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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '5184.in', 'ambient_counter': 222, 'ambient_order': 5184, 'ambient_tex': 'C_6^2:(D_4\\times D_9)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 648, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '5184.in.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3', 'D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '648.319', 'subgroup_hash': 319, 'subgroup_order': 648, 'subgroup_tex': 'C_6^2:C_{18}', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5184.in', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.g1'], 'contains': ['16.a1', '24.b1', '24.c1', '24.z1', '32.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4342, 3190, 2850, 4369], 'generators': [72, 3024, 288, 4048, 2592, 1728, 12], 'label': '5184.in.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '4.f1', '4.g1'], 'normal_contains': ['16.a1', '24.b1', '24.c1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '2592.ia', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '54.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 6, 12], 'aut_gens': [[1, 18, 108], [71, 420, 108], [443, 402, 270], [581, 192, 270]], 'aut_group': None, 'aut_hash': 6039055366955278584, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11664, 'aut_permdeg': 218, 'aut_perms': [355944259434437535033199640485927477214958161314576901547434333282774476029392896312382114015844939003946800879045112789819768474547253450070887025516603300373658568208989375754052863201518119123555539435655208532797739871313223063301140602666074642151387499936152680771623547377963334474412013958503310040560417549264960876340009907545308820557553145942683301693591681840645945097480679501066092361181743612777503477, 381828450536823333880162740816504836351667167628770249270766551901622179489811214788309988010939408826219580113291130758518568079037637192075711998463214318682328562321154072032548703245817226162289883890952340203915734819577999829304536866787667813087598592506564829106874133473772036417278240879713787309456200661733228238225753259283227639555270748220961211691970351086877374611485255125459093316712307285077100278, 221586162364176748734715696728204619278160970175794982405584095492258475624112850734828731010685566203913296111568910895359352711324035252979702782265606910822961701390054695823194998520657212117611393371345681622867431602162767589002796689648428414980076215820289701434971799277236046020507705186209847536374645280671578351430660261494500206727115916002305590883373681620688387334918263930119879425196077215440604860], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 1, 2, 2], [3, 1, 4, 1], [3, 3, 6, 1], [6, 1, 2, 2], [6, 1, 4, 1], [6, 3, 2, 4], [6, 3, 4, 2], [6, 3, 6, 1], [6, 3, 18, 2], [9, 12, 18, 1], [18, 12, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_3^3.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '81.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 81, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '144.183', 'autcentquo_hash': 183, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 1, 8], [3, 3, 6], [6, 1, 8], [6, 3, 58], [9, 12, 18], [18, 12, 18]], 'center_label': '18.5', 'center_order': 18, 'central_product': True, 'central_quotient': '36.11', 'commutator_count': 1, 'commutator_label': '12.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 319, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['324.59', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 1, 2, 4], [3, 3, 2, 3], [6, 1, 2, 4], [6, 3, 2, 29], [9, 12, 6, 3], [18, 12, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 18, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '72.47', 'hash': 319, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 6, 2], 'inner_gens': [[1, 180, 162], [595, 18, 108], [55, 18, 108]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 36, 'inner_split': True, 'inner_tex': 'C_3\\times A_4', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 54], [3, 66]], 'label': '648.319', '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': 'C6^2:C18', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 22, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 120, 'number_divisions': 50, 'number_normal_subgroups': 48, 'number_subgroup_autclasses': 92, 'number_subgroup_classes': 204, 'number_subgroups': 578, 'old_label': None, 'order': 648, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7], [3, 26], [6, 182], [9, 216], [18, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 6, 3, 3, 3, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[475, 18, 108], [11, 18, 594], [469, 450, 108], [289, 18, 108], [301, 30, 108], [443, 90, 162]], 'outer_group': '324.122', 'outer_hash': 122, 'outer_nilpotent': False, 'outer_order': 324, 'outer_permdeg': 12, 'outer_perms': [120114720, 121214281, 787947, 2219904, 92388960, 121929385], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3^2:S_3^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 9], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [3, 2], [6, 38]], 'representations': {'PC': {'code': 9691722979619294564299253459266540981, 'gens': [1, 4, 6], 'pres': [7, 2, 3, 3, 2, 3, 2, 3, 14, 50, 5043, 7822, 80, 8824, 8201, 6809, 10218, 124]}, 'GLZN': {'d': 2, 'p': 108, 'gens': [1895401, 67400531, 69914071, 1259785, 1263601, 91959049, 50850475]}, 'Perm': {'d': 24, 'gens': [87178291200, 29384732018353920013623, 4549904516261744640000, 56302717658372849762356, 83178852069462589440000, 482630400, 1037836800]}}, 'schur_multiplier': [3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 18], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:C_{18}', 'transitive_degree': 54, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [18, 18, 2, 18, 12, 6], 'aut_gens': [[1, 2, 36, 144, 864], [1893, 3050, 3852, 2736, 3600], [2541, 386, 2340, 2736, 3600], [2665, 3026, 36, 144, 864], [3965, 386, 396, 3168, 1584], [1821, 4354, 3852, 2880, 3600], [2893, 370, 3852, 2736, 4320]], 'aut_group': None, 'aut_hash': 4504041920383935304, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 31104, 'aut_permdeg': 128, 'aut_perms': [303330170308120232313781706963377930645197871747109763663089891425257180770881164560467537843938733059187189947385543855115222199386701580873887464467591227696161539461161801482130116021768292335101087682814714382744, 28285842797971647684909550868260183784214976888559054518890086572587746858988749926560920039749198801294327877008250254739209148117511591188655779622737923108569690133508520215958492058166947151288267513215940497234, 155520078484510891747010682940729890855118195801505987364881854866659157963476218407002312217360988159933399764901677349056301024157186720764159612636052964716552425322455242500560706613527653772304119113457636883792, 42566351454393072868344558072591994820816637718993951685130780731776002800172880276242110180889871798074917677388142366157292161460338202017913366308168430196919509183952115710105708645956218060126936415623736862035, 165151100007505162818840014428573025031930970895931897820816086853677963563754212256361896566665125443882433098409642348095060522947046933789040136821792635792381316787973705591831801764898880550375398911661445732166, 121346190723740633211585143260507235477040310728092601469798388976953321133361604825040825028312507048815737407950829926923818539827249000015515230867303342721509280654214262610290668744366894869835429503073165373608], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 18, 1, 1], [2, 54, 1, 1], [2, 54, 2, 1], [2, 108, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 1], [3, 12, 1, 1], [4, 18, 1, 1], [4, 54, 1, 1], [4, 54, 2, 1], [4, 108, 1, 4], [6, 2, 1, 2], [6, 4, 1, 3], [6, 4, 2, 1], [6, 6, 1, 7], [6, 6, 2, 2], [6, 12, 1, 13], [6, 12, 2, 6], [6, 36, 1, 1], [6, 108, 1, 1], [6, 108, 2, 2], [6, 216, 1, 1], [9, 24, 3, 1], [9, 48, 3, 1], [12, 36, 1, 1], [12, 108, 1, 1], [12, 108, 2, 2], [12, 216, 1, 3], [18, 24, 3, 1], [18, 48, 3, 2], [18, 48, 6, 1], [18, 144, 3, 1], [36, 144, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2.C_3^3.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '3888.fl', 'autcentquo_hash': 3044566718417071494, 'autcentquo_nilpotent': False, 'autcentquo_order': 3888, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3.(C_6\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 1], [2, 18, 1], [2, 54, 3], [2, 108, 2], [3, 2, 2], [3, 4, 1], [3, 6, 1], [3, 12, 1], [4, 18, 1], [4, 54, 3], [4, 108, 4], [6, 2, 2], [6, 4, 5], [6, 6, 11], [6, 12, 25], [6, 36, 1], [6, 108, 5], [6, 216, 1], [9, 24, 3], [9, 48, 3], [12, 36, 1], [12, 108, 5], [12, 216, 3], [18, 24, 3], [18, 48, 12], [18, 144, 3], [36, 144, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2592.ia', 'commutator_count': 1, 'commutator_label': '648.319', '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', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 222, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 18, 1, 1], [2, 54, 1, 3], [2, 108, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [3, 6, 1, 1], [3, 12, 1, 1], [4, 18, 1, 1], [4, 54, 1, 3], [4, 108, 1, 4], [6, 2, 1, 2], [6, 4, 1, 5], [6, 6, 1, 7], [6, 6, 2, 2], [6, 12, 1, 11], [6, 12, 2, 7], [6, 36, 1, 1], [6, 108, 1, 3], [6, 108, 2, 1], [6, 216, 1, 1], [9, 24, 3, 1], [9, 48, 3, 1], [12, 36, 1, 1], [12, 108, 1, 3], [12, 108, 2, 1], [12, 216, 1, 3], [18, 24, 3, 1], [18, 48, 3, 2], [18, 48, 6, 1], [18, 144, 3, 1], [36, 144, 3, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1088640, 'exponent': 36, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 4], [12, 1, 2]], 'familial': False, 'frattini_label': '18.5', 'frattini_quotient': '288.1028', 'hash': 7300808916637173434, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [4, 18, 2, 6, 6], 'inner_gens': [[1, 4930, 612, 3312, 864], [3893, 2, 1836, 3168, 1584], [289, 3530, 36, 720, 4320], [2881, 3026, 324, 144, 864], [1, 146, 1764, 144, 864]], 'inner_hash': 1704815488514258940, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': True, 'inner_tex': 'C_6^3.D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 26], [3, 8], [4, 20], [6, 22], [12, 27]], 'label': '5184.in', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:(D4*D9)', 'ngens': 10, '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, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 77, 'number_characteristic_subgroups': 71, 'number_conjugacy_classes': 111, 'number_divisions': 81, 'number_normal_subgroups': 75, 'number_subgroup_autclasses': 1744, 'number_subgroup_classes': 2030, 'number_subgroups': 44747, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 411], [3, 26], [4, 612], [6, 1182], [9, 216], [12, 1224], [18, 1080], [36, 432]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[73, 2, 36, 144, 864], [2881, 2398, 36, 3312, 864]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [720, 28], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [3, 8], [4, 5], [6, 22], [8, 1], [12, 20], [24, 7]], 'representations': {'PC': {'code': '505105589992926035108148705955090840558269701721725468965602453268218146079300078050300860248117680626885', 'gens': [1, 2, 5, 7, 9], 'pres': [10, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 25920, 98601, 51, 31202, 112, 963, 30604, 45914, 50874, 144, 231846, 110896, 47906, 1446, 206, 46087, 1327, 71298, 81028, 10848, 268, 115219, 50429, 9649]}, 'Perm': {'d': 26, 'gens': [1892830145609738051147647, 16860281725069006246854606, 33638286449541815413320257]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:(D_4\\times D_9)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 84, 'aut_gen_orders': [3, 3], 'aut_gens': [[1, 2, 4], [4, 5, 3], [2, 4, 1]], 'aut_group': '168.42', 'aut_hash': 42, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 168, 'aut_permdeg': 7, 'aut_perms': [4361, 244], 'aut_phi_ratio': 42.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSL(2,7)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '168.42', 'autcent_hash': 42, 'autcent_nilpotent': False, 'autcent_order': 168, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\PSL(2,7)', '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, 7]], 'center_label': '8.5', 'center_order': 8, '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', '2.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '8.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 8]], 'label': '8.5', 'linC_count': 28, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 28, 'linQ_dim': 3, 'linQ_dim_count': 28, 'linR_count': 28, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^3', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 8, 'number_divisions': 8, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 84, 'outer_gen_orders': [3, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[4, 5, 3], [2, 4, 1]], 'outer_group': '168.42', 'outer_hash': 42, 'outer_nilpotent': False, 'outer_order': 168, 'outer_permdeg': 7, 'outer_perms': [4361, 244], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\PSL(2,7)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -2, 2, 2]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16482, 16322, 3362]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [8156, 13286, 13933]}, 'Perm': {'d': 6, 'gens': [120, 6, 1]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
