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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '104162436.b', 'ambient_counter': 2, 'ambient_order': 104162436, 'ambient_tex': 'C_3^{12}.C_7.C_{28}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 104162436, 'counter': 1, 'cyclic': False, 'direct': None, 'hall': 42, 'label': '104162436.b.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.A', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '104162436.b', 'subgroup_hash': None, 'subgroup_order': 104162436, 'subgroup_tex': 'C_3^{12}.C_7.C_{28}', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '104162436.b', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [822952015705376902030639776142761405470019161226243, 1165816806485624483874613616085614637908415459955172], 'label': '104162436.b.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '28.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[822952015705376902030639776142761405470019161226243, 1165816806485624483874613616085614637908415459955172], [1268681190961741496776700476829085168705691043706211, 515152271857048944529334829620623710200829436769251], [889857605707446693317548218931709081331589792926243, 1198453417825578053498639677804317229842773052061316], [822951506435884672142974530481413258247996152487684, 1165816269699254197383148454843708501212213783023956], [857220457601789133143366578333941713023478359280643, 308605438572977804023887956548206748651824904707866], [889856559682878310956094880563651928295139941031824, 1198453927074404513706059431904071546048270778419171], [889857605718075328982435792723077915380099351152643, 1165817315754527045761256195854300514641284264457555], [822952552481119079101207707096282839461407355649424, 1165817315733860478474807930343263143371402962927959], [889857068921076135490091024828251761519966774558000, 1131547827802842221195494486101017806739878379523811], [889857605718075600336110574011608647489094435998147, 1198453417825578053507785909288290887696224659997316], [889857605707446693317548637786081729864108126814004, 1131547827812880407725663652855166862748497261171076], [822952552491747459858097389048885029079657112734000, 1165816806495662399041960544654684753576005745164535], [822952015694748521273750900721370257812959187585523, 1165816269699254197400832397633859075392687177650932], [822952015705376902030639776142756539666177164574000, 1131548364589212779032097942762572904544975186589412], [822952552491747459858096582465965087125387117889280, 1165816806495662399041960156874433670636201734643079], [822952015694748521273750900721375123616894589514483, 1165816269699254197400832397633863941196796979788676], [889857605728112989241783247361663312303098847902003, 1198453927084442683790551321349520513308798208495956], [822952552481119605345198857054053140673116996929427, 1131548364578584143349527651618355818745496788915175], [684109017619698584371413241025493592745933086873555, 1338096795201688709639552103314516489585004410354638], [411485428966325075615205022573035157480611461936880, 547803895763600776829334389052287069305038643097765]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 64997360064, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 531441, 1, 1], [3, 28, 52, 1], [3, 196, 52, 2], [3, 196, 104, 1], [3, 196, 312, 4], [3, 196, 624, 2], [4, 3720087, 2, 1], [7, 1458, 6, 1], [7, 531441, 6, 1], [7, 1062882, 3, 1], [7, 1062882, 6, 2], [14, 531441, 6, 1], [14, 1062882, 3, 1], [14, 1062882, 6, 3], [21, 20412, 312, 1], [28, 3720087, 12, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 531441, 1], [3, 28, 52], [3, 196, 2704], [4, 3720087, 2], [7, 1458, 6], [7, 531441, 6], [7, 1062882, 15], [14, 531441, 6], [14, 1062882, 21], [21, 20412, 312], [28, 3720087, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '104162436.b', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '7.1', '7.1'], 'composition_length': 16, 'conjugacy_classes_known': False, 'counter': 2, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 531441, 1, 1], [3, 28, 1, 52], [3, 196, 1, 2704], [4, 3720087, 2, 1], [7, 1458, 6, 1], [7, 531441, 6, 1], [7, 1062882, 3, 1], [7, 1062882, 6, 2], [14, 531441, 6, 1], [14, 1062882, 3, 1], [14, 1062882, 6, 3], [21, 20412, 6, 52], [28, 3720087, 12, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 84, 'exponents_of_order': [12, 2, 2], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '104162436.b', 'hash': 2735071318593301672, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 104162436, 'inner_split': None, 'inner_tex': 'C_3^{12}.C_7.C_{28}', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '104162436.b', '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': None, 'name': 'C3^12.C7.C28', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 3138, 'number_divisions': 2822, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 104162436, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 531441], [3, 531440], [4, 7440174], [7, 19140624], [14, 25509168], [21, 6368544], [28, 44641044]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 624, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [4, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '12311449535735501289331200348364179941201925740833278691240840175758205941984951478377302185929701473051614746478088932128238659442169257744068554422081019493695237476576393313736194392213900819510431609012760835136972171343069591628837444824775686319067065026561586038178461792719053420902257538181298674735631400307435362978031778547348652471251472114131389887382672443659815794680240466013714591574965284244274814500035721250039169903127004403841374617479909695910971781939', 'gens': [1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'pres': [16, -2, -2, -7, -7, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 32, 81, 5930839043, 1705997459, 72391907, 4348675524, 4037701940, 61877236, 153922212, 148307717, 3971060373, 352837, 76661, 1652151430, 1185430, 510422, 9363366, 1560799751, 5266824215, 752679, 10808503, 12773081672, 4214421816, 85624600, 306243560, 4229711369, 5421799065, 102907881, 396678297, 2113086986, 6315613946, 8210090, 544635226, 13462245899, 5569178523, 4559032171, 96743867, 17147224652, 1715191324, 696725164, 109383516, 3097558925, 9747719773, 4450910733, 703371933, 15975771854, 8481312030, 1007055886, 344247182, 4023011343, 11174170143, 5628379951, 66200127]}, 'Perm': {'d': 42, 'gens': [822952015705376902030639776142761405470019161226243, 1165816806485624483874613616085614637908415459955172]}}, 'schur_multiplier': [3, 3, 3], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [28], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 108, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^{12}.C_7.C_{28}', 'transitive_degree': 42, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '28.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[822952015705376902030639776142761405470019161226243, 1165816806485624483874613616085614637908415459955172], [1268681190961741496776700476829085168705691043706211, 515152271857048944529334829620623710200829436769251], [889857605707446693317548218931709081331589792926243, 1198453417825578053498639677804317229842773052061316], [822951506435884672142974530481413258247996152487684, 1165816269699254197383148454843708501212213783023956], [857220457601789133143366578333941713023478359280643, 308605438572977804023887956548206748651824904707866], [889856559682878310956094880563651928295139941031824, 1198453927074404513706059431904071546048270778419171], [889857605718075328982435792723077915380099351152643, 1165817315754527045761256195854300514641284264457555], [822952552481119079101207707096282839461407355649424, 1165817315733860478474807930343263143371402962927959], [889857068921076135490091024828251761519966774558000, 1131547827802842221195494486101017806739878379523811], [889857605718075600336110574011608647489094435998147, 1198453417825578053507785909288290887696224659997316], [889857605707446693317548637786081729864108126814004, 1131547827812880407725663652855166862748497261171076], [822952552491747459858097389048885029079657112734000, 1165816806495662399041960544654684753576005745164535], [822952015694748521273750900721370257812959187585523, 1165816269699254197400832397633859075392687177650932], [822952015705376902030639776142756539666177164574000, 1131548364589212779032097942762572904544975186589412], [822952552491747459858096582465965087125387117889280, 1165816806495662399041960156874433670636201734643079], [822952015694748521273750900721375123616894589514483, 1165816269699254197400832397633863941196796979788676], [889857605728112989241783247361663312303098847902003, 1198453927084442683790551321349520513308798208495956], [822952552481119605345198857054053140673116996929427, 1131548364578584143349527651618355818745496788915175], [684109017619698584371413241025493592745933086873555, 1338096795201688709639552103314516489585004410354638], [411485428966325075615205022573035157480611461936880, 547803895763600776829334389052287069305038643097765]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 64997360064, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 531441, 1, 1], [3, 28, 52, 1], [3, 196, 52, 2], [3, 196, 104, 1], [3, 196, 312, 4], [3, 196, 624, 2], [4, 3720087, 2, 1], [7, 1458, 6, 1], [7, 531441, 6, 1], [7, 1062882, 3, 1], [7, 1062882, 6, 2], [14, 531441, 6, 1], [14, 1062882, 3, 1], [14, 1062882, 6, 3], [21, 20412, 312, 1], [28, 3720087, 12, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 531441, 1], [3, 28, 52], [3, 196, 2704], [4, 3720087, 2], [7, 1458, 6], [7, 531441, 6], [7, 1062882, 15], [14, 531441, 6], [14, 1062882, 21], [21, 20412, 312], [28, 3720087, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '104162436.b', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '7.1', '7.1'], 'composition_length': 16, 'conjugacy_classes_known': False, 'counter': 2, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 531441, 1, 1], [3, 28, 1, 52], [3, 196, 1, 2704], [4, 3720087, 2, 1], [7, 1458, 6, 1], [7, 531441, 6, 1], [7, 1062882, 3, 1], [7, 1062882, 6, 2], [14, 531441, 6, 1], [14, 1062882, 3, 1], [14, 1062882, 6, 3], [21, 20412, 6, 52], [28, 3720087, 12, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 84, 'exponents_of_order': [12, 2, 2], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '104162436.b', 'hash': 2735071318593301672, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 104162436, 'inner_split': None, 'inner_tex': 'C_3^{12}.C_7.C_{28}', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '104162436.b', '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': None, 'name': 'C3^12.C7.C28', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 3138, 'number_divisions': 2822, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 104162436, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 531441], [3, 531440], [4, 7440174], [7, 19140624], [14, 25509168], [21, 6368544], [28, 44641044]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 624, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [4, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '12311449535735501289331200348364179941201925740833278691240840175758205941984951478377302185929701473051614746478088932128238659442169257744068554422081019493695237476576393313736194392213900819510431609012760835136972171343069591628837444824775686319067065026561586038178461792719053420902257538181298674735631400307435362978031778547348652471251472114131389887382672443659815794680240466013714591574965284244274814500035721250039169903127004403841374617479909695910971781939', 'gens': [1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], 'pres': [16, -2, -2, -7, -7, -3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 32, 81, 5930839043, 1705997459, 72391907, 4348675524, 4037701940, 61877236, 153922212, 148307717, 3971060373, 352837, 76661, 1652151430, 1185430, 510422, 9363366, 1560799751, 5266824215, 752679, 10808503, 12773081672, 4214421816, 85624600, 306243560, 4229711369, 5421799065, 102907881, 396678297, 2113086986, 6315613946, 8210090, 544635226, 13462245899, 5569178523, 4559032171, 96743867, 17147224652, 1715191324, 696725164, 109383516, 3097558925, 9747719773, 4450910733, 703371933, 15975771854, 8481312030, 1007055886, 344247182, 4023011343, 11174170143, 5628379951, 66200127]}, 'Perm': {'d': 42, 'gens': [822952015705376902030639776142761405470019161226243, 1165816806485624483874613616085614637908415459955172]}}, 'schur_multiplier': [3, 3, 3], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [28], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 108, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^{12}.C_7.C_{28}', 'transitive_degree': 42, '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': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
