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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1632.782', 'ambient_counter': 782, 'ambient_order': 1632, 'ambient_tex': 'D_{12}.C_{68}', 'central': False, 'central_factor': False, 'centralizer_order': 136, 'characteristic': False, 'core_order': 204, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1632.782.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '204.10', 'subgroup_hash': 10, 'subgroup_order': 204, 'subgroup_tex': 'S_3\\times C_{34}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1632.782', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '192.458', 'aut_weyl_index': 16, 'centralizer': '12.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'contains': ['16.a1.a1', '16.c1.b1', '24.d1.b1', '136.b1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2029, 2489, 8482, 1512, 9301, 809, 473, 8892], 'generators': [683, 816, 1088, 96], 'label': '1632.782.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.b1', '4.c1.b1', '4.d1.a1'], 'normal_contains': ['16.a1.a1', '136.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '48.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.b1', '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': '68.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 48, 'aut_gen_orders': [2, 2, 48], 'aut_gens': [[1, 2], [103, 134], [1, 70], [171, 122]], 'aut_group': '192.458', 'aut_hash': 458, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 21, 'aut_perms': [1, 5231810321689079527, 36570358607118336048], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [3, 2, 1, 1], [6, 2, 1, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 3, 32, 1], [51, 2, 16, 1], [102, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6\\times C_{16}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '32.16', 'autcent_hash': 16, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{16}', '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, 2, 1], [6, 2, 1], [17, 1, 16], [34, 1, 16], [34, 3, 32], [51, 2, 16], [102, 2, 16]], 'center_label': '34.2', 'center_order': 34, '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', '17.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['2.1', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [6, 2, 1, 1], [17, 1, 16, 1], [34, 1, 16, 1], [34, 3, 16, 2], [51, 2, 16, 1], [102, 2, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 54, 'exponent': 102, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 17], 'faithful_reps': [[2, 0, 16]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '204.10', 'hash': 10, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 70], [137, 2]], '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': 32, 'irrQ_dim': 32, 'irrR_degree': 4, 'irrep_stats': [[1, 68], [2, 34]], 'label': '204.10', 'linC_count': 16, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 6, 'linQ_dim': 18, 'linQ_dim_count': 6, 'linR_count': 56, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'S3*C34', 'ngens': 4, '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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 102, 'number_divisions': 12, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 20, 'number_subgroups': 32, 'old_label': None, 'order': 204, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 7], [3, 2], [6, 2], [17, 16], [34, 112], [51, 32], [102, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 16, 'outer_gen_orders': [2, 16], 'outer_gen_pows': [0, 0], 'outer_gens': [[103, 134], [1, 146]], 'outer_group': '32.16', 'outer_hash': 16, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 18, 'outer_perms': [358565759719996, 1495530904623], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{16}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 17], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [16, 4], [32, 2]], 'representations': {'PC': {'code': 8030710960881695, 'gens': [1, 2], 'pres': [4, -2, -2, -3, -17, 561, 21, 1682, 46]}, 'GLFp': {'d': 2, 'p': 103, 'gens': [51358226, 10712, 24040016]}, 'Perm': {'d': 22, 'gens': [6, 1, 53652269665821260160, 30]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 34], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3\\times C_{34}', 'transitive_degree': 102, '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': '272.46', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 48, 'aut_gen_orders': [4, 16, 24, 16, 24, 16, 4], 'aut_gens': [[1, 2, 4], [817, 1227, 1277], [817, 274, 1340], [1, 546, 892], [1, 546, 1604], [1, 546, 1012], [817, 411, 1133], [1, 1227, 1629]], 'aut_group': None, 'aut_hash': 2544182652908832968, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 36, 'aut_perms': [349252573953844141885927485027431661768886, 167027204384833586388645069356895553759155, 16901008636240420565806088818059481168299, 99372865685229440400452527631149988916541, 216155688835595041501498861724828130822465, 124771262786838994824779180270283994343589, 223046638896191569585013137566477604408948], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 2, 1], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 6, 2, 1], [6, 2, 1, 1], [6, 4, 1, 1], [8, 2, 4, 1], [8, 3, 4, 1], [8, 6, 2, 1], [12, 2, 2, 1], [12, 4, 1, 1], [17, 1, 16, 1], [24, 4, 4, 1], [34, 1, 16, 1], [34, 2, 16, 1], [34, 6, 32, 1], [51, 2, 16, 1], [68, 1, 32, 1], [68, 2, 16, 1], [68, 6, 32, 1], [102, 2, 16, 1], [102, 4, 16, 1], [136, 2, 64, 1], [136, 3, 64, 1], [136, 6, 32, 1], [204, 2, 32, 1], [204, 4, 16, 1], [408, 4, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2\\times C_{16}\\times C_2^2\\times D_4)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 16, 'autcent_group': '256.55608', 'autcent_hash': 55608, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{16}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 6, 2], [3, 2, 1], [4, 1, 2], [4, 2, 1], [4, 6, 2], [6, 2, 1], [6, 4, 1], [8, 2, 4], [8, 3, 4], [8, 6, 2], [12, 2, 2], [12, 4, 1], [17, 1, 16], [24, 4, 4], [34, 1, 16], [34, 2, 16], [34, 6, 32], [51, 2, 16], [68, 1, 32], [68, 2, 16], [68, 6, 32], [102, 2, 16], [102, 4, 16], [136, 2, 64], [136, 3, 64], [136, 6, 32], [204, 2, 32], [204, 4, 16], [408, 4, 64]], 'center_label': '68.2', 'center_order': 68, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '17.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 782, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['17.1', 1], ['96.114', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 6, 1, 2], [3, 2, 1, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 6, 1, 2], [6, 2, 1, 1], [6, 4, 1, 1], [8, 2, 2, 2], [8, 3, 4, 1], [8, 6, 2, 1], [12, 2, 2, 1], [12, 4, 1, 1], [17, 1, 16, 1], [24, 4, 2, 2], [34, 1, 16, 1], [34, 2, 16, 1], [34, 6, 16, 2], [51, 2, 16, 1], [68, 1, 32, 1], [68, 2, 16, 1], [68, 6, 16, 2], [102, 2, 16, 1], [102, 4, 16, 1], [136, 2, 32, 2], [136, 3, 64, 1], [136, 6, 32, 1], [204, 2, 32, 1], [204, 4, 16, 1], [408, 4, 32, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 412608, 'exponent': 408, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 17], 'faithful_reps': [[4, 0, 32]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '408.44', 'hash': 782, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 6], 'inner_gens': [[1, 818, 820], [817, 2, 548], [817, 1090, 4]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 128, 'irrQ_dim': 128, 'irrR_degree': 8, 'irrep_stats': [[1, 272], [2, 204], [4, 34]], 'label': '1632.782', 'linC_count': 9248, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 8, 'linQ_dim': 24, 'linQ_dim_count': 8, 'linR_count': 128, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D12.C68', '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 42, 'number_conjugacy_classes': 510, 'number_divisions': 40, 'number_normal_subgroups': 74, 'number_subgroup_autclasses': 92, 'number_subgroup_classes': 124, 'number_subgroups': 228, 'old_label': None, 'order': 1632, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 16], [6, 6], [8, 32], [12, 8], [17, 16], [24, 16], [34, 240], [51, 32], [68, 256], [102, 96], [136, 512], [204, 128], [408, 256]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 16, 'outer_gen_orders': [2, 2, 2, 16], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 411, 1493], [1, 818, 4], [1, 2, 1228], [1, 2, 772]], 'outer_group': '128.2136', 'outer_hash': 2136, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 22, 'outer_perms': [355687428096000, 51090942171709440000, 121645100408832000, 1401602636313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{16}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 17], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 2], [8, 2], [16, 8], [32, 8], [64, 2], [128, 2]], 'representations': {'PC': {'code': 82920104996447471953417647260631296710463717407, 'gens': [1, 2, 3], 'pres': [7, -2, -2, -2, -2, -2, -3, -17, 11453, 17222, 5763, 58, 15354, 80, 9811, 102, 23532, 166]}, 'Perm': {'d': 36, 'gens': [10351567956098342626286933200028295168000, 22144607681913169144187802263394877440000, 32832481285392441935668919680098631680000, 22324392524313, 41977551012093356596801678721875968000000, 53804508417687063773607761113757614080000, 128047474114560000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 68], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{12}.C_{68}', 'transitive_degree': 816, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1, 2], [1, 3], [5, 3]], 'aut_group': '8.3', 'aut_hash': 3, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 4, 'aut_perms': [1, 22], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.3', 'autcent_hash': 3, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_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, 3], [4, 1, 4]], 'center_label': '8.2', 'center_order': 8, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '2.1', '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, 8]], 'label': '8.2', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 4, 'linQ_dim': 3, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C4', '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': 8, 'number_divisions': 6, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 4]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 3], [5, 3]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 6, 'pgroup': 2, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2]], 'representations': {'PC': {'code': 34, 'gens': [1, 2], 'pres': [3, -2, 2, -2, 16]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [3362, 16426]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [251, 504]}, 'Perm': {'d': 6, 'gens': [22, 120, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
