_2c | P_41_2_2 | P4122 | P4122 |
+---------+-----------------+-----------------+--------------+--------------+
| 92 | p_4abw_2nw | P_41_21_2 | P41212 | P41212 |
+---------+-----------------+-----------------+--------------+--------------+
| 93 | p_4c_2 | P_42_2_2 | P4222 | P4222 |
+---------+-----------------+-----------------+--------------+--------------+
| 94 | p_4n_2n | P_42_21_2 | P42212 | P42212 |
+---------+-----------------+-----------------+--------------+--------------+
| 95 | p_4cw_2c | P_43_2_2 | P4322 | P4322 |
+---------+-----------------+-----------------+--------------+--------------+
| 96 | p_4nw_2abw | P_43_21_2 | P43212 | P43212 |
+---------+-----------------+-----------------+--------------+--------------+
| 97 | i_4_2 | I_4_2_2 | I422 | I422 |
+---------+-----------------+-----------------+--------------+--------------+
| 98 | i_4bw_2bw | I_41_2_2 | I4122 | I4122 |
+---------+-----------------+-----------------+--------------+--------------+
| 99 | p_4\_-2 | P_4_m_m | P4mm | P4mm |
+---------+-----------------+-----------------+--------------+--------------+
| 100 | p_4\_-2ab | P_4_b_m | P4bm | P4bm |
+---------+-----------------+-----------------+--------------+--------------+
| 101 | p_4c\_-2c | P_42_c_m | P42cm | P42cm |
+---------+-----------------+-----------------+--------------+--------------+
| 102 | p_4n\_-2n | P_42_n_m | P42nm | P42nm |
+---------+-----------------+-----------------+--------------+--------------+
| 103 | p_4\_-2c | P_4_c_c | P4cc | P4cc |
+---------+-----------------+-----------------+--------------+--------------+
| 104 | p_4\_-2n | P_4_n_c | P4nc | P4nc |
+---------+-----------------+-----------------+--------------+--------------+
| 105 | p_4c\_-2 | P_42_m_c | P42mc | P42mc |
+---------+-----------------+-----------------+--------------+--------------+
| 106 | p_4c\_-2ab | P_42_b_c | P42bc | P42bc |
+---------+-----------------+-----------------+--------------+--------------+
| 107 | i_4\_-2 | I_4_m_m | I4mm | I4mm |
+---------+-----------------+-----------------+--------------+--------------+
| 108 | i_4\_-2c | I_4_c_m | I4cm | I4cm |
+---------+-----------------+-----------------+--------------+--------------+
| 109 | i_4bw\_-2 | I_41_m_d | I41md | I41md |
+---------+-----------------+-----------------+--------------+--------------+
| 110 | i_4bw\_-2c | I_41_c_d | I41cd | I41cd |
+---------+-----------------+-----------------+--------------+--------------+
| 111 | p\_-4_2 | P\_-4_2_m | P-42m | P-42m |
+---------+-----------------+-----------------+--------------+--------------+
| 112 | p\_-4_2c | P\_-4_2_c | P-42c | P-42c |
+---------+-----------------+-----------------+--------------+--------------+
| 113 | p\_-4_2ab | P\_-4_21_m | P-421m | P-421m |
+---------+-----------------+-----------------+--------------+--------------+
| 114 | p\_-4_2n | P\_-4_21_c | P-421c | P-421c |
+---------+-----------------+-----------------+--------------+--------------+
| 115 | p\_-4\_-2 | P\_-4_m_2 | P-4m2 | P-4m2 |
+---------+-----------------+-----------------+--------------+--------------+
| 116 | p\_-4\_-2c | P\_-4_c_2 | P-4c2 | P-4c2 |
+---------+-----------------+-----------------+--------------+--------------+
| 117 | p\_-4\_-2ab | P\_-4_b_2 | P-4b2 | P-4b2 |
+---------+-----------------+-----------------+--------------+--------------+
| 118 | p\_-4\_-2n | P\_-4_n_2 | P-4n2 | P-4n2 |
+---------+-----------------+-----------------+--------------+--------------+
| 119 | i\_-4\_-2 | I\_-4_m_2 | I-4m2 | I-4m2 |
+---------+-----------------+-----------------+--------------+--------------+
| 120 | i\_-4\_-2c | I\_-4_c_2 | I-4c2 | I-4c2 |
+---------+-----------------+-----------------+--------------+--------------+
| 121 | i\_-4_2 | I\_-4_2_m | I-42m | I-42m |
+---------+-----------------+-----------------+--------------+--------------+
| 122 | i\_-4_2bw | I\_-4_2_d | I-42d | I-42d |
+---------+-----------------+-----------------+--------------+--------------+
| 123 | -p_4_2 | P_4/m_m_m | P4/mmm | P4/mmm |
+---------+-----------------+-----------------+--------------+--------------+
| 124 | -p_4_2c | P_4/m_c_c | P4/mcc | P4/mcc |
+---------+-----------------+-----------------+--------------+--------------+
| 125:1 | p_4_2\_-1ab | P_4/n_b_m:1 | P4/nbm:1 | P4/nbm |
+---------+-----------------+-----------------+--------------+--------------+
| 125:2 | -p_4a_2b | P_4/n_b_m:2 | P4/nbm:2 | P4/nbm |
+---------+-----------------+-----------------+--------------+--------------+
| 126:1 | p_4_2\_-1n | P_4/n_n_c:1 | P4/nnc:1 | P4/nnc |
+---------+-----------------+-----------------+--------------+--------------+
| 126:2 | -p_4a_2bc | P_4/n_n_c:2 | P4/nnc:2 | P4/nnc |
+---------+-----------------+-----------------+--------------+--------------+
| 127 | -p_4_2ab | P_4/m_b_m | P4/mbm | P4/mbm |
+---------+-----------------+-----------------+--------------+--------------+
| 128 | -p_4_2n | P_4/m_n_c | P4/mnc | P4/mnc |
+---------+-----------------+-----------------+--------------+--------------+
| 129:1 | p_4ab_2ab\_-1ab | P_4/n_m_m:1 | P4/nmm:1 | P4/nmm |
+---------+-----------------+-----------------+--------------+--------------+
| 129:2 | -p_4a_2a | P_4/n_m_m:2 | P4/nmm:2 | P4/nmm |
+---------+-----------------+-----------------+--------------+--------------+
| 130:1 | p_4ab_2n\_-1ab | P_4/n_c_c:1 | P4/ncc:1 | P4/ncc |
+---------+-----------------+-----------------+--------------+--------------+
| 130:2 | -p_4a_2ac | P_4/n_c_c:2 | P4/ncc:2 | P4/ncc |
+---------+-----------------+-----------------+--------------+--------------+
| 131 | -p_4c_2 | P_42/m_m_c | P42/mmc | P42/mmc |
+---------+-----------------+-----------------+--------------+--------------+
| 132 | -p_4c_2c | P_42/m_c_m | P42/mcm | P42/mcm |
+---------+-----------------+-----------------+--------------+--------------+
| 133:1 | p_4n_2c\_-1n | P_42/n_b_c:1 | P42/nbc:1 | P42/nbc |
+---------+-----------------+-----------------+--------------+--------------+
| 133:2 | -p_4ac_2b | P_42/n_b_c:2 | P42/nbc:2 | P42/nbc |
+---------+-----------------+-----------------+--------------+--------------+
| 134:1 | p_4n_2\_-1n | P_42/n_n_m:1 | P42/nnm:1 | P42/nnm |
+---------+-----------------+-----------------+--------------+--------------+
| 134:2 | -p_4ac_2bc | P_42/n_n_m:2 | P42/nnm:2 | P42/nnm |
+---------+-----------------+-----------------+--------------+--------------+
| 135 | -p_4c_2ab | P_42/m_b_c | P42/mbc | P42/mbc |
+---------+-----------------+-----------------+--------------+--------------+
| 136 | -p_4n_2n | P_42/m_n_m | P42/mnm | P42/mnm |
+---------+-----------------+-----------------+--------------+--------------+
| 137:1 | p_4n_2n\_-1n | P_42/n_m_c:1 | P42/nmc:1 | P42/nmc |
+---------+-----------------+-----------------+--------------+--------------+
| 137:2 | -p_4ac_2a | P_42/n_m_c:2 | P42/nmc:2 | P42/nmc |
+---------+-----------------+-----------------+--------------+--------------+
| 138:1 | p_4n_2ab\_-1n | P_42/n_c_m:1 | P42/ncm:1 | P42/ncm |
+---------+-----------------+-----------------+--------------+--------------+
| 138:2 | -p_4ac_2ac | P_42/n_c_m:2 | P42/ncm:2 | P42/ncm |
+---------+-----------------+-----------------+--------------+--------------+
| 139 | -i_4_2 | I_4/m_m_m | I4/mmm | I4/mmm |
+---------+-----------------+-----------------+--------------+--------------+
| 140 | -i_4_2c | I_4/m_c_m | I4/mcm | I4/mcm |
+---------+-----------------+-----------------+--------------+--------------+
| 141:1 | i_4bw_2bw\_-1bw | I_41/a_m_d:1 | I41/amd:1 | I41/amd |
+---------+-----------------+-----------------+--------------+--------------+
| 141:2 | -i_4bd_2 | I_41/a_m_d:2 | I41/amd:2 | I41/amd |
+---------+-----------------+-----------------+--------------+--------------+
| 142:1 | i_4bw_2aw\_-1bw | I_41/a_c_d:1 | I41/acd:1 | I41/acd |
+---------+-----------------+-----------------+--------------+--------------+
| 142:2 | -i_4bd_2c | I_41/a_c_d:2 | I41/acd:2 | I41/acd |
+---------+-----------------+-----------------+--------------+--------------+
| 143 | p_3 | P_3 | P3 | P3 |
+---------+-----------------+-----------------+--------------+--------------+
| 144 | p_31 | P_31 | P31 | P31 |
+---------+-----------------+-----------------+--------------+--------------+
| 145 | p_32 | P_32 | P32 | P32 |
+---------+-----------------+-----------------+--------------+--------------+
| 146:h | r_3 | R_3:h | R3:h | R3 |
+---------+-----------------+-----------------+--------------+--------------+
| 146:r | p_3* | R_3:r | R3:r | R3 |
+---------+-----------------+-----------------+--------------+--------------+
| 147 | -p_3 | P\_-3 | P-3 | P-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 148:h | -r_3 | R\_-3:h | R-3:h | R-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 148:r | -p_3* | R\_-3:r | R-3:r | R-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 149 | p_3_2 | P_3_1_2 | P312 | P312 |
+---------+-----------------+-----------------+--------------+--------------+
| 150 | p_3_2" | P_3_2_1 | P321 | P321 |
+---------+-----------------+-----------------+--------------+--------------+
| 151 | p_31_2\_(0_0_4) | P_31_1_2 | P3112 | P3112 |
+---------+-----------------+-----------------+--------------+--------------+
| 152 | p_31_2" | P_31_2_1 | P3121 | P3121 |
+---------+-----------------+-----------------+--------------+--------------+
| 153 | p_32_2\_(0_0_2) | P_32_1_2 | P3212 | P3212 |
+---------+-----------------+-----------------+--------------+--------------+
| 154 | p_32_2" | P_32_2_1 | P3221 | P3221 |
+---------+-----------------+-----------------+--------------+--------------+
| 155:h | r_3_2" | R_3_2:h | R32:h | R32 |
+---------+-----------------+-----------------+--------------+--------------+
| 155:r | p_3*_2 | R_3_2:r | R32:r | R32 |
+---------+-----------------+-----------------+--------------+--------------+
| 156 | p_3\_-2" | P_3_m_1 | P3m1 | P3m1 |
+---------+-----------------+-----------------+--------------+--------------+
| 157 | p_3\_-2 | P_3_1_m | P31m | P31m |
+---------+-----------------+-----------------+--------------+--------------+
| 158 | p_3\_-2"c | P_3_c_1 | P3c1 | P3c1 |
+---------+-----------------+-----------------+--------------+--------------+
| 159 | p_3\_-2c | P_3_1_c | P31c | P31c |
+---------+-----------------+-----------------+--------------+--------------+
| 160:h | r_3\_-2" | R_3_m:h | R3m:h | R3m |
+---------+-----------------+-----------------+--------------+--------------+
| 160:r | p_3*\_-2 | R_3_m:r | R3m:r | R3m |
+---------+-----------------+-----------------+--------------+--------------+
| 161:h | r_3\_-2"c | R_3_c:h | R3c:h | R3c |
+---------+-----------------+-----------------+--------------+--------------+
| 161:r | p_3*\_-2n | R_3_c:r | R3c:r | R3c |
+---------+-----------------+-----------------+--------------+--------------+
| 162 | -p_3_2 | P\_-3_1_m | P-31m | P-31m |
+---------+-----------------+-----------------+--------------+--------------+
| 163 | -p_3_2c | P\_-3_1_c | P-31c | P-31c |
+---------+-----------------+-----------------+--------------+--------------+
| 164 | -p_3_2" | P\_-3_m_1 | P-3m1 | P-3m1 |
+---------+-----------------+-----------------+--------------+--------------+
| 165 | -p_3_2"c | P\_-3_c_1 | P-3c1 | P-3c1 |
+---------+-----------------+-----------------+--------------+--------------+
| 166:h | -r_3_2" | R\_-3_m:h | R-3m:h | R-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 166:r | -p_3*_2 | R\_-3_m:r | R-3m:r | R-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 167:h | -r_3_2"c | R\_-3_c:h | R-3c:h | R-3c |
+---------+-----------------+-----------------+--------------+--------------+
| 167:r | -p_3*_2n | R\_-3_c:r | R-3c:r | R-3c |
+---------+-----------------+-----------------+--------------+--------------+
| 168 | p_6 | P_6 | P6 | P6 |
+---------+-----------------+-----------------+--------------+--------------+
| 169 | p_61 | P_61 | P61 | P61 |
+---------+-----------------+-----------------+--------------+--------------+
| 170 | p_65 | P_65 | P65 | P65 |
+---------+-----------------+-----------------+--------------+--------------+
| 171 | p_62 | P_62 | P62 | P62 |
+---------+-----------------+-----------------+--------------+--------------+
| 172 | p_64 | P_64 | P64 | P64 |
+---------+-----------------+-----------------+--------------+--------------+
| 173 | p_6c | P_63 | P63 | P63 |
+---------+-----------------+-----------------+--------------+--------------+
| 174 | p\_-6 | P\_-6 | P-6 | P-6 |
+---------+-----------------+-----------------+--------------+--------------+
| 175 | -p_6 | P_6/m | P6/m | P6/m |
+---------+-----------------+-----------------+--------------+--------------+
| 176 | -p_6c | P_63/m | P63/m | P63/m |
+---------+-----------------+-----------------+--------------+--------------+
| 177 | p_6_2 | P_6_2_2 | P622 | P622 |
+---------+-----------------+-----------------+--------------+--------------+
| 178 | p_61_2\_(0_0_5) | P_61_2_2 | P6122 | P6122 |
+---------+-----------------+-----------------+--------------+--------------+
| 179 | p_65_2\_(0_0_1) | P_65_2_2 | P6522 | P6522 |
+---------+-----------------+-----------------+--------------+--------------+
| 180 | p_62_2\_(0_0_4) | P_62_2_2 | P6222 | P6222 |
+---------+-----------------+-----------------+--------------+--------------+
| 181 | p_64_2\_(0_0_2) | P_64_2_2 | P6422 | P6422 |
+---------+-----------------+-----------------+--------------+--------------+
| 182 | p_6c_2c | P_63_2_2 | P6322 | P6322 |
+---------+-----------------+-----------------+--------------+--------------+
| 183 | p_6\_-2 | P_6_m_m | P6mm | P6mm |
+---------+-----------------+-----------------+--------------+--------------+
| 184 | p_6\_-2c | P_6_c_c | P6cc | P6cc |
+---------+-----------------+-----------------+--------------+--------------+
| 185 | p_6c\_-2 | P_63_c_m | P63cm | P63cm |
+---------+-----------------+-----------------+--------------+--------------+
| 186 | p_6c\_-2c | P_63_m_c | P63mc | P63mc |
+---------+-----------------+-----------------+--------------+--------------+
| 187 | p\_-6_2 | P\_-6_m_2 | P-6m2 | P-6m2 |
+---------+-----------------+-----------------+--------------+--------------+
| 188 | p\_-6c_2 | P\_-6_c_2 | P-6c2 | P-6c2 |
+---------+-----------------+-----------------+--------------+--------------+
| 189 | p\_-6\_-2 | P\_-6_2_m | P-62m | P-62m |
+---------+-----------------+-----------------+--------------+--------------+
| 190 | p\_-6c\_-2c | P\_-6_2_c | P-62c | P-62c |
+---------+-----------------+-----------------+--------------+--------------+
| 191 | -p_6_2 | P_6/m_m_m | P6/mmm | P6/mmm |
+---------+-----------------+-----------------+--------------+--------------+
| 192 | -p_6_2c | P_6/m_c_c | P6/mcc | P6/mcc |
+---------+-----------------+-----------------+--------------+--------------+
| 193 | -p_6c_2 | P_63/m_c_m | P63/mcm | P63/mcm |
+---------+-----------------+-----------------+--------------+--------------+
| 194 | -p_6c_2c | P_63/m_m_c | P63/mmc | P63/mmc |
+---------+-----------------+-----------------+--------------+--------------+
| 195 | p_2_2_3 | P_2_3 | P23 | P23 |
+---------+-----------------+-----------------+--------------+--------------+
| 196 | f_2_2_3 | F_2_3 | F23 | F23 |
+---------+-----------------+-----------------+--------------+--------------+
| 197 | i_2_2_3 | I_2_3 | I23 | I23 |
+---------+-----------------+-----------------+--------------+--------------+
| 198 | p_2ac_2ab_3 | P_21_3 | P213 | P213 |
+---------+-----------------+-----------------+--------------+--------------+
| 199 | i_2b_2c_3 | I_21_3 | I213 | I213 |
+---------+-----------------+-----------------+--------------+--------------+
| 200 | -p_2_2_3 | P_m\_-3 | Pm-3 | Pm-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 201:1 | p_2_2_3\_-1n | P_n\_-3:1 | Pn-3:1 | Pn-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 201:2 | -p_2ab_2bc_3 | P_n\_-3:2 | Pn-3:2 | Pn-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 202 | -f_2_2_3 | F_m\_-3 | Fm-3 | Fm-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 203:1 | f_2_2_3\_-1d | F_d\_-3:1 | Fd-3:1 | Fd-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 203:2 | -f_2uv_2vw_3 | F_d\_-3:2 | Fd-3:2 | Fd-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 204 | -i_2_2_3 | I_m\_-3 | Im-3 | Im-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 205 | -p_2ac_2ab_3 | P_a\_-3 | Pa-3 | Pa-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 206 | -i_2b_2c_3 | I_a\_-3 | Ia-3 | Ia-3 |
+---------+-----------------+-----------------+--------------+--------------+
| 207 | p_4_2_3 | P_4_3_2 | P432 | P432 |
+---------+-----------------+-----------------+--------------+--------------+
| 208 | p_4n_2_3 | P_42_3_2 | P4232 | P4232 |
+---------+-----------------+-----------------+--------------+--------------+
| 209 | f_4_2_3 | F_4_3_2 | F432 | F432 |
+---------+-----------------+-----------------+--------------+--------------+
| 210 | f_4d_2_3 | F_41_3_2 | F4132 | F4132 |
+---------+-----------------+-----------------+--------------+--------------+
| 211 | i_4_2_3 | I_4_3_2 | I432 | I432 |
+---------+-----------------+-----------------+--------------+--------------+
| 212 | p_4acd_2ab_3 | P_43_3_2 | P4332 | P4332 |
+---------+-----------------+-----------------+--------------+--------------+
| 213 | p_4bd_2ab_3 | P_41_3_2 | P4132 | P4132 |
+---------+-----------------+-----------------+--------------+--------------+
| 214 | i_4bd_2c_3 | I_41_3_2 | I4132 | I4132 |
+---------+-----------------+-----------------+--------------+--------------+
| 215 | p\_-4_2_3 | P\_-4_3_m | P-43m | P-43m |
+---------+-----------------+-----------------+--------------+--------------+
| 216 | f\_-4_2_3 | F\_-4_3_m | F-43m | F-43m |
+---------+-----------------+-----------------+--------------+--------------+
| 217 | i\_-4_2_3 | I\_-4_3_m | I-43m | I-43m |
+---------+-----------------+-----------------+--------------+--------------+
| 218 | p\_-4n_2_3 | P\_-4_3_n | P-43n | P-43n |
+---------+-----------------+-----------------+--------------+--------------+
| 219 | f\_-4a_2_3 | F\_-4_3_c | F-43c | F-43c |
+---------+-----------------+-----------------+--------------+--------------+
| 220 | i\_-4bd_2c_3 | I\_-4_3_d | I-43d | I-43d |
+---------+-----------------+-----------------+--------------+--------------+
| 221 | -p_4_2_3 | P_m\_-3_m | Pm-3m | Pm-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 222:1 | p_4_2_3\_-1n | P_n\_-3_n:1 | Pn-3n:1 | Pn-3n |
+---------+-----------------+-----------------+--------------+--------------+
| 222:2 | -p_4a_2bc_3 | P_n\_-3_n:2 | Pn-3n:2 | Pn-3n |
+---------+-----------------+-----------------+--------------+--------------+
| 223 | -p_4n_2_3 | P_m\_-3_n | Pm-3n | Pm-3n |
+---------+-----------------+-----------------+--------------+--------------+
| 224:1 | p_4n_2_3\_-1n | P_n\_-3_m:1 | Pn-3m:1 | Pn-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 224:2 | -p_4bc_2bc_3 | P_n\_-3_m:2 | Pn-3m:2 | Pn-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 225 | -f_4_2_3 | F_m\_-3_m | Fm-3m | Fm-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 226 | -f_4a_2_3 | F_m\_-3_c | Fm-3c | Fm-3c |
+---------+-----------------+-----------------+--------------+--------------+
| 227:1 | f_4d_2_3\_-1d | F_d\_-3_m:1 | Fd-3m:1 | Fd-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 227:2 | -f_4vw_2vw_3 | F_d\_-3_m:2 | Fd-3m:2 | Fd-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 228:1 | f_4d_2_3\_-1ad | F_d\_-3_c:1 | Fd-3c:1 | Fd-3c |
+---------+-----------------+-----------------+--------------+--------------+
| 228:2 | -f_4ud_2vw_3 | F_d\_-3_c:2 | Fd-3c:2 | Fd-3c |
+---------+-----------------+-----------------+--------------+--------------+
| 229 | -i_4_2_3 | I_m\_-3_m | Im-3m | Im-3m |
+---------+-----------------+-----------------+--------------+--------------+
| 230 | -i_4bd_2c_3 | I_a\_-3_d | Ia-3d | Ia-3d |
+---------+-----------------+-----------------+--------------+--------------+
"""