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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2716', 'ambient_counter': 2716, 'ambient_order': 1344, 'ambient_tex': 'C_6.(C_4\\times D_{28})', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 672, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.2716.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '672.237', 'subgroup_hash': 237, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}.D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.2716', 'aut_centralizer_order': 4, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '336.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.e1.a1', '4.f1.a1', '6.g1.a1', '14.g1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2955, 4566, 6539, 5294, 3492, 4556, 5734, 4005], 'generators': [3, 448, 676, 336, 168, 192, 672], 'label': '1344.2716.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.e1.a1', '4.d1.a1', '4.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '336.149', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '336.149'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 2, 6, 6, 12, 6, 6, 4], 'aut_gens': [[1, 4], [523, 92], [467, 668], [1, 246], [217, 94], [25, 102], [657, 78], [369, 388], [345, 500]], 'aut_group': None, 'aut_hash': 7058334312241270196, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16128, 'aut_permdeg': 176, 'aut_perms': [177083510572611258835206050846320311757012659953675436345709511806564662019920123683101262395321494956991184569844843709900215647594985763540695451139209166292361947224125724766242544734175030481056763129527501542956085735643193050447979063750235120234580619806174263564682367389158434901861608132656393165743671038106556, 132305021106622611702104612283007617373210924423162268700870317289830321324981620378402073031106671333209626967984529017175840692306555418772695870094407319987866607596864561921764932573544251088856748205284374518733075037265345338237742719686620439991304461790051492445735674239275951954290748919264218304535339574971465, 616898215976830267811505566657263924776590163886110956846501461544863286329078018105647576371514801776794113823858577134988363342853743397990313880619619958200168468498111791151369270593271002766884036485326107194176766458799550332116632059631218011434722950763205278183124653563515063732142663651845416149103184304151, 190503560668570169983136202498996306613472201388826077860091111085264890889478230392153155438515132736172197704201382622609862715167272523208073662069223416998947741155428598880983079066527351320922965268766940712421239561959303060037603558725380091662984483333808986415907717586349543410109312568244971883122175753124886, 135937731964261742106055616018389674639983556602404336451209466505506343267238659581662942706538640722793410307915906944504356223715767221430417001215495087216034354294897373178114105383531181538325724179591443432981295085616646416415792111849119401310963846232636970334378406757564115625777946497941804223272255043499074, 179749259448686297851947030201325053194405561087388588031963972524463630338676820059513347882511864362869931982086484698093761948756877783119310588930668235868284450100884910903139911736611528526867844368114900393195656943209897825925946267037938835848739094983464901619727140520812265600053521655867273417075344095376254, 97358809901767212903994432553305067817166441916971390703585856007991702331084660016589935435446767187566203605356122027322750622355847282618827173687001156803933447779200961396861749979257825252204543546192766990227478876898649578485684233755285024601689055286882789458966691131938340916544308884116230081068722206587705, 54342541488314132328316002260761822408701913301180111171673247233247812146495187564000653684924054270198575271983116525722975706528852288556817934379907383192619898575911992138480885670237070102589638794349052746349462027446981116195421173233849622326984872235815254220370193591274617395616518439015084549916831203406100], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 84, 2, 2], [6, 2, 1, 3], [7, 2, 3, 1], [8, 2, 4, 1], [12, 2, 2, 2], [14, 2, 3, 3], [21, 2, 6, 1], [24, 2, 8, 1], [28, 2, 6, 2], [42, 2, 6, 3], [56, 2, 24, 1], [84, 2, 12, 2], [168, 2, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1008.906', 'autcentquo_hash': 906, 'autcentquo_nilpotent': False, 'autcentquo_order': 1008, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 84, 4], [6, 2, 3], [7, 2, 3], [8, 2, 4], [12, 2, 4], [14, 2, 9], [21, 2, 6], [24, 2, 8], [28, 2, 12], [42, 2, 18], [56, 2, 24], [84, 2, 24], [168, 2, 48]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '168.36', 'commutator_count': 1, 'commutator_label': '84.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 237, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 84, 1, 2], [4, 84, 2, 1], [6, 2, 1, 3], [7, 2, 3, 1], [8, 2, 4, 1], [12, 2, 2, 2], [14, 2, 3, 3], [21, 2, 6, 1], [24, 2, 8, 1], [28, 2, 6, 2], [42, 2, 6, 3], [56, 2, 24, 1], [84, 2, 12, 2], [168, 2, 48, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 168, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '84.14', 'hash': 237, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 84], 'inner_gens': [[1, 334], [347, 4]], 'inner_hash': 36, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'D_{84}', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 166]], 'label': '672.237', 'linC_count': 192, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 32, 'linQ_dim': 14, 'linQ_dim_count': 16, 'linR_count': 108, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84.D4', 'ngens': 7, '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, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 30, 'number_characteristic_subgroups': 39, 'number_conjugacy_classes': 174, 'number_divisions': 31, 'number_normal_subgroups': 41, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 84, 'number_subgroups': 652, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 340], [6, 6], [7, 6], [8, 8], [12, 8], [14, 18], [21, 12], [24, 16], [28, 24], [42, 36], [56, 48], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 452], [1, 340], [3, 4], [1, 454], [1, 292]], 'outer_group': '96.231', 'outer_hash': 231, 'outer_nilpotent': True, 'outer_order': 96, 'outer_permdeg': 13, 'outer_perms': [41064, 479001600, 3628800, 744, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 5], [6, 2], [8, 2], [12, 5], [24, 5], [48, 2]], 'representations': {'PC': {'code': 5270393052861772116983572999072378376075, 'gens': [1, 2, 3], 'pres': [7, -2, -2, 2, -2, -2, -3, -7, 14, 7016, 58, 18595, 80, 22964, 102, 26885, 166, 28230]}, 'GLZN': {'d': 2, 'p': 78, 'gens': [11863825, 25151309, 795029, 714910, 17631961, 23443553, 27209681]}, 'Perm': {'d': 22, 'gens': [2439325310911696809, 44357889, 91578240, 16, 135732240, 93405312000, 55969571858264064000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{84}.D_4', 'transitive_degree': 672, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 6, 6, 6, 6, 6, 6, 12, 28, 6], 'aut_gens': [[1, 2, 8], [629, 1014, 828], [1205, 230, 1048], [581, 6, 1144], [917, 114, 1208], [385, 1014, 1308], [1, 338, 524], [917, 1234, 108], [145, 790, 1096], [241, 674, 572], [1057, 902, 1196]], 'aut_group': None, 'aut_hash': 5255589997166976132, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 76, 'aut_perms': [1371925242141516793580746341247666218601114641544876713515065913252134099616094560176708300149092481648803540343, 1250827666161109583713345474658474920781807033404276890642731396547534786834830730088743506928820191214880729565, 979984247360773397490926949572660171156257820950419976840585445570919572797730928010522783618933195735692089792, 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2, 1], [12, 4, 1, 2], [12, 56, 2, 2], [14, 2, 3, 3], [21, 4, 3, 1], [24, 4, 4, 1], [28, 2, 6, 2], [28, 12, 6, 2], [42, 4, 3, 3], [56, 4, 12, 1], [56, 12, 12, 1], [84, 4, 6, 2], [168, 4, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1008.906', 'autcentquo_hash': 906, 'autcentquo_nilpotent': False, 'autcentquo_order': 1008, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 6, 4], [4, 28, 4], [4, 84, 4], [6, 2, 3], [7, 2, 3], [8, 4, 2], [8, 12, 2], [12, 4, 2], [12, 56, 4], [14, 2, 9], [21, 4, 3], [24, 4, 4], [28, 2, 12], [28, 12, 12], [42, 4, 9], [56, 4, 12], [56, 12, 12], [84, 4, 12], [168, 4, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '336.149', 'commutator_count': 1, 'commutator_label': '84.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2716, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 6, 2, 2], [4, 28, 1, 2], [4, 28, 2, 1], [4, 84, 1, 2], [4, 84, 2, 1], [6, 2, 1, 3], [7, 2, 3, 1], [8, 4, 2, 1], [8, 12, 1, 2], [12, 4, 1, 2], [12, 56, 1, 2], [12, 56, 2, 1], [14, 2, 3, 3], [21, 4, 3, 1], [24, 4, 4, 1], [28, 2, 6, 2], [28, 12, 6, 2], [42, 4, 3, 3], [56, 4, 12, 1], [56, 12, 6, 2], [84, 4, 6, 2], [168, 4, 24, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10752, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2716, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 84], 'inner_gens': [[1, 678, 780], [5, 2, 232], [1253, 1122, 8]], 'inner_hash': 149, 'inner_nilpotent': False, 'inner_order': 336, 'inner_split': None, 'inner_tex': 'S_3\\times D_{28}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 60], [4, 68]], 'label': '1344.2716', 'linC_count': 192, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 152, 'linQ_dim': 16, 'linQ_dim_count': 16, 'linR_count': 72, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.(C4*D28)', '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, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 144, 'number_divisions': 45, 'number_normal_subgroups': 74, 'number_subgroup_autclasses': 184, 'number_subgroup_classes': 216, 'number_subgroups': 1588, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 476], [6, 6], [7, 6], [8, 32], [12, 232], [14, 18], [21, 12], [24, 16], [28, 168], [42, 36], [56, 192], [84, 48], [168, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 912, 0, 512, 1152, 0], 'outer_gens': [[1205, 1014, 444], [241, 674, 572], [389, 6, 1336], [1301, 562, 1016], [1153, 1014, 348], [1, 338, 524]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 192, 'outer_perms': [170442631972567820409474121584110168361480324103518494115779734776646134295950167065124572080972484180306961106520738641787277862018663995645181393144037252596629213711176385520636101522901178919606954863299864362048884453238303062997950082682952889598290466549788795298395308927680583895317370329642177669650057855688002819521221002244635331109196414245900, 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11279115237680986864334149239244643242595541564496334927963150102778168667679424873159160903575299285309258988603281124640573035369132872628658065164443711538477763786423704514037196171111480496565674721892621175127956248872977533278677558853910566526654349592083604594775313006162956385542754883580662035882419247224112092522587377720457579762922599820989], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 7], [6, 4], [8, 2], [12, 6], [24, 6], [48, 2]], 'representations': {'PC': {'code': 79238447993863849739566662197694298823625540237545469567371374584291083, 'gens': [1, 2, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 5376, 10849, 41, 16226, 4050, 24963, 3723, 91, 35204, 9292, 116, 19973, 22285, 141, 46598, 14350, 222, 73735]}, 'Perm': {'d': 30, 'gens': [305292256521398230336080117967, 51373800639369815040, 409805665629298577, 539080928542276567, 669445860923048280, 798023019859233840, 1175091669949317120000, 9452345886333784620057231360000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.(C_4\\times D_{28})', 'transitive_degree': 1344, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
