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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.2865', 'ambient_counter': 2865, 'ambient_order': 1344, 'ambient_tex': 'D_{84}.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1344, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '1344.2865.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, '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': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1344.2865', 'subgroup_hash': 2865, 'subgroup_order': 1344, 'subgroup_tex': 'D_{84}.D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.2865', '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': '672.a1.a1', 'complements': ['1344.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '7.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 336, 448, 168, 672, 192, 2, 4], 'label': '1344.2865.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', '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': 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': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 14, 42, 6, 12, 6, 12, 84], 'aut_gens': [[1, 2, 4, 8], [117, 1314, 4, 636], [673, 962, 4, 904], [1121, 354, 4, 8], [789, 834, 676, 1160], [789, 162, 4, 1212], [1013, 722, 4, 536], [677, 866, 676, 40], [901, 34, 676, 680]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 88, 'aut_perms': [4497663518367917035967062121527631786655868644586868170191506275561441713848711379023047460383762183657801713283582954183882797843, 19164484487662132746080499596134089368258438396502042434110621175188986055484617503045935183483168393304955335783592562521975876420130, 175265366735937971157797783139781127083323764043191738073170086995793293322479097136982915909655732628878546708134981128206226588915762, 134338457940878511072805539853013923087176053005956598710927633164729868509776265283792943238657214959672189958136188433524435135803757, 10659127102585799554812634293950737840532663789396979436237264085748177536327311490544469970465879738466729146041583185790385171650548, 126171815513268709493217145150297753191037228180993940096201829816618166326508410650587758271036035256963477020935124994172297094717654, 108750872539973774810077007056633931798667432258120930536294448619251221232458775986164126762278617808302744170955664486647424294521096, 95916918492181524660907997910718099659744671461188262600636421191006634696987129829331897068181116731038717675605265158237693834095940], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 6896085666905541017, 'autcentquo_nilpotent': False, 'autcentquo_order': 4032, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 24, 1], [4, 56, 1], [4, 84, 1], [6, 2, 1], [6, 4, 1], [7, 2, 3], [8, 4, 2], [8, 24, 1], [8, 42, 2], [8, 56, 1], [8, 84, 1], [12, 4, 2], [12, 56, 2], [14, 2, 3], [14, 4, 3], [21, 4, 3], [24, 8, 2], [24, 56, 2], [28, 4, 6], [28, 24, 6], [42, 4, 3], [42, 8, 3], [56, 8, 6], [56, 24, 6], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.605', 'commutator_count': 2, 'commutator_label': '168.39', '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': 2865, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2865, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 2, 84], 'inner_gens': [[1, 338, 4, 236], [1009, 2, 4, 328], [1, 2, 4, 680], [453, 1026, 676, 8]], 'inner_hash': 605, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 38], [4, 34], [8, 10]], 'label': '1344.2865', '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': 'D84.D4', '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': 36, 'number_characteristic_subgroups': 52, 'number_conjugacy_classes': 90, 'number_divisions': 36, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 200, 'number_subgroup_classes': 200, 'number_subgroups': 1684, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 168], [6, 6], [7, 6], [8, 256], [12, 120], [14, 18], [21, 12], [24, 128], [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, 6], 'outer_gen_pows': [0, 0, 1008, 0], 'outer_gens': [[1, 2, 4, 904], [1, 674, 4, 8], [337, 2, 4, 904], [1, 338, 676, 536]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [744, 3628800, 24, 40323], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 3], [6, 4], [8, 3], [12, 4], [24, 5], [48, 1]], 'representations': {'PC': {'code': 202797249805044787670014709171568860180977740773134860985790476770059, 'gens': [1, 2, 3, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 5376, 5409, 8073, 7555, 5259, 5459, 91, 45444, 13132, 116, 44549, 31501, 141, 28678, 35854, 222, 36879]}, 'Perm': {'d': 42, 'gens': [816438677858700483452020063364007257365088185692, 8701128753596821002912997869098109044, 26340670275379773640968878294828373, 3974861169727848189186688964589, 34840860416302983971454251705973597, 43337613556404296642408707668437709, 303916116658416027343136804044800000000, 35085403596887862568986022075080631753113600000000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [12, 14, 42, 6, 12, 6, 12, 84], 'aut_gens': [[1, 2, 4, 8], [117, 1314, 4, 636], [673, 962, 4, 904], [1121, 354, 4, 8], [789, 834, 676, 1160], [789, 162, 4, 1212], [1013, 722, 4, 536], [677, 866, 676, 40], [901, 34, 676, 680]], 'aut_group': None, 'aut_hash': 9161810123478319507, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32256, 'aut_permdeg': 88, 'aut_perms': [4497663518367917035967062121527631786655868644586868170191506275561441713848711379023047460383762183657801713283582954183882797843, 19164484487662132746080499596134089368258438396502042434110621175188986055484617503045935183483168393304955335783592562521975876420130, 175265366735937971157797783139781127083323764043191738073170086995793293322479097136982915909655732628878546708134981128206226588915762, 134338457940878511072805539853013923087176053005956598710927633164729868509776265283792943238657214959672189958136188433524435135803757, 10659127102585799554812634293950737840532663789396979436237264085748177536327311490544469970465879738466729146041583185790385171650548, 126171815513268709493217145150297753191037228180993940096201829816618166326508410650587758271036035256963477020935124994172297094717654, 108750872539973774810077007056633931798667432258120930536294448619251221232458775986164126762278617808302744170955664486647424294521096, 95916918492181524660907997910718099659744671461188262600636421191006634696987129829331897068181116731038717675605265158237693834095940], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^2', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': None, 'autcentquo_hash': 6896085666905541017, 'autcentquo_nilpotent': False, 'autcentquo_order': 4032, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 84, 1], [3, 2, 1], [4, 2, 2], [4, 24, 1], [4, 56, 1], [4, 84, 1], [6, 2, 1], [6, 4, 1], [7, 2, 3], [8, 4, 2], [8, 24, 1], [8, 42, 2], [8, 56, 1], [8, 84, 1], [12, 4, 2], [12, 56, 2], [14, 2, 3], [14, 4, 3], [21, 4, 3], [24, 8, 2], [24, 56, 2], [28, 4, 6], [28, 24, 6], [42, 4, 3], [42, 8, 3], [56, 8, 6], [56, 24, 6], [84, 4, 6], [84, 8, 3], [168, 8, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '672.605', 'commutator_count': 2, 'commutator_label': '168.39', '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': 2865, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 84, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 24, 1, 1], [4, 56, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 1], [7, 2, 3, 1], [8, 4, 2, 1], [8, 24, 1, 1], [8, 42, 2, 1], [8, 56, 1, 1], [8, 84, 1, 1], [12, 4, 1, 2], [12, 56, 2, 1], [14, 2, 3, 1], [14, 4, 3, 1], [21, 4, 3, 1], [24, 8, 2, 1], [24, 56, 2, 1], [28, 4, 3, 2], [28, 24, 6, 1], [42, 4, 3, 1], [42, 8, 3, 1], [56, 8, 6, 1], [56, 24, 6, 1], [84, 4, 6, 1], [84, 8, 3, 1], [168, 8, 12, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21504, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 6]], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '168.50', 'hash': 2865, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 2, 84], 'inner_gens': [[1, 338, 4, 236], [1009, 2, 4, 328], [1, 2, 4, 680], [453, 1026, 676, 8]], 'inner_hash': 605, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 38], [4, 34], [8, 10]], 'label': '1344.2865', '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': 'D84.D4', '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': 36, 'number_characteristic_subgroups': 52, 'number_conjugacy_classes': 90, 'number_divisions': 36, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 200, 'number_subgroup_classes': 200, 'number_subgroups': 1684, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 87], [3, 2], [4, 168], [6, 6], [7, 6], [8, 256], [12, 120], [14, 18], [21, 12], [24, 128], [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, 6], 'outer_gen_pows': [0, 0, 1008, 0], 'outer_gens': [[1, 2, 4, 904], [1, 674, 4, 8], [337, 2, 4, 904], [1, 338, 676, 536]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [744, 3628800, 24, 40323], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 3], [6, 4], [8, 3], [12, 4], [24, 5], [48, 1]], 'representations': {'PC': {'code': 202797249805044787670014709171568860180977740773134860985790476770059, 'gens': [1, 2, 3, 4], 'pres': [8, -2, -2, -2, 2, -2, -2, -3, -7, 5376, 5409, 8073, 7555, 5259, 5459, 91, 45444, 13132, 116, 44549, 31501, 141, 28678, 35854, 222, 36879]}, 'Perm': {'d': 42, 'gens': [816438677858700483452020063364007257365088185692, 8701128753596821002912997869098109044, 26340670275379773640968878294828373, 3974861169727848189186688964589, 34840860416302983971454251705973597, 43337613556404296642408707668437709, 303916116658416027343136804044800000000, 35085403596887862568986022075080631753113600000000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{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': 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}
