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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1536.408528972', 'ambient_counter': 408528972, 'ambient_order': 1536, 'ambient_tex': 'C_4^4:C_6', 'central': True, 'central_factor': False, 'centralizer_order': 1536, 'characteristic': False, 'core_order': 2, 'counter': 290, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1536.408528972.768.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '768.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '768.1083579', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1083579, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^3:C_{12}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1536.408528972', 'aut_centralizer_order': 147456, 'aut_label': '768.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1.1', 'aut_weyl_index': 589824, 'centralizer': '1.a1', 'complements': ['2.b1'], 'conjugacy_class_count': 4, 'contained_in': ['256.b1', '384.a1', '384.i1', '384.j1'], 'contains': ['1536.a1'], 'core': '768.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [4928, 8312, 4134, 8584], 'generators': [30863], 'label': '1536.408528972.768.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '768.b1', 'normal_contained_in': ['192.e1', '384.a1'], 'normal_contains': ['1536.a1'], 'normalizer': '1.a1', 'old_label': '768.b1', 'projective_image': '768.1083579', 'quotient_action_image': '1.1', 'quotient_action_kernel': '768.1083579', 'quotient_action_kernel_order': 768, 'quotient_fusion': None, 'short_label': '768.b1', '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': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '96.161', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 12, 8, 12], 'aut_gens': [[5012, 64591, 21645, 37957, 61575], [12720, 45131, 40009, 12299, 61447], [47484, 13443, 20557, 14347, 63495], [17713, 14411, 21645, 14339, 30727], [30012, 29775, 23565, 12427, 28815]], 'aut_group': None, 'aut_hash': 4645396269811067549, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 589824, 'aut_permdeg': 56, 'aut_perms': [229819364343089540504261924105149159921768284885700313311318829776430132085, 148502469976811971522441776285241308846751795231982462914542232135512273981, 263812470123953476125732313668067071097171536018268859459479767338576448592, 237001278420793719594028771139287185298918507206848796104646456696001313985], 'aut_phi_ratio': 1152.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [2, 3, 1, 1], [2, 3, 3, 1], [2, 3, 4, 1], [3, 16, 2, 1], [4, 1, 24, 1], [4, 3, 4, 1], [4, 3, 12, 1], [4, 3, 16, 1], [4, 3, 24, 1], [4, 3, 96, 1], [6, 16, 6, 1], [6, 16, 8, 1], [12, 16, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:C_3.D_4\\times C_2^6.S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '1536.408569020', 'autcent_hash': 2246280721724691594, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '384.5677', 'autcentquo_hash': 5677, 'autcentquo_nilpotent': False, 'autcentquo_order': 384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 3, 8], [3, 16, 2], [4, 1, 24], [4, 3, 152], [6, 16, 14], [12, 16, 48]], 'center_label': '32.21', 'center_order': 32, 'central_product': True, 'central_quotient': '48.3', 'commutator_count': 1, 'commutator_label': '16.2', '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', '2.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 408528972, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 2], ['48.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 3, 1, 8], [3, 16, 2, 1], [4, 1, 2, 12], [4, 3, 2, 76], [6, 16, 2, 7], [12, 16, 4, 12]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 1820, 'exponent': 12, 'exponents_of_order': [9, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '96.228', 'hash': 408528972, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 4, 4, 2, 2], 'inner_gens': [[5012, 15499, 22733, 40133, 63495], [6100, 64591, 21645, 37957, 61575], [24464, 64591, 21645, 37957, 61575], [39836, 64591, 21645, 37957, 61575], [39836, 64591, 21645, 37957, 61575]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'C_4^2:C_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 96], [3, 160]], 'label': '1536.408528972', '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': 'C4^4:C6', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 256, 'number_divisions': 124, 'number_normal_subgroups': 216, 'number_subgroup_autclasses': 294, 'number_subgroup_classes': 4772, 'number_subgroups': 14640, 'old_label': None, 'order': 1536, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 31], [3, 32], [4, 480], [6, 224], [12, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [6, 12, 4, 4], 'outer_gen_pows': [4097, 4097, 4097, 4097], 'outer_gens': [[2843, 31823, 55365, 21577, 61583], [1525, 15491, 5185, 54473, 63631], [63928, 31823, 56453, 55309, 61575], [8144, 62671, 56453, 20621, 30727]], 'outer_group': None, 'outer_hash': 8042116705591706982, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 28, 'outer_perms': [46173623565590068000183637887, 103363244748833430467307358209, 178928912229471998583672419416, 216019542388153297023159079816], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^6.(D_4\\times S_4)', 'pc_rank': None, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [3, 8], [4, 12], [6, 76]], 'representations': {'PC': {'code': '7446621540230583991228019622116446903929364051733029168959093198593517863800216468420996224', 'gens': [1, 4, 6, 8, 10], 'pres': [10, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 20, 51, 51843, 3613, 12983, 113, 4804, 3014, 1224, 74165, 37815, 18565, 175, 8406, 856, 2126, 17287, 12497, 4347, 237, 79209, 44419, 19829]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4105, 39041, 13507, 21709, 36873, 13511, 51027, 4161, 12291, 4225]}, 'Perm': {'d': 18, 'gens': [447685648583040, 732386784291289, 1175774172249846, 126940221722574, 1552218583547766, 858017012031055, 414, 858015531475614, 147862651915440, 858017012031054]}}, 'schur_multiplier': [2, 2, 4, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 12], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^4:C_6', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.20', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 12, 6, 24], 'aut_gens': [[13816, 20557, 40009, 55429], [20311, 38089, 20557, 21705], [18327, 40009, 53445, 55429], [4059, 55365, 23565, 23617], [48432, 40009, 54277, 40005], [1883, 53445, 56453, 56393]], 'aut_group': None, 'aut_hash': 4933082910378035565, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 36864, 'aut_permdeg': 44, 'aut_perms': [2447044159410418746483178014276100848922015426828893906, 183148653889409783948236742528558183584641284801667954, 181670350556242078007313098463109589097556259431185834, 1433909594027362328582148288467783855398214970057350779, 235088731968877919048872909926203605584589148327749163], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 1, 1], [2, 3, 3, 1], [3, 16, 2, 1], [4, 1, 12, 1], [4, 3, 4, 1], [4, 3, 12, 2], [4, 3, 48, 1], [6, 16, 6, 1], [12, 16, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^2:C_3.D_4\\times \\GL(2,\\mathbb{Z}/4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '96.195', 'autcent_hash': 195, 'autcent_nilpotent': False, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(2,\\mathbb{Z}/4)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '384.5677', 'autcentquo_hash': 5677, 'autcentquo_nilpotent': False, 'autcentquo_order': 384, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2.\\GL(2,\\mathbb{Z}/4)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [3, 16, 2], [4, 1, 12], [4, 3, 76], [6, 16, 6], [12, 16, 24]], 'center_label': '16.2', 'center_order': 16, 'central_product': True, 'central_quotient': '48.3', 'commutator_count': 1, 'commutator_label': '16.2', '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': 1083579, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['4.1', 2], ['48.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [3, 16, 2, 1], [4, 1, 2, 6], [4, 3, 2, 38], [6, 16, 2, 3], [12, 16, 4, 6]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 4, 'exponent': 12, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.14', 'frattini_quotient': '48.49', 'hash': 1083579, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 4, 4, 1], 'inner_gens': [[13816, 7361, 56453, 55429], [32180, 20557, 40009, 55429], [14648, 20557, 40009, 55429], [13816, 20557, 40009, 55429]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'C_4^2:C_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [3, 80]], 'label': '768.1083579', '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': 'C4^3:C12', '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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 128, 'number_divisions': 62, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': 114, 'number_subgroup_classes': 736, 'number_subgroups': 2298, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 32], [4, 240], [6, 96], [12, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 12, 2, 2], 'outer_gen_pows': [14780, 4097, 4097, 4097, 4097, 4097], 'outer_gens': [[13816, 56453, 20557, 55429], [46576, 20557, 40009, 20485], [63928, 20557, 40009, 20485], [2843, 40009, 53445, 54465], [48504, 20557, 40009, 20485], [46576, 20557, 40009, 22669]], 'outer_group': '768.1088764', 'outer_hash': 1088764, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [5160, 362880, 87454085, 40285563, 7, 16], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'D_4\\times \\GL(2,\\mathbb{Z}/4)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [4, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [3, 4], [4, 6], [6, 38]], 'representations': {'PC': {'code': '2116506949864223234087412696874824509941878346729818887730845248', 'gens': [1, 4, 6, 8], 'pres': [9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 18, 46, 2595, 2820, 669, 102, 4324, 2713, 1102, 3245, 3578, 833, 158, 7566, 771, 1914, 214]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [110457570525, 112033125003, 61054693752, 142235062787, 60282673600, 122109387504, 91157612969, 25200739578, 95713057258]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4105, 21697, 39041, 21709, 36873, 40013, 51027, 4161, 4225]}, 'Perm': {'d': 16, 'gens': [1602280119720, 355466361600, 2704965984009, 4397439071520, 530026887729, 529823306880, 16, 3141108514200, 283456216]}}, 'schur_multiplier': [4, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4, 12], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^3:C_{12}', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
