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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.46343', 'ambient_counter': 46343, 'ambient_order': 1728, 'ambient_tex': 'C_2^3.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 36, 'counter': 453, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.46343.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.46343', 'aut_centralizer_order': 288, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 288, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.j1.a1', '24.k1.a1', '24.m1.a1', '24.p1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '144.a1.a1', '144.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2094, 3016, 9118, 821, 1012, 7426, 8873, 8975], 'generators': [17190769, 7705165, 8046913, 595057], 'label': '1728.46343.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '96.b1.b1', '96.b1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '864.4673', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 2, 6], 'aut_gens': [[1, 6], [5, 6], [1, 30], [31, 6]], 'aut_group': '24.14', 'aut_hash': 14, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [7, 127, 856], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 1, 2], [3, 2, 3], [6, 1, 2], [6, 2, 3], [6, 3, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 12, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 3, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 6, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 0, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '36.12', 'hash': 12, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 30], [13, 6]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 4, 'irrep_stats': [[1, 12], [2, 6]], 'label': '36.12', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 7, 'linQ_dim': 4, 'linQ_dim_count': 7, 'linR_count': 7, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6*S3', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 18, 'number_divisions': 12, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 22, 'number_subgroups': 36, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 7], [3, 8], [6, 20]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[19, 6], [5, 6]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 8, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2]], 'representations': {'PC': {'code': 403784533, 'gens': [1, 3], 'pres': [4, -2, -3, -2, -3, 8, 362, 34, 387]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16858573, 35931481]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [56, 687, 1718]}, 'Perm': {'d': 8, 'gens': [720, 1, 30, 5760]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\times S_3', 'transitive_degree': 12, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 2, 6, 2, 12, 12], 'aut_gens': [[31669655, 17190769, 17760224, 4403503, 890233], [10415927, 17190769, 31818860, 4403503, 894937], [31523243, 24300877, 17467400, 32644087, 25487491], [10415927, 17190769, 49518806, 32943967, 894937], [23014478, 24303229, 42657362, 29593381, 25787371], [19374596, 17193121, 11882081, 29593381, 25492195], [31523243, 17188417, 22799207, 4703383, 894937], [19374596, 17193121, 19372013, 29593381, 25492195]], 'aut_group': None, 'aut_hash': 5675430861318798311, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 24, 'aut_perms': [558200764841319136894680, 187808383078767926841296, 506343450669998798051520, 15146362027394791567997, 333987105201051521714918, 188780635576487580210359, 566550645939695999673982], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 9, 2, 1], [2, 12, 1, 1], [2, 36, 1, 2], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 1, 1], [3, 16, 1, 2], [3, 32, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 18, 1, 2], [4, 36, 1, 2], [4, 54, 1, 1], [4, 108, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 4], [6, 6, 2, 1], [6, 8, 1, 1], [6, 12, 1, 2], [6, 12, 2, 1], [6, 16, 1, 2], [6, 18, 2, 1], [6, 24, 1, 1], [6, 24, 2, 2], [6, 32, 1, 1], [6, 36, 2, 1], [6, 48, 2, 1], [6, 72, 1, 1], [12, 12, 1, 1], [12, 12, 2, 1], [12, 24, 1, 1], [12, 24, 2, 2], [12, 36, 1, 1], [12, 36, 2, 1], [12, 48, 2, 1], [12, 72, 1, 1], [12, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_2^2.D_6^2\\times S_3', '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': '864.4673', 'autcentquo_hash': 4673, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 4], [2, 9, 2], [2, 12, 1], [2, 36, 2], [2, 108, 1], [3, 2, 2], [3, 4, 1], [3, 8, 1], [3, 16, 2], [3, 32, 1], [4, 6, 1], [4, 12, 1], [4, 18, 2], [4, 36, 2], [4, 54, 1], [4, 108, 1], [6, 2, 2], [6, 4, 1], [6, 6, 6], [6, 8, 1], [6, 12, 4], [6, 16, 2], [6, 18, 2], [6, 24, 5], [6, 32, 1], [6, 36, 2], [6, 48, 2], [6, 72, 1], [12, 12, 3], [12, 24, 5], [12, 36, 3], [12, 48, 2], [12, 72, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '864.4673', 'commutator_count': 1, 'commutator_label': '216.173', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 46343, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['288.855', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 9, 1, 2], [2, 12, 1, 1], [2, 36, 1, 2], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 8, 1, 1], [3, 16, 1, 2], [3, 32, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [4, 18, 1, 2], [4, 36, 1, 2], [4, 54, 1, 1], [4, 108, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 1, 6], [6, 8, 1, 1], [6, 12, 1, 2], [6, 12, 2, 1], [6, 16, 1, 2], [6, 18, 1, 2], [6, 24, 1, 3], [6, 24, 2, 1], [6, 32, 1, 1], [6, 36, 2, 1], [6, 48, 1, 2], [6, 72, 1, 1], [12, 12, 1, 1], [12, 12, 2, 1], [12, 24, 1, 1], [12, 24, 2, 2], [12, 36, 1, 1], [12, 36, 2, 1], [12, 48, 2, 1], [12, 72, 1, 1], [12, 72, 2, 1]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 161280, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4673', 'hash': 46343, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 6, 6, 6], 'inner_gens': [[31669655, 17190769, 11882081, 4403503, 25787371], [31669655, 17190769, 17760224, 4403503, 894937], [47908004, 17190769, 17760224, 7754089, 25787371], [31669655, 17190769, 35460254, 4403503, 890233], [6776045, 17193121, 17467400, 4403503, 890233]], 'inner_hash': 4673, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': 'S_4\\times S_3^2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 22], [3, 8], [4, 13], [6, 14], [8, 2], [12, 5]], 'label': '1728.46343', 'linC_count': 144, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 448, 'linQ_dim': 9, 'linQ_dim_count': 448, 'linR_count': 1088, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^3.S3^3', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 57, 'number_characteristic_subgroups': 60, 'number_conjugacy_classes': 72, 'number_divisions': 63, 'number_normal_subgroups': 72, 'number_subgroup_autclasses': 952, 'number_subgroup_classes': 1104, 'number_subgroups': 15012, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 223], [3, 80], [4, 288], [6, 560], [12, 576]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [592705, 592705, 592705], 'outer_gens': [[31669655, 24303229, 17760224, 4403503, 890233], [31669655, 17190769, 17760224, 32943967, 890233], [31669655, 17190769, 5020637, 4403503, 25787371]], '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': 5, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [3, 8], [4, 13], [6, 10], [8, 4], [12, 5], [24, 1]], 'representations': {'PC': {'code': 1367080563112233573322771577047607953141623689965693085336336991082517, 'gens': [1, 2, 3, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 1190, 74, 1443, 102, 1444, 12983, 6188, 3605, 158, 3048, 31111, 51856, 7801, 11698, 1987, 214, 46673]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [21298627, 7705165, 35310251, 1042546, 892585, 595057, 25782667, 29300557, 598555]}, 'Perm': {'d': 14, 'gens': [368063, 811576, 997925040, 367920, 518918400, 325, 435, 6266937600, 13412044800]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3.S_3^3', 'transitive_degree': 72, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 2, 2], 'aut_gens': [[143, 127, 576, 126, 121], [719, 127, 304, 126, 7], [16, 127, 576, 126, 121], [719, 127, 576, 7, 126], [143, 127, 702, 126, 121], [136, 127, 583, 126, 121]], 'aut_group': '48.48', 'aut_hash': 48, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 6, 'aut_perms': [269, 450, 244, 94, 444], '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, 6, 2, 1], [6, 8, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_4', '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': 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, 6, 2], [6, 8, 1]], 'center_label': '2.1', 'center_order': 2, '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', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 48, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.12', 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, 6, 1, 2], [6, 8, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '48.48', 'hash': 48, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 3, 2, 2], 'inner_gens': [[143, 127, 304, 121, 126], [143, 127, 576, 126, 121], [415, 127, 576, 121, 7], [136, 127, 697, 126, 121], [136, 127, 583, 126, 121]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 3, 4], 'irrC_degree': 3, 'irrQ_degree': 3, 'irrQ_dim': 3, 'irrR_degree': 3, 'irrep_stats': [[1, 4], [2, 2], [3, 4]], 'label': '48.48', 'linC_count': 2, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 2, 'linQ_dim': 3, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*S4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_conjugacy_classes': 10, 'number_divisions': 10, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 33, 'number_subgroups': 98, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 19], [3, 8], [4, 12], [6, 8]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[16, 127, 576, 126, 121]], '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': 4, 'perfect': False, 'permutation_degree': 6, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 4]], 'representations': {'PC': {'code': 44643202623812656708, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -3, -2, 2, 101, 26, 122, 483, 248, 193, 304, 459, 89]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [10320, 9038]}, 'Lie': [{'d': 3, 'q': 3, 'gens': [1557, 1699, 13205], 'family': 'GO'}, {'d': 3, 'q': 3, 'gens': [1557, 1699, 13205], 'family': 'CO'}], 'GLFp': {'d': 3, 'p': 3, 'gens': [16120, 18391, 13286, 6922, 13843]}, 'Perm': {'d': 6, 'gens': [143, 127, 576, 126, 121]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times S_4', 'transitive_degree': 6, 'wreath_data': ['24.b1.a1', '8.b1.a1', '24.d1.a1', '3T2'], 'wreath_product': True}
