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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1085463', 'ambient_counter': 1085463, 'ambient_order': 768, 'ambient_tex': 'C_4^3.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 196, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1085463.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.b1.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '768.1085463', 'aut_centralizer_order': 256, 'aut_label': '192.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 256, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.d1.a1', '96.a1.a1', '96.bd1.a1', '96.bd1.b1', '96.be1.a1', '96.bf1.a1'], 'contains': ['384.b1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [675, 4641, 8933, 5068, 1089, 4957, 8895, 5294], 'generators': [480, 384], 'label': '768.1085463.192.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.b1.a1', 'normal_contained_in': ['48.b1.a1', '96.a1.a1'], 'normal_contains': ['768.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '768.1085463', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.36', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': 24, 'aut_gen_orders': [2, 8, 6, 2, 4, 8], 'aut_gens': [[1, 2, 48, 192], [9, 22, 576, 144], [289, 298, 336, 192], [17, 38, 192, 336], [17, 22, 144, 336], [281, 214, 48, 624], [673, 538, 624, 576]], 'aut_group': '1536.408634478', 'aut_hash': 6147557801735190301, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1536, 'aut_permdeg': 40, 'aut_perms': [688675533904742182825601042718450586773702064307, 111675197077125363331924878034753149123863734136, 318347644735081491400710033457293970219054199046, 359171287582596096637795240765673217031240290519, 523856831818777568094587151150130948729198680636, 215699824298899558331277601044910507155280219036], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 2, 1], [3, 32, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [4, 6, 1, 4], [4, 6, 2, 2], [4, 12, 2, 3], [6, 32, 1, 1], [8, 4, 4, 1], [8, 12, 4, 3], [8, 24, 2, 2], [8, 24, 4, 1], [12, 32, 2, 1], [24, 32, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:C_3.C_2^5', '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': 24, 'autcentquo_group': '192.956', 'autcentquo_hash': 956, 'autcentquo_nilpotent': False, 'autcentquo_order': 192, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 2], [3, 32, 1], [4, 1, 2], [4, 3, 2], [4, 6, 8], [4, 12, 6], [6, 32, 1], [8, 4, 4], [8, 12, 12], [8, 24, 8], [12, 32, 2], [24, 32, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '192.956', 'commutator_count': 1, 'commutator_label': '48.3', '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', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1085463, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 2], [3, 32, 1, 1], [4, 1, 2, 1], [4, 3, 2, 1], [4, 6, 1, 4], [4, 6, 2, 2], [4, 12, 1, 2], [4, 12, 2, 2], [6, 32, 1, 1], [8, 4, 4, 1], [8, 12, 4, 3], [8, 24, 1, 2], [8, 24, 2, 1], [8, 24, 4, 1], [12, 32, 2, 1], [24, 32, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 8]], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '48.48', 'hash': 1085463, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 6, 4, 4], 'inner_gens': [[1, 34, 336, 192], [17, 2, 192, 336], [673, 626, 48, 192], [1, 50, 48, 192]], 'inner_hash': 956, 'inner_nilpotent': False, 'inner_order': 192, 'inner_split': True, 'inner_tex': 'C_4^2:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 16], [2, 8], [3, 16], [6, 16]], 'label': '768.1085463', 'linC_count': 8, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 12, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 16, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C4^3.D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 27, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 56, 'number_divisions': 30, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 201, 'number_subgroup_classes': 220, 'number_subgroups': 1236, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 31], [3, 32], [4, 128], [6, 32], [8, 352], [12, 64], [24, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 38, 48, 192], [1, 26, 48, 192], [25, 2, 48, 192]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 8, 'outer_perms': [18498, 12316, 5329], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, '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, 8], [8, 1], [12, 5], [24, 1]], 'representations': {'PC': {'code': '47276443836644047500707977673786400134610185857181929986217934989147295326246838105607724048', 'gens': [1, 2, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 2, 2, 2, 613, 46, 542, 74, 1443, 102, 1444, 18149, 5198, 4559, 3920, 1175, 158, 30246, 12111, 7584, 3057, 1932, 12112, 2617, 5650, 691, 214, 19457, 1970, 4895, 530]}, 'Perm': {'d': 20, 'gens': [1450387266814080, 122398340524151337, 12568, 18498, 264031574717433600, 135208323908985600, 1799466751716480, 392684164248499200, 2160477806860800]}}, '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_4^3.D_6', 'transitive_degree': 24, '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}
