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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.2142', 'ambient_counter': 2142, 'ambient_order': 384, 'ambient_tex': 'C_4^2.D_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 384, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '384.2142.1.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': '384.2142', 'subgroup_hash': 2142, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2.D_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.2142', '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': '96.a1.a1', 'complements': ['384.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.d1.b1', '2.d1.c1', '2.d1.d1', '3.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 288, 16, 2, 4, 128, 192, 8], 'label': '384.2142.1.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.c1', '2.d1.d1', '2.d1.a1', '2.d1.b1'], '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 6, 2, 12, 2, 4, 12, 4], 'aut_gens': [[1, 2, 8, 32], [129, 10, 24, 32], [177, 10, 8, 240], [129, 290, 24, 224], [17, 210, 216, 160], [161, 218, 24, 240], [257, 102, 24, 368], [177, 222, 216, 352], [33, 98, 216, 48], [109, 306, 216, 240]], 'aut_group': None, 'aut_hash': 4671954392677295563, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 80, 'aut_perms': [24525899754836897730409544507823833659732881749057262607484550760442369477767062410674702823209217539429952859935255506, 37056614006995424700319039417648017021584774687959509624381081095549485011610073094708769221964536346723077158995628227, 24401332389637643864317227282572276899699698611699940787700107471723088226247291330578828783978473808999124138386954548, 46612021681099682021942466058667765995048336471358879642701580324813060874393367033189184503597612238491932055590600977, 63974432934387507315616883704779646731441048267768567593190756509263338102324486736386053877149695909728131379844854290, 51651661482794285263072581426814726524613008622444055898697998673781887717627385142147986997736825359003783549751639496, 37228940113123409965901251179060512515449804945871161816387265883524157504420401639674373084155295999961596066284873655, 39041016418574622614767615415513093632816803291956234899756510398843711467732099265595147737086688283016904558706308487, 10648501163546730821473903039860921709367079084626997500802977923163554362096091651172857204979584840274227389410655671], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 4], [4, 8, 4, 1], [4, 24, 2, 2], [6, 2, 1, 3], [6, 2, 4, 1], [8, 24, 4, 1], [12, 4, 2, 6], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^4.C_2^6.C_2^2)', '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': 6, 'autcentquo_group': '192.1542', 'autcentquo_hash': 1542, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 8, 4], [4, 24, 4], [6, 2, 7], [8, 24, 4], [12, 4, 12], [12, 8, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.134', 'commutator_count': 1, 'commutator_label': '24.9', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2142, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 4], [4, 8, 2, 2], [4, 24, 1, 4], [6, 2, 1, 3], [6, 2, 2, 2], [8, 24, 2, 2], [12, 4, 2, 6], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2142, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 2, 6], 'inner_gens': [[1, 114, 8, 352], [305, 2, 200, 240], [1, 194, 8, 32], [65, 210, 8, 32]], 'inner_hash': 134, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'C_2^2.D_{12}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 18]], 'label': '384.2142', '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': 'C4^2.D12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 47, 'number_conjugacy_classes': 54, 'number_divisions': 34, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 150, 'number_subgroup_classes': 208, 'number_subgroups': 638, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 152], [6, 14], [8, 96], [12, 112]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 8, 0, 4, 0, 0, 0], 'outer_gens': [[193, 2, 216, 32], [1, 206, 8, 48], [193, 2, 24, 32], [13, 22, 8, 240], [1, 2, 8, 160], [193, 6, 24, 48], [193, 2, 8, 32]], 'outer_group': '128.2323', 'outer_hash': 2323, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [40682903, 303182783, 167410087, 263265840, 40723343, 40723327, 40723320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 8], [8, 4], [16, 2]], 'representations': {'PC': {'code': 3769954433052780822946939351533261420096257, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 1664, 1825, 41, 482, 3211, 91, 16901, 5773, 141, 17926, 166, 16391]}, 'Perm': {'d': 35, 'gens': [322928442543169319568419549863154143797, 626064152435907814705321902093100423837, 43688286655680870436465418463641566700, 939667320566100256264573034452543086824, 1226535138978594646261590000688047623055, 1226535138978594646261590000631480320000, 1226535138978594646261590007488310484050, 6758061133824000]}}, 'schur_multiplier': [2, 4], '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_4^2.D_{12}', 'transitive_degree': 96, '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': 12, 'aut_gen_orders': [6, 12, 6, 2, 12, 2, 4, 12, 4], 'aut_gens': [[1, 2, 8, 32], [129, 10, 24, 32], [177, 10, 8, 240], [129, 290, 24, 224], [17, 210, 216, 160], [161, 218, 24, 240], [257, 102, 24, 368], [177, 222, 216, 352], [33, 98, 216, 48], [109, 306, 216, 240]], 'aut_group': None, 'aut_hash': 4671954392677295563, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 80, 'aut_perms': [24525899754836897730409544507823833659732881749057262607484550760442369477767062410674702823209217539429952859935255506, 37056614006995424700319039417648017021584774687959509624381081095549485011610073094708769221964536346723077158995628227, 24401332389637643864317227282572276899699698611699940787700107471723088226247291330578828783978473808999124138386954548, 46612021681099682021942466058667765995048336471358879642701580324813060874393367033189184503597612238491932055590600977, 63974432934387507315616883704779646731441048267768567593190756509263338102324486736386053877149695909728131379844854290, 51651661482794285263072581426814726524613008622444055898697998673781887717627385142147986997736825359003783549751639496, 37228940113123409965901251179060512515449804945871161816387265883524157504420401639674373084155295999961596066284873655, 39041016418574622614767615415513093632816803291956234899756510398843711467732099265595147737086688283016904558706308487, 10648501163546730821473903039860921709367079084626997500802977923163554362096091651172857204979584840274227389410655671], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 4], [4, 8, 4, 1], [4, 24, 2, 2], [6, 2, 1, 3], [6, 2, 4, 1], [8, 24, 4, 1], [12, 4, 2, 6], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^4.C_2^6.C_2^2)', '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': 6, 'autcentquo_group': '192.1542', 'autcentquo_hash': 1542, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 8, 4], [4, 24, 4], [6, 2, 7], [8, 24, 4], [12, 4, 12], [12, 8, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.134', 'commutator_count': 1, 'commutator_label': '24.9', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2142, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 1, 4], [4, 8, 2, 2], [4, 24, 1, 4], [6, 2, 1, 3], [6, 2, 2, 2], [8, 24, 2, 2], [12, 4, 2, 6], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2142, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 2, 6], 'inner_gens': [[1, 114, 8, 352], [305, 2, 200, 240], [1, 194, 8, 32], [65, 210, 8, 32]], 'inner_hash': 134, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'C_2^2.D_{12}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 18]], 'label': '384.2142', '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': 'C4^2.D12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 47, 'number_conjugacy_classes': 54, 'number_divisions': 34, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 150, 'number_subgroup_classes': 208, 'number_subgroups': 638, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 152], [6, 14], [8, 96], [12, 112]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 8, 0, 4, 0, 0, 0], 'outer_gens': [[193, 2, 216, 32], [1, 206, 8, 48], [193, 2, 24, 32], [13, 22, 8, 240], [1, 2, 8, 160], [193, 6, 24, 48], [193, 2, 8, 32]], 'outer_group': '128.2323', 'outer_hash': 2323, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 12, 'outer_perms': [40682903, 303182783, 167410087, 263265840, 40723343, 40723327, 40723320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 8], [8, 4], [16, 2]], 'representations': {'PC': {'code': 3769954433052780822946939351533261420096257, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 1664, 1825, 41, 482, 3211, 91, 16901, 5773, 141, 17926, 166, 16391]}, 'Perm': {'d': 35, 'gens': [322928442543169319568419549863154143797, 626064152435907814705321902093100423837, 43688286655680870436465418463641566700, 939667320566100256264573034452543086824, 1226535138978594646261590000688047623055, 1226535138978594646261590000631480320000, 1226535138978594646261590007488310484050, 6758061133824000]}}, 'schur_multiplier': [2, 4], '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_4^2.D_{12}', 'transitive_degree': 96, '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}
