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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34016', 'ambient_counter': 34016, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 337, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34016.24.K', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.34016', 'aut_centralizer_order': None, 'aut_label': '24.K', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.D', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.F', '12.E', '12.N', '12.P', '12.BG', '12.CO', '12.DV', '12.DW'], 'contains': ['48.B', '48.CH', '72.H', '72.Z'], 'core': '24.K', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 864, 48, 72], 'label': '1728.34016.24.K', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.K', 'normal_contained_in': ['8.F', '12.E', '12.N', '12.P'], 'normal_contains': ['48.B', '72.H'], 'normalizer': '1.a1', 'old_label': '24.k1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.K', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 3], 'aut_gens': [[1, 12], [1, 60], [5, 12], [5, 18], [41, 12], [7, 12], [25, 12]], 'aut_group': '96.209', 'aut_hash': 209, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 9, 'aut_perms': [5047, 120, 1, 136, 7, 45360], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 3, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 2], [6, 2, 4, 1], [12, 3, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', '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, 3], [3, 1, 2], [3, 2, 3], [4, 3, 4], [6, 1, 6], [6, 2, 9], [12, 3, 8]], 'center_label': '12.5', 'center_order': 12, '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', '2.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 29, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.1', 1], ['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 3, 2, 2], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [12, 3, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 12, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '36.12', 'hash': 29, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 60], [25, 12]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 12]], 'label': '72.29', 'linC_count': 96, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 4, 'linQ_dim': 5, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6:C12', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, '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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 36, 'number_divisions': 20, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 37, 'number_subgroups': 54, 'old_label': None, 'order': 72, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 12], [6, 24], [12, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 18], [41, 12], [11, 12], [7, 12]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 6]], 'representations': {'PC': {'code': 14483972954469, 'gens': [1, 4], 'pres': [5, -2, -2, -3, -2, -3, 10, 26, 1203, 58, 1204]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [140699802150, 706131050962]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [33562260, 15426728, 34603218, 5426393, 34363418]}, 'Perm': {'d': 12, 'gens': [43908487, 1, 5760, 87091200, 30]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6:C_{12}', '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 12, 144], [73, 10, 60, 144], [865, 2, 60, 144], [1, 82, 60, 720], [1, 866, 60, 144], [1, 2, 84, 144], [1, 10, 924, 144], [1, 10, 60, 216], [1, 10, 12, 1008], [1, 10, 12, 144], [1, 2, 60, 144], [1, 2, 12, 720], [869, 2, 12, 144], [1, 50, 12, 144], [1, 2, 588, 144]], 'aut_group': '6912.ht', 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 55296, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 18, 2, 1], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 2, 3], [4, 12, 1, 3], [4, 18, 2, 2], [4, 27, 4, 1], [4, 36, 1, 2], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 36, 2, 1], [6, 72, 1, 1], [12, 8, 1, 3], [12, 8, 2, 3], [12, 8, 4, 1], [12, 12, 2, 6], [12, 24, 1, 6], [12, 24, 2, 6], [12, 36, 2, 2], [12, 72, 1, 2]], 'aut_supersolvable': None, 'aut_tex': 'C_2\\times C_2^4.\\SL(3,3)', 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 18, 2], [2, 36, 1], [2, 108, 1], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 4, 1], [4, 6, 6], [4, 12, 3], [4, 18, 4], [4, 27, 4], [4, 36, 2], [6, 2, 9], [6, 4, 9], [6, 8, 3], [6, 36, 2], [6, 72, 1], [12, 8, 13], [12, 12, 12], [12, 24, 18], [12, 36, 4], [12, 72, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '108.45', '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': 34016, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 18, 1, 2], [2, 36, 1, 1], [2, 108, 1, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 1, 2], [4, 6, 2, 2], [4, 12, 1, 3], [4, 18, 2, 2], [4, 27, 2, 2], [4, 36, 1, 2], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 36, 1, 2], [6, 72, 1, 1], [12, 8, 1, 5], [12, 8, 2, 4], [12, 12, 1, 4], [12, 12, 2, 4], [12, 24, 1, 10], [12, 24, 2, 4], [12, 36, 2, 2], [12, 72, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 44291520, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '432.759', 'hash': 34016, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 432, 'inner_split': None, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 36], [4, 42], [8, 14]], 'label': '1728.34016', '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*C4).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': 78, 'number_characteristic_subgroups': 164, 'number_conjugacy_classes': 108, 'number_divisions': 88, 'number_normal_subgroups': 178, 'number_subgroup_autclasses': 1070, 'number_subgroup_classes': 1254, 'number_subgroups': 10724, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 183], [3, 26], [4, 328], [6, 222], [12, 968]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '128.2328', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 128, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^7', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 24], [4, 24], [8, 22], [16, 2]], 'representations': {'PC': {'code': 56989215184448169178005591610291720756369045214276984001621798665801, 'gens': [1, 2, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 648, 181, 46, 23546, 5852, 1092, 102, 2713, 130, 2606, 13614, 34035, 8349, 186, 8674, 214, 7811]}, 'Perm': {'d': 25, 'gens': [6469326638214721, 623925032935913701944744, 622798606164711372037224, 27810410897461800, 6469326633369600, 16551600, 1320703288040697200640000, 3, 1938954779260553134080000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_4).S_3^3', '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': '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': [2, 2, 3, 3, 2, 2], 'aut_gens': [[1, 2, 4], [1, 2, 20], [1, 2, 5], [12, 15, 5], [1, 10, 4], [1, 14, 4], [1, 15, 4]], 'aut_group': '144.183', 'aut_hash': 183, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 144, 'aut_permdeg': 7, 'aut_perms': [1, 120, 144, 3, 744, 1680], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 4, 1], [3, 2, 1, 1], [6, 2, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'S_4', '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, 3], [2, 3, 4], [3, 2, 1], [6, 2, 3]], 'center_label': '4.2', 'center_order': 4, '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', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [3, 2, 1, 1], [6, 2, 1, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 28, 'exponent': 6, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '24.14', 'hash': 14, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 3], 'inner_gens': [[1, 2, 4], [1, 2, 20], [1, 10, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 4]], 'label': '24.14', 'linC_count': 12, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 12, 'linQ_dim': 3, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*D6', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 12, 'number_divisions': 12, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 32, 'number_subgroups': 54, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 15], [3, 2], [6, 6]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 2, 5], [13, 14, 17], [1, 15, 4], [1, 14, 4]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4]], 'representations': {'PC': {'code': 5123137, 'gens': [1, 2, 3], 'pres': [4, -2, -2, -2, -3, 126, 34, 135]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [16325, 16295, 3362]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [7426, 8156, 16849, 13286]}, 'Perm': {'d': 7, 'gens': [127, 7, 16, 840]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times D_6', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
