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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.5547', 'ambient_counter': 5547, 'ambient_order': 960, 'ambient_tex': 'C_2^2:C_{12}\\times C_{20}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 10, 'counter': 131, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.5547.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.161', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 161, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.5547', 'aut_centralizer_order': 4096, 'aut_label': '96.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 4096, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1'], 'contains': ['192.a1', '480.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7168, 6708, 5764, 3396], 'generators': [480, 192], 'label': '960.5547.96.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1', '48.b1', '48.c1'], 'normal_contains': ['192.a1', '480.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '96.161', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.161', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.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': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [7]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4], [10, 1, 4]], 'center_label': '10.2', 'center_order': 10, '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', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 10]], 'label': '10.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C10', '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': 10, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[7]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2]], 'representations': {'PC': {'code': 83, 'gens': [1], 'pres': [2, -2, -5, 4]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504]}, 'Perm': {'d': 7, 'gens': [720, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}', 'transitive_degree': 10, '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': '480.919', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 4, 4, 4, 4, 4, 4, 4], 'aut_gens': [[1, 4, 16, 96], [9, 542, 88, 96], [11, 61, 568, 96], [481, 493, 504, 288], [491, 495, 498, 288], [11, 54, 498, 864], [1, 532, 568, 96], [491, 495, 88, 288], [1, 61, 570, 96]], 'aut_group': None, 'aut_hash': 8698486613335582263, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 16384, 'aut_permdeg': 38, 'aut_perms': [4538112127840715333439242754149833854154616, 10243520692410912599167918231857124803024908, 153238793482986265820933200050003439668759797, 163223021293707870262928381179324771849612628, 334323266058059014799032591441158742449016179, 5368683914001931404662972623817737194971581, 163223021295653069009120544965482642343787500, 10202214161055048265219213209854525094672695], 'aut_phi_ratio': 64.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 4, 1], [3, 1, 2, 1], [4, 1, 8, 1], [4, 2, 4, 1], [4, 2, 16, 1], [5, 1, 4, 1], [6, 1, 2, 3], [6, 1, 8, 1], [6, 2, 8, 1], [10, 1, 4, 3], [10, 1, 16, 1], [10, 2, 16, 1], [12, 1, 16, 1], [12, 2, 8, 1], [12, 2, 32, 1], [15, 1, 8, 1], [20, 1, 32, 1], [20, 2, 16, 1], [20, 2, 64, 1], [30, 1, 8, 3], [30, 1, 32, 1], [30, 2, 32, 1], [60, 1, 64, 1], [60, 2, 32, 1], [60, 2, 128, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7.C_2^6.C_2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 6104977612496723973, 'autcent_nilpotent': True, 'autcent_order': 8192, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': '(C_2^{10}\\times C_4).C_2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [3, 1, 2], [4, 1, 8], [4, 2, 20], [5, 1, 4], [6, 1, 14], [6, 2, 8], [10, 1, 28], [10, 2, 16], [12, 1, 16], [12, 2, 40], [15, 1, 8], [20, 1, 32], [20, 2, 80], [30, 1, 56], [30, 2, 32], [60, 1, 64], [60, 2, 160]], 'center_label': '240.185', 'center_order': 240, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5547, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.3', 1], ['3.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 1, 2, 1], [4, 1, 2, 4], [4, 2, 2, 10], [5, 1, 4, 1], [6, 1, 2, 7], [6, 2, 2, 4], [10, 1, 4, 7], [10, 2, 4, 4], [12, 1, 4, 4], [12, 2, 4, 10], [15, 1, 8, 1], [20, 1, 8, 4], [20, 2, 8, 10], [30, 1, 8, 7], [30, 2, 8, 4], [60, 1, 16, 4], [60, 2, 16, 10]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 16926, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '120.47', 'hash': 5547, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2, 1], 'inner_gens': [[1, 4, 16, 96], [1, 4, 496, 96], [1, 484, 16, 96], [1, 4, 16, 96]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 480], [2, 120]], 'label': '960.5547', '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': 'C2^2:C12*C20', 'ngens': 8, 'nilpotency_class': 2, 'nilpotent': True, '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 600, 'number_divisions': 104, 'number_normal_subgroups': 292, 'number_subgroup_autclasses': 172, 'number_subgroup_classes': 516, 'number_subgroups': 740, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 48], [5, 4], [6, 30], [10, 60], [12, 96], [15, 8], [20, 192], [30, 120], [60, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 4, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[9, 493, 80, 288], [11, 63, 80, 864], [481, 6, 562, 672], [489, 5, 90, 96], [489, 540, 82, 288], [1, 543, 570, 96], [481, 61, 82, 96]], 'outer_group': None, 'outer_hash': 4486320118586182155, 'outer_nilpotent': True, 'outer_order': 4096, 'outer_permdeg': 512, 'outer_perms': 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6.C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 24], [4, 26], [8, 26], [16, 18], [32, 2]], 'representations': {'PC': {'code': 13389922110126589096647524371, 'gens': [1, 3, 5, 7], 'pres': [8, -2, -2, -2, -2, -2, -3, -2, -5, 16, 66, 4980, 116, 166]}, 'GLZN': {'d': 2, 'p': 44, 'gens': [2486917, 1959255, 1832467, 766665, 85669, 1487589, 1788885, 86153]}, 'Perm': {'d': 20, 'gens': [134451161761956480, 2796012535680, 243645888245760000, 10080, 96, 127370880, 378095736066048000, 1314028759680]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 60], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2:C_{12}\\times C_{20}', 'transitive_degree': 480, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, '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': [2, 2, 2, 6, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 8], [49, 54, 56], [1, 50, 8], [1, 2, 40], [1, 75, 34], [1, 54, 8], [1, 54, 60], [1, 50, 56], [1, 26, 40], [53, 50, 12]], 'aut_group': '3072.bjj', 'aut_hash': 3278739220350440602, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 26, 'aut_perms': [156599506467661408882560, 156290489358596340678150, 1, 267810879463645168873558446, 156598898240815284791046, 2508820767086692523195520, 49067179719652537489161384, 15618248412000798990155431, 49067179719799053264666840], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [3, 1, 2, 1], [4, 1, 24, 1], [6, 1, 6, 1], [6, 1, 8, 1], [12, 1, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^7:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '3072.bjj', 'autcent_hash': 3278739220350440602, 'autcent_nilpotent': False, 'autcent_order': 3072, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^7:S_4', '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, 7], [3, 1, 2], [4, 1, 24], [6, 1, 14], [12, 1, 48]], 'center_label': '96.161', 'center_order': 96, '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', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 161, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 12], [6, 1, 2, 7], [12, 1, 4, 12]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 91, 'exponent': 12, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '24.15', 'hash': 161, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 8], [1, 2, 8], [1, 2, 8]], '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, 96]], 'label': '96.161', 'linC_count': 46592, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 192, 'linQ_dim': 6, 'linQ_dim_count': 192, 'linR_count': 1536, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C4*C12', 'ngens': 6, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 96, 'number_divisions': 40, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 108, 'number_subgroups': 108, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [6, 14], [12, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 6, 2, 2, 2, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[49, 54, 56], [1, 50, 8], [1, 2, 40], [1, 75, 34], [1, 54, 8], [1, 54, 60], [1, 50, 56], [1, 26, 40], [53, 50, 12]], 'outer_group': '3072.bjj', 'outer_hash': 3278739220350440602, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 26, 'outer_perms': [156599506467661408882560, 156290489358596340678150, 1, 267810879463645168873558446, 156598898240815284791046, 2508820767086692523195520, 49067179719652537489161384, 15618248412000798990155431, 49067179719799053264666840], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^7:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, '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], [4, 12]], 'representations': {'PC': {'code': 638607951489, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, -2, -2, -3, 31, 69, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [91655872443238928, 125101750005088212, 58438776791332585]}, 'GLFp': {'d': 3, 'p': 13, 'gens': [10319436418, 9789111396, 6526074264, 6878714910, 4548416880, 6762482606]}, 'Perm': {'d': 13, 'gens': [11612160, 2400, 479001600, 4, 3669120, 744]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 12], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4\\times C_{12}', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
