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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '576.1921', 'ambient_counter': 1921, 'ambient_order': 576, 'ambient_tex': '(C_6\\times C_{12}).D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 576, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '576.1921.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '576.1921', 'subgroup_hash': 1921, 'subgroup_order': 576, 'subgroup_tex': '(C_6\\times C_{12}).D_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '576.1921', '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': '144.a1.a1', 'complements': ['576.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '9.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4952, 4157, 6049, 6449, 4188, 3728, 5897, 2921], 'generators': [1, 8, 288, 2, 440, 192, 400, 444], 'label': '576.1921.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '144.115', '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': '144.115'}
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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': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 6, 6, 12, 6, 4, 6], 'aut_gens': [[1, 2, 16, 48], [541, 406, 16, 544], [197, 266, 416, 80], [377, 230, 416, 336], [369, 218, 16, 336], [113, 54, 208, 240], [433, 306, 16, 336], [205, 338, 208, 256], [265, 470, 208, 528]], 'aut_group': None, 'aut_hash': 8939065649976405965, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 96, 'aut_perms': [261587041125841358268784463700862643782967109487246117896059337861072072332414949357497640459351346594788451835451434205075419613767916214928990354513, 111912065732340439210537171156093043866872475564265796487100106992829490824501014839015569003636442459416534959207247144734786202939200271123776842025, 83957504967010858076362944841769187648700447650496552260656583889355537629265628112866323423121568371919702980924122505434135722674659813493439179304, 775992801873655945373303526309956397666797105060810452808673607652658067431011335471348558641984079627484039158991365276073901236475944822108000694967, 190461641023381337100806284902540725354658971843758656216437081230829773643500799676619323540741938633449918127977834586553068554882974886112383363703, 242865849853725769332555899977823700128363464135272857641874605544563859311135592333492390919586128341334254876782740248892959659647770079979656330544, 194226940351358048535479856162872832855784233916075504458790830344504822557325344722222690949326754578358843285164947946886271858570499230917593423665, 71335920382413807550928391377352973782152418662997436679378459798639883490423332608085188551366489572675044936287456015583518127354099665648266377032], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 4, 1, 2], [4, 2, 1, 2], [4, 18, 1, 2], [4, 24, 2, 1], [4, 36, 1, 1], [6, 4, 1, 6], [8, 12, 4, 1], [8, 36, 4, 1], [12, 4, 2, 2], [12, 8, 1, 2], [12, 24, 4, 1], [24, 12, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_3\\times C_6).C_2^6.C_2^2', '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': 12, 'autcentquo_group': '288.1031', 'autcentquo_hash': 1031, 'autcentquo_nilpotent': False, 'autcentquo_order': 288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 4, 2], [4, 2, 2], [4, 18, 2], [4, 24, 2], [4, 36, 1], [6, 4, 6], [8, 12, 4], [8, 36, 4], [12, 4, 4], [12, 8, 2], [12, 24, 4], [24, 12, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '144.115', 'commutator_count': 1, 'commutator_label': '72.34', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1921, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 4, 1, 2], [4, 2, 1, 2], [4, 18, 1, 2], [4, 24, 1, 2], [4, 36, 1, 1], [6, 4, 1, 6], [8, 12, 4, 1], [8, 36, 4, 1], [12, 4, 2, 2], [12, 8, 1, 2], [12, 24, 2, 2], [24, 12, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '72.40', 'hash': 1921, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 4, 3, 6], 'inner_gens': [[1, 446, 416, 48], [149, 2, 416, 368], [225, 226, 16, 48], [1, 306, 16, 48]], 'inner_hash': 115, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3^2:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10], [4, 25], [8, 2]], 'label': '576.1921', 'linC_count': 80, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 67, 'linQ_dim': 12, 'linQ_dim_count': 15, 'linR_count': 54, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C6*C12).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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 45, 'number_divisions': 28, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 102, 'number_subgroup_classes': 117, 'number_subgroups': 666, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 124], [6, 24], [8, 192], [12, 128], [24, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 432], 'outer_gens': [[9, 2, 16, 48], [289, 2, 16, 48], [1, 10, 16, 48], [441, 2, 16, 336], [1, 442, 16, 48]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 4, '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, 4], [4, 11], [8, 7], [16, 2]], 'representations': {'PC': {'code': 2249747364022147516250950247064585484889384193096017673, 'gens': [1, 2, 5, 6], 'pres': [8, 2, 2, 2, 2, 3, 2, 2, 3, 3520, 7137, 41, 290, 66, 16644, 8332, 340, 8845, 2901, 141, 3150, 6742, 166, 7183, 6167]}, 'GLZN': {'d': 2, 'p': 63, 'gens': [13752640, 10921387, 12536320, 13321437, 2574226, 2000384, 12697294, 336043]}, 'Perm': {'d': 22, 'gens': [13160722247776412, 51212944367854983293, 256097839090880507, 2890861747200, 4296764121742, 19342, 5000609551601664000, 104864478926118912000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_6\\times C_{12}).D_4', 'transitive_degree': 192, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 6, 6, 12, 6, 4, 6], 'aut_gens': [[1, 2, 16, 48], [541, 406, 16, 544], [197, 266, 416, 80], [377, 230, 416, 336], [369, 218, 16, 336], [113, 54, 208, 240], [433, 306, 16, 336], [205, 338, 208, 256], [265, 470, 208, 528]], 'aut_group': None, 'aut_hash': 8939065649976405965, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 96, 'aut_perms': [261587041125841358268784463700862643782967109487246117896059337861072072332414949357497640459351346594788451835451434205075419613767916214928990354513, 111912065732340439210537171156093043866872475564265796487100106992829490824501014839015569003636442459416534959207247144734786202939200271123776842025, 83957504967010858076362944841769187648700447650496552260656583889355537629265628112866323423121568371919702980924122505434135722674659813493439179304, 775992801873655945373303526309956397666797105060810452808673607652658067431011335471348558641984079627484039158991365276073901236475944822108000694967, 190461641023381337100806284902540725354658971843758656216437081230829773643500799676619323540741938633449918127977834586553068554882974886112383363703, 242865849853725769332555899977823700128363464135272857641874605544563859311135592333492390919586128341334254876782740248892959659647770079979656330544, 194226940351358048535479856162872832855784233916075504458790830344504822557325344722222690949326754578358843285164947946886271858570499230917593423665, 71335920382413807550928391377352973782152418662997436679378459798639883490423332608085188551366489572675044936287456015583518127354099665648266377032], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 4, 1, 2], [4, 2, 1, 2], [4, 18, 1, 2], [4, 24, 2, 1], [4, 36, 1, 1], [6, 4, 1, 6], [8, 12, 4, 1], [8, 36, 4, 1], [12, 4, 2, 2], [12, 8, 1, 2], [12, 24, 4, 1], [24, 12, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_3\\times C_6).C_2^6.C_2^2', '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': 12, 'autcentquo_group': '288.1031', 'autcentquo_hash': 1031, 'autcentquo_nilpotent': False, 'autcentquo_order': 288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 4, 2], [4, 2, 2], [4, 18, 2], [4, 24, 2], [4, 36, 1], [6, 4, 6], [8, 12, 4], [8, 36, 4], [12, 4, 4], [12, 8, 2], [12, 24, 4], [24, 12, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '144.115', 'commutator_count': 1, 'commutator_label': '72.34', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1921, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 4, 1, 2], [4, 2, 1, 2], [4, 18, 1, 2], [4, 24, 1, 2], [4, 36, 1, 1], [6, 4, 1, 6], [8, 12, 4, 1], [8, 36, 4, 1], [12, 4, 2, 2], [12, 8, 1, 2], [12, 24, 2, 2], [24, 12, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '72.40', 'hash': 1921, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 4, 3, 6], 'inner_gens': [[1, 446, 416, 48], [149, 2, 416, 368], [225, 226, 16, 48], [1, 306, 16, 48]], 'inner_hash': 115, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'S_3^2:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 10], [4, 25], [8, 2]], 'label': '576.1921', 'linC_count': 80, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 67, 'linQ_dim': 12, 'linQ_dim_count': 15, 'linR_count': 54, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C6*C12).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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 25, 'number_conjugacy_classes': 45, 'number_divisions': 28, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 102, 'number_subgroup_classes': 117, 'number_subgroups': 666, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 124], [6, 24], [8, 192], [12, 128], [24, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 432], 'outer_gens': [[9, 2, 16, 48], [289, 2, 16, 48], [1, 10, 16, 48], [441, 2, 16, 336], [1, 442, 16, 48]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 4, '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, 4], [4, 11], [8, 7], [16, 2]], 'representations': {'PC': {'code': 2249747364022147516250950247064585484889384193096017673, 'gens': [1, 2, 5, 6], 'pres': [8, 2, 2, 2, 2, 3, 2, 2, 3, 3520, 7137, 41, 290, 66, 16644, 8332, 340, 8845, 2901, 141, 3150, 6742, 166, 7183, 6167]}, 'GLZN': {'d': 2, 'p': 63, 'gens': [13752640, 10921387, 12536320, 13321437, 2574226, 2000384, 12697294, 336043]}, 'Perm': {'d': 22, 'gens': [13160722247776412, 51212944367854983293, 256097839090880507, 2890861747200, 4296764121742, 19342, 5000609551601664000, 104864478926118912000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_6\\times C_{12}).D_4', 'transitive_degree': 192, '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}
