-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.2017', 'ambient_counter': 2017, 'ambient_order': 1600, 'ambient_tex': 'D_{50}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 400, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.2017.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.54', 'subgroup_hash': 54, 'subgroup_order': 400, 'subgroup_tex': 'C_2^2\\times D_{50}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1600.2017', 'aut_centralizer_order': 128, 'aut_label': '4.d1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '12000.cn', 'aut_weyl_index': 128, 'centralizer': '100.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1'], 'contains': ['8.a1', '8.b1', '8.e1', '8.f1', '8.g1', '20.f1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6583, 3475, 6761, 6544], 'generators': [1, 320, 8, 800, 2, 64], 'label': '1600.2017.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1'], 'normal_contains': ['8.a1', '8.b1', '8.e1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '200.12', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '100.3'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 2100, 'aut_gen_orders': [20, 20], 'aut_gens': [[1, 2, 4, 8], [200, 2, 341, 339], [200, 1, 231, 75]], 'aut_group': None, 'aut_hash': 8170964205122769949, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 672000, 'aut_permdeg': 200, 'aut_perms': [290956289346164904689879986352899066739281411984955782127521395483677549511023851593126741807765235417415958478482877177463289010961121460717673013318028578903711148271370752891437488614724163000727880313347440927858225202930465764535599765705198071569296932779349064562934552110315434727912751766973604442829380408047110811000706782464255054499863671694884957485162887064622, 545180319721842334147885884280149960609187822920882883824758034807346335973064655583724259940829753000807998056945788512390066831084822121641424043892043812906264905689263179031568610743195215741554138992959932302728954982428897739190715407282283265671766526428804533248474399985603806536009558057371811366042425903826188893587428030405463403754637895258913211108745385103531], 'aut_phi_ratio': 4200.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1], [2, 25, 8, 1], [5, 2, 2, 1], [10, 2, 14, 1], [25, 2, 10, 1], [50, 2, 70, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_{25}.C_{10}\\times C_2^3.\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '1344.11686', 'autcent_hash': 11686, 'autcent_nilpotent': False, 'autcent_order': 1344, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^3:\\GL(3,2)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 100, 'autcentquo_group': '500.18', 'autcentquo_hash': 18, 'autcentquo_nilpotent': False, 'autcentquo_order': 500, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{25}:C_{20}', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 25, 8], [5, 2, 2], [10, 2, 14], [25, 2, 10], [50, 2, 70]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '50.1', 'commutator_count': 1, 'commutator_label': '25.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 54, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 3], ['50.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 25, 1, 8], [5, 2, 2, 1], [10, 2, 2, 7], [25, 2, 10, 1], [50, 2, 10, 7]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 11625, 'exponent': 50, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '5.1', 'frattini_quotient': '80.51', 'hash': 54, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 50, 'inner_gen_orders': [1, 1, 2, 25], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 392], [1, 2, 20, 8]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 50, 'inner_split': False, 'inner_tex': 'D_{25}', 'inner_used': [3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 96]], 'label': '400.54', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*D50', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 112, 'number_divisions': 32, 'number_normal_subgroups': 99, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 201, 'number_subgroups': 1629, 'old_label': None, 'order': 400, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 207], [5, 4], [10, 28], [25, 20], [50, 140]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 420, 'outer_gen_orders': [10, 10, 2, 2, 20, 20, 5], 'outer_gen_pows': [0, 0, 4, 4, 0, 0, 0], 'outer_gens': [[1, 2, 206, 328], [1, 2, 6, 328], [1, 2, 4, 56], [1, 2, 205, 56], [201, 202, 206, 104], [1, 3, 207, 106], [1, 2, 4, 248]], 'outer_group': '13440.g', 'outer_hash': 2430954659866472455, 'outer_nilpotent': False, 'outer_order': 13440, 'outer_permdeg': 15, 'outer_perms': [475819185648, 642911273328, 1, 361726081921, 193676316529, 25558367089, 1824], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^3:\\GL(3,2)\\times C_{10}', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 31, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [4, 8], [20, 8]], 'representations': {'PC': {'code': 335092662979084255247, 'gens': [1, 2, 3, 4], 'pres': [6, -2, -2, -2, -2, -5, -5, 2367, 69, 2896, 178, 2897]}, 'GLZN': {'d': 2, 'p': 75, 'gens': [10968776, 19663201, 20671924, 423001, 10267524, 427099]}, 'Perm': {'d': 31, 'gens': [18905202616396433400453430736767, 288, 127, 126, 292695328787833755215361221927040, 567454601015787278329725848682240]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times D_{50}', 'transitive_degree': 200, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 600, 'aut_gen_orders': [50, 20, 4, 12], 'aut_gens': [[1, 2, 4, 16], [1, 803, 692, 176], [802, 1, 1270, 1555], [1, 3, 645, 114], [803, 801, 694, 785]], 'aut_group': None, 'aut_hash': 5575644851816430853, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536000, 'aut_permdeg': 400, 'aut_perms': [59219161333612990714158250285887022590574557731762091550920459574341613449770820203205909741522567345408074384654532957560981211210479012602764285060959552671535230692825884372916865091919590702969834278584883129555066180136127192767624884141139289720946112596252018454919967776862933064020341527059402530445126504259504971676233932103823007679129254422889678652301595999395718870999512143273912420003782145062238542340437858592109152019837185847516872641665720151716557923892073205280110594295482721552921336846430905059978156055353710270394273652866223640774587948434164517259822288495034071793020985877973855794344207107210848612990767630495359931495245443376384657101668235925391737031512606240970467449702143230609828148944214940768113294913139467910413514096354725489123430159291445678430151411278710382447773841527249120326483071333059856997275055495439573686750, 35399855600060670825008596306751981481038981056041102313128781054242932941565878011210211031687041012226948983621664278358001891224787011890062252590890520502725808075821544556690314977480084889236624610704881562705160936884648696198212876896031227306329144068597788914283168705319044061082933071576631440558850151842326027916096564078843678398720386027184271311630528076108856818640612800531172347928333985745398613489224935694938222216748598131334384468714118308006874858542227158740625273192012242564078437744048365234269606084777708656570367375506965103210250423974145215964955472165248953856969819547794927906152289225692871482007590785165052947257552720305571150300868865808083025939818607876151539228376664154813698946289042873873446243650658740826845655867360432136609412219227289258055277016296378751545007811983541636929856380050582132359202553058296170774671, 174837667031038431651932014816735952355262866803290869924308470199070995682148468578711226643910815198814160383412657349552211717460854030479535704112190625157153449693115097406505673881299341313489111997088219770434008972219873906441868184479460760015520205231242709714987693717639410750383629350208186794661156820911332591961714991818528778106077000067608630227346626852860101671476141431146597925448364125225951524578467748333259414874693747515856221031395101188755591664316683036389420511300760850049098827857243781725494366065327614631985343822356670782010980309236157098558792625530155094420360984281781766966619438827225281531909567065810232870885300086235126820251397766823475451644744214594112333204962433170914267613738818325516114658381757881087578012496456065152377535290578143499377614297826080584733299153697037878468854409144760166521319558711193889, 29014972513896897373772438574650137020753372741523834815147807052281712898064609603515545584402120394508213874127769323910755795898742130467850470678499596221505989058241280704278824627193257381256865309342601340059873272849914236122182451072428957561524341597693546766299561132294535836325581557412288656128838466569466493017025501774498435252196136501230043578838673903090665335791844949777293848742091795345429633850286988906886766329168267208442892117864500838968568404322968028235461528543509470215280642036151916480950503161268979320134344459424910915087541657802112127320376520907668242121559916936561534545873387037566287587618189470939122952367955798326746780224342417556830793047241799877127931335011027343211261995406966604280415125964646526699165784314825778794174706583617090513236258666714859835883278703307658022883571877208925371561603723356839937317914], 'aut_phi_ratio': 2400.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 25, 1, 2], [2, 25, 6, 1], [4, 2, 4, 1], [4, 50, 4, 1], [4, 50, 8, 2], [5, 4, 1, 1], [10, 4, 1, 1], [10, 4, 6, 1], [20, 4, 8, 1], [25, 4, 5, 1], [50, 4, 5, 1], [50, 4, 30, 1], [100, 4, 40, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.C_{75}.C_{10}.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '1536.408640869', 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 100, 'autcentquo_group': '1000.97', 'autcentquo_hash': 97, 'autcentquo_nilpotent': False, 'autcentquo_order': 1000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{50}:C_{20}', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 25, 8], [4, 2, 4], [4, 50, 20], [5, 4, 1], [10, 4, 7], [20, 4, 8], [25, 4, 5], [50, 4, 35], [100, 4, 40]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '200.12', 'commutator_count': 1, 'commutator_label': '50.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2017, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['400.31', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 25, 1, 8], [4, 2, 1, 4], [4, 50, 1, 4], [4, 50, 2, 8], [5, 4, 1, 1], [10, 4, 1, 7], [20, 4, 2, 4], [25, 4, 5, 1], [50, 4, 5, 7], [100, 4, 10, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1302000, 'exponent': 100, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '10.2', 'frattini_quotient': '160.236', 'hash': 2017, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 100, 'inner_gen_orders': [1, 1, 4, 50], 'inner_gens': [[1, 2, 4, 16], [1, 2, 4, 16], [1, 2, 4, 688], [1, 2, 932, 16]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'C_{50}:C_4', 'inner_used': [3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 96]], 'label': '1600.2017', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D50.C2^4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 136, 'number_divisions': 56, 'number_normal_subgroups': 223, 'number_subgroup_autclasses': 117, 'number_subgroup_classes': 627, 'number_subgroups': 6963, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 207], [4, 1008], [5, 4], [10, 28], [20, 32], [25, 20], [50, 140], [100, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 60, 'outer_gen_orders': [30, 20, 10], 'outer_gen_pows': [400, 0, 400], 'outer_gens': [[802, 3, 404, 337], [802, 1, 406, 272], [801, 2, 807, 144]], 'outer_group': None, 'outer_hash': 4476515232621970857, 'outer_nilpotent': False, 'outer_order': 7680, 'outer_permdeg': 21, 'outer_perms': [7555512435352738223, 33500002924723606, 6423298056375895], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5.(C_{10}\\times S_4)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 8], [8, 4], [20, 8], [40, 4]], 'representations': {'PC': {'code': 1193130324844057535839625264195785334592748301582351, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -5, -5, 66, 6900, 3948, 116, 16533, 9437, 141, 16150, 10782, 334, 15383, 10271]}, 'GLZN': {'d': 2, 'p': 100, 'gens': [1000049, 1000043, 1002501, 1002001, 49000049, 99000099, 1005001, 1000401]}, 'Perm': {'d': 33, 'gens': [17791240785870100264277990882590200, 5167, 5176, 11640, 26313186315544576572877665023865600, 5160, 297145204793936267465944484402457600, 568775331443610282121076663164627200]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{50}.C_2^4', 'transitive_degree': 400, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
