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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '256.17397', 'ambient_counter': 17397, 'ambient_order': 256, 'ambient_tex': 'C_2^2.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 265, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.17397.64.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.203', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 203, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.17397', 'aut_centralizer_order': None, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '32.d1', '32.e1', '32.f1', '32.g1', '32.r1', '32.s1', '32.t1', '32.u1', '32.v1', '32.w1'], 'contains': ['128.a1', '128.c1'], 'core': '64.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2667, 6090, 2662, 6203], 'generators': [72, 64], 'label': '256.17397.64.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '64.b1', 'normal_contained_in': ['32.c1', '32.d1', '32.e1', '32.f1', '32.g1'], 'normal_contains': ['128.a1'], 'normalizer': '1.a1', 'old_label': '64.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': 8, 'aut_gen_orders': [8, 2, 8, 4, 2, 4, 4, 4], 'aut_gens': [[1, 2, 4, 16, 128], [233, 139, 108, 49, 200], [1, 34, 44, 112, 192], [169, 171, 36, 57, 200], [225, 35, 236, 145, 136], [9, 139, 108, 209, 200], [169, 98, 164, 184, 128], [161, 35, 172, 241, 136], [169, 98, 164, 184, 128]], 'aut_group': None, 'aut_hash': 6958122025019133529, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 40, 'aut_perms': [18785214724329937991705650142497949839530082166, 812141712746367711726011618806419931522942621415, 502432434896921340706890439817073114081547030260, 16619736727235786282924130389576135468266478880, 18781022208076784377278098915193919130242165224, 219035214251499903913239698907452531868302554205, 179803165370586360322605580015957707398806174107, 219035214251499903913239698907452531868302554205], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 2, 2, 1], [2, 4, 2, 1], [2, 4, 4, 1], [2, 8, 1, 1], [2, 8, 2, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 2, 1], [4, 8, 1, 1], [4, 8, 2, 1], [4, 8, 4, 2], [4, 16, 1, 2], [8, 8, 2, 1], [8, 8, 4, 1], [8, 16, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_2^4.C_2^5.C_2^2', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '256.55643', 'autcentquo_hash': 55643, 'autcentquo_nilpotent': True, 'autcentquo_order': 256, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^5:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 4, 6], [2, 8, 3], [4, 2, 4], [4, 4, 2], [4, 8, 11], [4, 16, 2], [8, 8, 6], [8, 16, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.1142', 'commutator_count': 1, 'commutator_label': '16.10', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 17397, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 4, 1, 6], [2, 8, 1, 3], [4, 2, 1, 4], [4, 4, 1, 2], [4, 8, 1, 7], [4, 8, 2, 2], [4, 16, 1, 2], [8, 8, 1, 4], [8, 8, 2, 1], [8, 16, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 322560, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[8, 0, 2]], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '16.14', 'hash': 17397, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 4, 2], 'inner_gens': [[1, 2, 76, 16, 192], [1, 2, 132, 112, 128], [73, 130, 4, 176, 192], [1, 34, 228, 16, 128], [65, 2, 68, 16, 128]], 'inner_hash': 1142, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': True, 'inner_tex': 'C_2^4:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 20], [4, 2], [8, 2]], 'label': '256.17397', '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.D4^2', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, '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': 21, 'number_characteristic_subgroups': 39, 'number_conjugacy_classes': 40, 'number_divisions': 37, 'number_normal_subgroups': 133, 'number_subgroup_autclasses': 295, 'number_subgroup_classes': 668, 'number_subgroups': 1799, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 55], [4, 136], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 96, 40, 8], 'outer_gens': [[1, 66, 4, 16, 128], [1, 98, 36, 16, 128], [73, 171, 36, 153, 200], [233, 139, 68, 57, 200]], 'outer_group': '32.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 16, 'outer_perms': [5800737348096, 12845504030154, 13020341237279, 18182689455561], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 32, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 4], [16, 1]], 'representations': {'PC': {'code': 5465869407996220034286556477578172162356, 'gens': [1, 2, 3, 5, 8], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 1826, 1594, 66, 1163, 2252, 1780, 428, 116, 2317, 1173, 141, 12295, 3095]}, 'Perm': {'d': 32, 'gens': [16985058263327362631807751265019393, 101975790215895262428145539430230352, 135955991562369039230941840932864000, 67977995780968282257602718863923200, 33988952657421979333957955978023663, 25903229681844523013167, 25199055155429228508132113875036937, 8231691320578226211046411712681647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2.D_4^2', 'transitive_degree': 32, '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': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2], 'aut_gens': [[3591, 1827, 2879, 529], [3591, 801, 1833, 1555], [3591, 1827, 827, 529], [3591, 1795, 2847, 2613], [1539, 1827, 795, 529], [3591, 1795, 779, 2581], [3591, 3879, 795, 2581], [3591, 3879, 795, 529], [3591, 1827, 3853, 529], [3591, 3847, 827, 529], [3591, 769, 3885, 529], [1571, 1795, 2847, 529], [3591, 1827, 795, 529]], 'aut_group': '4096.brr', 'aut_hash': 3229352106809273273, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 24, 'aut_perms': [71975355662698285575000, 311916349939454594634816, 317548516849264815217920, 363143489500390933335248, 524774402571214059299136, 381791987338677469799040, 19198290187247733285120, 337768488344369037295303, 16945422927676164633600, 121630514163558298219576, 6221365873248035327413, 363722565343587990244432], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 4, 1], [2, 4, 4, 1], [4, 2, 4, 2], [4, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.D_4^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 8092891664598236742, 'autcent_nilpotent': True, 'autcent_order': 2048, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8.C_2^3', '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], [2, 4, 4], [4, 2, 8], [4, 4, 4]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '8.5', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 203, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['32.28', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [2, 4, 1, 4], [4, 2, 1, 4], [4, 2, 2, 2], [4, 4, 1, 4]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 1260, 'exponent': 4, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '16.14', 'hash': 203, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2, 2], 'inner_gens': [[3591, 1827, 2879, 529], [3591, 1827, 827, 529], [3591, 3847, 2879, 561], [3591, 1827, 2847, 529]], 'inner_hash': 5, 'inner_nilpotent': True, 'inner_order': 8, 'inner_split': False, 'inner_tex': 'C_2^3', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12]], 'label': '64.203', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, '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': 'C2^3:D4', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 13, 'number_conjugacy_classes': 28, 'number_divisions': 26, 'number_normal_subgroups': 97, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 213, 'number_subgroups': 353, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 31], [4, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 2, 4, 4], 'outer_gen_pows': [513, 513, 513, 513, 513], 'outer_gens': [[1571, 1827, 3901, 1587], [1571, 2853, 779, 2581], [3591, 1795, 1801, 3639], [3623, 2853, 827, 2613], [1539, 3879, 1833, 1555]], 'outer_group': '512.752493', 'outer_hash': 7064241158567032655, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [151269797198894022509122422879748149862872630022491922613285601137796329124078773729062089446689578695387044967822067735544251563951521744801746560910185496165509924933083104797774869065049258209330598093434130785505, 352243192704781459268706288589426788116764464482221640638255897771219752220198977539156305413509400141701095662544585638479618863591181539230530934425703631093121303722857996862657312533315385377907077709774471635361, 7372588316443189115882930465709745039387355955527156745326047912022076713972413406531606161615038431961422283704405166820478793462804163462315763042022936055196802885166616066417100275038714601312988182066409624, 201080627974242774406948584712245358925489920433384479952439031368808406110718728664502067593274404381079726192631737196636079791853108669071826765487843049230473556157129366346331817650129149740197056369147439526992, 6216871315043012317085344369497771754589618450890293299282089665473476530458165777333814514525602072503833862076198394293013172801725864576213028860532891823462409623344390447878758684883541648128643894959679800153], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4.C_2^5', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 2]], 'representations': {'PC': {'code': 292129113108, 'gens': [1, 2, 3, 5], 'pres': [6, 2, 2, 2, 2, 2, 2, 116, 50, 376, 88]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705686952884, 141602720900, 705946294634, 706204575934]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 156, 8645, 5523, 2665, 1801]}, 'GLZq': {'d': 2, 'q': 8, 'gens': [2853, 529, 1817, 1827, 545, 1539]}, 'Perm': {'d': 10, 'gens': [5165, 367929, 806520, 368056, 16, 367920]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3:D_4', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
