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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34719', 'ambient_counter': 34719, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1049, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34719.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.963', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 963, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.34719', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.j1.a1', '144.a1.a1', '144.h1.a1', '144.m1.a1', '144.p1.a1', '144.q1.a1', '144.r1.a1'], 'contains': ['576.a1.a1', '864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 48], 'label': '1728.34719.288.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['96.b1.a1', '96.a1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [5]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', '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': 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], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, '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', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 6]], 'label': '6.2', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C6', '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': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], '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': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, '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], [937, 2, 12, 720], [865, 2, 12, 144], [1, 938, 12, 720], [1, 874, 12, 144], [1, 10, 996, 144], [1, 2, 876, 720], [1, 2, 12, 1656], [1, 2, 60, 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': None, '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], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 2], [4, 12, 1, 4], [4, 36, 1, 4], [4, 54, 2, 2], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 36, 2, 1], [6, 72, 1, 1], [12, 2, 4, 1], [12, 4, 2, 2], [12, 4, 4, 2], [12, 8, 2, 1], [12, 8, 4, 1], [12, 12, 2, 8], [12, 12, 4, 4], [12, 24, 1, 4], [12, 24, 2, 2], [12, 36, 2, 1], [12, 72, 1, 3]], 'aut_supersolvable': None, 'aut_tex': None, '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], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 2, 2], [4, 6, 4], [4, 12, 4], [4, 36, 4], [4, 54, 4], [6, 2, 9], [6, 4, 9], [6, 8, 3], [6, 36, 2], [6, 72, 1], [12, 2, 4], [12, 4, 12], [12, 8, 6], [12, 12, 32], [12, 24, 8], [12, 36, 2], [12, 72, 3]], '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': 34719, '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], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 2], [4, 12, 1, 4], [4, 36, 1, 4], [4, 54, 1, 2], [4, 54, 2, 1], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 36, 1, 2], [6, 72, 1, 1], [12, 2, 4, 1], [12, 4, 2, 2], [12, 4, 4, 2], [12, 8, 2, 1], [12, 8, 4, 1], [12, 12, 2, 14], [12, 12, 4, 1], [12, 24, 1, 6], [12, 24, 2, 1], [12, 36, 2, 1], [12, 72, 1, 3]], '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': 34719, '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, 40], [4, 57], [8, 10]], 'label': '1728.34719', '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': 123, 'number_divisions': 85, 'number_normal_subgroups': 170, 'number_subgroup_autclasses': 992, 'number_subgroup_classes': 1120, 'number_subgroups': 8180, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 75], [3, 26], [4, 436], [6, 222], [12, 968]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, '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, 17], [8, 22], [16, 6]], 'representations': {'PC': {'code': 56989138930542028478732192873900303017070803287064058668935883505225, 'gens': [1, 2, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 8424, 15733, 46, 23546, 5852, 31539, 16644, 102, 2713, 130, 2606, 34035, 3813, 186, 8674, 214, 7811]}, 'Perm': {'d': 25, 'gens': [700461682999437291609736, 109135124733894091257743, 1373587407106612262616240, 2017690908682692821356800, 112735425196800, 2591026047698446245888000, 325, 435, 45360]}}, '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': 192, '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': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [3, 6, 3, 6, 6, 2, 6, 6, 2, 2], 'aut_gens': [[1, 2, 4, 24], [1, 10, 4, 24], [216, 10, 21, 169], [1, 2, 100, 24], [145, 10, 4, 24], [1, 2, 212, 24], [1, 2, 148, 120], [145, 10, 212, 168], [217, 10, 148, 264], [1, 10, 164, 24], [1, 146, 52, 120]], 'aut_group': '3456.ma', 'aut_hash': 4660583108391961210, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 18, 'aut_perms': [15787502368725, 2807274633925244, 253092079328004, 4305053441139165, 313774921083263, 316296340443782, 4480213260919051, 3238539689756349, 316123464416804, 200969130943085], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 1], [2, 6, 3, 1], [2, 18, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 3, 1], [4, 6, 1, 1], [4, 6, 3, 1], [4, 18, 3, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 2, 1], [6, 12, 3, 1], [12, 4, 3, 2], [12, 6, 2, 1], [12, 8, 3, 1], [12, 12, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times D_6^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '216.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 4], [2, 18, 1], [3, 2, 2], [3, 4, 1], [4, 2, 3], [4, 6, 4], [4, 18, 3], [6, 2, 2], [6, 4, 1], [6, 6, 2], [6, 12, 3], [12, 4, 6], [12, 6, 2], [12, 8, 3], [12, 12, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '144.192', 'commutator_count': 1, 'commutator_label': '18.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 963, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 4], [2, 18, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 3], [4, 6, 1, 4], [4, 18, 1, 3], [6, 2, 1, 2], [6, 4, 1, 1], [6, 6, 2, 1], [6, 12, 1, 3], [12, 4, 1, 6], [12, 6, 2, 1], [12, 8, 1, 3], [12, 12, 1, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 567840, 'exponent': 12, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, -1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '144.192', 'hash': 963, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 6, 6], 'inner_gens': [[1, 2, 148, 168], [1, 2, 164, 24], [145, 154, 4, 120], [145, 2, 196, 24]], 'inner_hash': 192, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'D_6^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 16], [4, 9], [8, 1]], 'label': '288.963', '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.D6^2', 'ngens': 7, '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': 22, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 42, 'number_divisions': 40, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 138, 'number_subgroup_classes': 311, 'number_subgroups': 1026, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 43], [3, 8], [4, 84], [6, 56], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 1, 0], 'outer_gens': [[145, 2, 20, 120], [1, 2, 5, 121], [217, 146, 237, 49]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 136, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 5], [8, 3]], 'representations': {'PC': {'code': 67913428953573821693248164953938569, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -3, -2, -2, -3, 1008, 3110, 1731, 58, 234, 5884, 1068, 102, 2539, 124, 2372]}, 'Perm': {'d': 22, 'gens': [51347038454810790690, 51469040988541770862, 4491668938879, 5545058991595, 7209695610612, 109724236256194560000, 160578290600792064000]}}, 'schur_multiplier': [2, 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.D_6^2', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
