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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.154796', 'ambient_counter': 154796, 'ambient_order': 1152, 'ambient_tex': 'C_2.S_4\\times C_{24}', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 6, 'counter': 197, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.154796.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.958', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 958, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_8\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1152.154796', 'aut_centralizer_order': 768, 'aut_label': '192.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 768, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.f1.a1', '96.g1.a1', '96.h1.a1', '96.h1.b1'], 'contains': ['384.a1.a1', '576.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1750, 3618, 7935, 3915, 6650, 4918, 7041, 4374], 'generators': [576, 384], 'label': '1152.154796.192.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.b1.a1', '96.a1.a1'], 'normal_contains': ['384.a1.a1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '192.958', 'quotient_action_image': '1.1', 'quotient_action_kernel': '192.958', 'quotient_action_kernel_order': 192, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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, 1], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, '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', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6', 'ngens': 2, '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, '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': '48.23', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 2, 4, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 48, 96], [649, 742, 48, 720], [1, 530, 48, 1056], [809, 178, 864, 1008], [601, 926, 48, 672], [809, 598, 864, 816], [809, 406, 864, 432], [49, 166, 48, 720], [49, 818, 624, 480]], 'aut_group': '1536.408641059', 'aut_hash': 1418641417957792246, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 34, 'aut_perms': [85748099142489563495436004113198223251, 185212312286345391349714283415446442172, 7706279770678692907939268300349338743, 118432311855220848671953061537096641943, 81684449264863633901069847458736305763, 168788987975197998876549697594158819485, 173605212526301097045280298083097747530, 182833581153216585348191046857844531617], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [4, 1, 2, 2], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 2, 2], [6, 1, 2, 3], [6, 8, 1, 3], [6, 8, 2, 3], [8, 1, 8, 1], [8, 6, 4, 3], [8, 6, 8, 1], [8, 12, 4, 1], [12, 1, 4, 2], [12, 6, 2, 2], [12, 6, 4, 1], [12, 8, 2, 2], [12, 8, 4, 2], [12, 12, 4, 2], [24, 1, 16, 1], [24, 6, 8, 3], [24, 6, 16, 1], [24, 8, 8, 1], [24, 8, 16, 1], [24, 12, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6\\times S_4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [3, 8, 3], [4, 1, 4], [4, 6, 4], [4, 12, 4], [6, 1, 6], [6, 8, 9], [8, 1, 8], [8, 6, 20], [8, 12, 4], [12, 1, 8], [12, 6, 8], [12, 8, 12], [12, 12, 8], [24, 1, 16], [24, 6, 40], [24, 8, 24], [24, 12, 8]], 'center_label': '48.23', 'center_order': 48, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '24.3', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 154796, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['48.28', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 8, 1, 1], [3, 8, 2, 1], [4, 1, 2, 2], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 1, 2], [4, 12, 2, 1], [6, 1, 2, 3], [6, 8, 1, 3], [6, 8, 2, 3], [8, 1, 4, 2], [8, 6, 2, 2], [8, 6, 4, 4], [8, 12, 4, 1], [12, 1, 4, 2], [12, 6, 2, 2], [12, 6, 4, 1], [12, 8, 2, 2], [12, 8, 4, 2], [12, 12, 2, 2], [12, 12, 4, 1], [24, 1, 8, 2], [24, 6, 4, 2], [24, 6, 8, 4], [24, 8, 4, 2], [24, 8, 8, 2], [24, 12, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 24, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '144.188', 'hash': 154796, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 2], 'inner_gens': [[1, 418, 624, 144], [785, 2, 288, 720], [577, 338, 48, 672], [49, 626, 624, 96]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 72], [3, 48], [4, 24]], 'label': '1152.154796', 'linC_count': 1024, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 8, 'linR_count': 272, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2.S4*C24', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 192, 'number_divisions': 58, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 196, 'number_subgroup_classes': 221, 'number_subgroups': 786, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 76], [6, 78], [8, 176], [12, 248], [24, 544]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 338, 48, 672], [25, 2, 48, 96], [1, 26, 48, 96], [1, 38, 48, 96], [1, 770, 48, 480], [1, 578, 48, 96]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [4, 11], [6, 6], [8, 12], [12, 4], [16, 6], [24, 2], [32, 1]], 'representations': {'PC': {'code': '706524432834429534789121090798842611919510825119919618056353986345991692500327953', 'gens': [1, 2, 6, 7], 'pres': [9, -2, -2, -2, -2, -3, -2, 2, -2, -3, 5184, 7525, 46, 21278, 74, 15267, 102, 36004, 33701, 7790, 12335, 1976, 3119, 698, 9078, 22695, 15900, 5703, 4011, 933, 186, 214]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [120406, 178873, 80557, 74096, 62054, 43861, 37048, 38503, 9580]}, 'Perm': {'d': 27, 'gens': [453760580333021203811207544, 8443704, 3, 12506424, 3719544, 854364920750201319782400, 870729871040446976573414400, 1291861510299837637882444800, 1711455689043410443535001600]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 24], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2.S_4\\times C_{24}', 'transitive_degree': 384, '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': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 2, 2], 'aut_gens': [[311607, 161009, 557585, 573457], [949732, 560932, 49665, 573457], [836391, 145121, 557585, 573457], [836391, 161009, 557585, 573457], [311607, 137209, 557585, 573457], [949732, 145137, 49665, 557585], [311607, 685793, 557585, 573457], [835879, 145137, 557585, 573457]], 'aut_group': '192.1537', 'aut_hash': 1537, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 10, 'aut_perms': [40447, 1, 289, 127, 45360, 367920, 806400], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 2, 1], [3, 8, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [4, 6, 2, 3], [6, 8, 1, 1], [8, 1, 4, 1], [8, 3, 4, 1], [8, 6, 4, 2], [12, 8, 2, 1], [24, 8, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^3\\times S_4', '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': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 2], [3, 8, 1], [4, 1, 2], [4, 3, 2], [4, 6, 6], [6, 8, 1], [8, 1, 4], [8, 3, 4], [8, 6, 8], [12, 8, 2], [24, 8, 4]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '12.3', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 958, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 2], [3, 8, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [4, 6, 1, 2], [4, 6, 2, 2], [6, 8, 1, 1], [8, 1, 4, 1], [8, 3, 4, 1], [8, 6, 4, 2], [12, 8, 2, 1], [24, 8, 4, 1]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 36, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 0, 8]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '48.48', 'hash': 958, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 2], 'inner_gens': [[311607, 560932, 557585, 49665], [902405, 161009, 573457, 49665], [311607, 685793, 557585, 573457], [835879, 668897, 557585, 573457]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 3, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 6, 'irrep_stats': [[1, 16], [2, 8], [3, 16]], 'label': '192.958', 'linC_count': 8, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 8, 'linQ_dim': 7, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C8*S4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 40, 'number_divisions': 20, 'number_normal_subgroups': 19, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 79, 'number_subgroups': 246, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 19], [3, 8], [4, 44], [6, 8], [8, 64], [12, 16], [24, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [32769, 32769, 32769], 'outer_gens': [[311607, 153065, 557585, 573457], [311607, 145121, 557585, 573457], [836391, 161009, 557585, 573457]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 3], [6, 2], [8, 1], [12, 2]], 'representations': {'PC': {'code': 917108607371842692266639547586771060317873924, 'gens': [1, 2, 6, 7], 'pres': [7, -2, -2, -2, -2, -3, -2, 2, 477, 36, 422, 58, 1123, 80, 1124, 2028, 1531, 530, 411, 7062, 3541, 608, 909, 181]}, 'GLFq': {'d': 3, 'q': 9, 'gens': [87646943, 133611126, 86106566, 107079024, 325511162, 344426264, 215266415]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [33281, 557073, 573969, 294921, 36111, 124284, 98307]}, 'Perm': {'d': 12, 'gens': [3634129, 12569, 18523, 5329, 3991680, 40279680, 87091200]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_8\\times S_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
