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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.10898', 'ambient_counter': 10898, 'ambient_order': 960, 'ambient_tex': 'F_5\\times C_2.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': True, 'core_order': 240, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10898.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '240.102', 'subgroup_hash': 102, 'subgroup_order': 240, 'subgroup_tex': 'C_{10}.S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.10898', 'aut_centralizer_order': 10, 'aut_label': '4.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '192.1469', 'aut_weyl_index': 10, 'centralizer': '96.a1.a1', 'complements': ['240.h1.b1', '240.h1.a1', '240.f1.a1', '240.g1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.a1.a1', '12.l1.a1', '16.b1.a1', '20.a1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9319, 3277, 1066, 1182, 5045, 8870, 8871, 1130], 'generators': [1, 480, 8, 744, 192, 720], 'label': '960.10898.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['8.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '480.1189', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.186'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', '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, 12, 2, 2], 'aut_gens': [[93811, 493131, 804384], [175277, 431381, 804384], [860493, 493131, 804384], [233493, 493131, 863968], [175277, 236057, 804384], [93811, 193929, 804384]], 'aut_group': '192.1469', 'aut_hash': 1469, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 192, 'aut_permdeg': 10, 'aut_perms': [40320, 1, 45510, 367920, 1174320], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 8, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [5, 1, 4, 1], [6, 8, 1, 1], [8, 6, 2, 1], [10, 1, 4, 1], [15, 8, 4, 1], [20, 6, 4, 1], [20, 12, 4, 1], [30, 8, 4, 1], [40, 6, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_4', '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], [3, 8, 1], [4, 6, 1], [4, 12, 1], [5, 1, 4], [6, 8, 1], [8, 6, 2], [10, 1, 4], [15, 8, 4], [20, 6, 4], [20, 12, 4], [30, 8, 4], [40, 6, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '24.12', 'commutator_count': 1, 'commutator_label': '24.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 102, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['48.28', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 8, 1, 1], [4, 6, 1, 1], [4, 12, 1, 1], [5, 1, 4, 1], [6, 8, 1, 1], [8, 6, 2, 1], [10, 1, 4, 1], [15, 8, 4, 1], [20, 6, 4, 1], [20, 12, 4, 1], [30, 8, 4, 1], [40, 6, 8, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 108, 'exponent': 120, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[2, 0, 8], [4, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '120.37', 'hash': 102, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 3, 1], 'inner_gens': [[93811, 922095, 804384], [233493, 493131, 804384], [93811, 493131, 804384]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'S_4', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 4, 'irrep_stats': [[1, 10], [2, 15], [3, 10], [4, 5]], 'label': '240.102', 'linC_count': 8, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 12, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C10.S4', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 40, 'number_divisions': 14, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 26, 'number_subgroups': 70, 'old_label': None, 'order': 240, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 18], [5, 4], [6, 8], [8, 12], [10, 4], [15, 32], [20, 72], [30, 32], [40, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [29792, 29792], 'outer_gens': [[860493, 493131, 804384], [93811, 493131, 863968]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [3, 2], [4, 4], [8, 1], [12, 2], [16, 2]], 'representations': {'PC': {'code': 80709308904830168126992709308675, 'gens': [1, 2, 3, 4], 'pres': [6, -2, -3, -2, 2, -2, -5, 720, 49, 3350, 548, 374, 3171, 225, 543, 69, 88]}, 'GLFp': {'d': 2, 'p': 31, 'gens': [93811, 493131, 804384]}, 'Perm': {'d': 21, 'gens': [2824580909745750960, 33, 40600003817853360, 5374589565653728560, 7952930666349143040, 10514844129330747360]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}.S_4', 'transitive_degree': 80, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 2, 2, 12, 10, 2], 'aut_gens': [[1, 2, 24, 48], [17, 10, 504, 72], [481, 482, 24, 48], [1, 482, 24, 48], [9, 2, 240, 360], [265, 170, 504, 48], [745, 242, 24, 528]], 'aut_group': '1920.240396', 'aut_hash': 3782145897709286038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 22, 'aut_perms': [160936486510495179032, 148427319603752338772, 74349588061, 82565894122045943108, 4987764641877018692, 212155771422485324312], 'aut_phi_ratio': 7.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 8, 1, 1], [4, 5, 2, 2], [4, 6, 1, 1], [4, 12, 1, 1], [4, 30, 1, 3], [4, 60, 1, 3], [5, 4, 1, 1], [6, 8, 1, 1], [6, 40, 1, 2], [8, 6, 2, 1], [8, 30, 2, 3], [10, 4, 1, 1], [12, 40, 2, 2], [15, 32, 1, 1], [20, 24, 1, 1], [20, 48, 1, 1], [30, 32, 1, 1], [40, 24, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times F_5\\times S_4', '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': 60, 'autcentquo_group': '480.1189', 'autcentquo_hash': 1189, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [3, 8, 1], [4, 5, 4], [4, 6, 1], [4, 12, 1], [4, 30, 3], [4, 60, 3], [5, 4, 1], [6, 8, 1], [6, 40, 2], [8, 6, 2], [8, 30, 6], [10, 4, 1], [12, 40, 4], [15, 32, 1], [20, 24, 1], [20, 48, 1], [30, 32, 1], [40, 24, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '480.1189', 'commutator_count': 1, 'commutator_label': '120.15', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10898, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['20.3', 1], ['48.28', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 8, 1, 1], [4, 5, 2, 2], [4, 6, 1, 1], [4, 12, 1, 1], [4, 30, 1, 1], [4, 30, 2, 1], [4, 60, 1, 1], [4, 60, 2, 1], [5, 4, 1, 1], [6, 8, 1, 1], [6, 40, 1, 2], [8, 6, 2, 1], [8, 30, 2, 1], [8, 30, 4, 1], [10, 4, 1, 1], [12, 40, 2, 2], [15, 32, 1, 1], [20, 24, 1, 1], [20, 48, 1, 1], [30, 32, 1, 1], [40, 24, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, -1, 2], [16, -1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '480.1189', 'hash': 10898, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 12, 2, 10], 'inner_gens': [[1, 10, 720, 312], [17, 2, 744, 600], [745, 242, 24, 528], [265, 938, 504, 48]], 'inner_hash': 1189, 'inner_nilpotent': False, 'inner_order': 480, 'inner_split': True, 'inner_tex': 'F_5\\times S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 12], [3, 8], [4, 6], [8, 3], [12, 2], [16, 1]], 'label': '960.10898', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'F5*C2.S4', 'ngens': 8, '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': 31, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 40, 'number_divisions': 28, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 134, 'number_subgroup_classes': 140, 'number_subgroups': 1198, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 11], [3, 8], [4, 308], [5, 4], [6, 88], [8, 192], [10, 4], [12, 160], [15, 32], [20, 72], [30, 32], [40, 48]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 482, 24, 48], [1, 26, 504, 528]], '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': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 7], [6, 2], [8, 3], [12, 2], [16, 2]], 'representations': {'PC': {'code': 6719295704378429454534285939689781794092755915739209425194503478483958418047235, 'gens': [1, 2, 5, 6], 'pres': [8, -2, -2, -2, -3, -2, 2, -2, -5, 3840, 161, 41, 482, 66, 515, 28804, 14892, 2420, 3748, 836, 14981, 14413, 11253, 4781, 1093, 141, 18830, 12118, 166, 12303, 12311]}, 'GLZN': {'d': 2, 'p': 35, 'gens': [1134191, 686886, 43121, 1243383, 184474, 42904, 257256, 502806]}, 'Perm': {'d': 21, 'gens': [9, 2839204369220083200, 16, 9627899287432320, 34, 5374945241585065440, 7953015653212775760, 10516264090295443920]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'F_5\\times C_2.S_4', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '4.1', '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], [3]], '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], [4, 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], [4, 1, 2]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, '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': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 4, 'exponents_of_order': [2], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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, 4]], 'label': '4.1', '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': 'C4', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 1], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3]], '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': 4, 'pgroup': 2, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -2, -2, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [56, 15], 'family': 'CSOPlus'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [21]}, 'Perm': {'d': 4, 'gens': [22, 7]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
