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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.13721', 'ambient_counter': 13721, 'ambient_order': 384, 'ambient_tex': '(C_4\\times D_4).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 96, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13721.4.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.17', 'subgroup_hash': 17, 'subgroup_order': 96, 'subgroup_tex': 'C_4.D_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.13721', 'aut_centralizer_order': 16, 'aut_label': '4.bb1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '384.20133', 'aut_weyl_index': 16, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.l1.a1', '2.n1.a1'], 'contains': ['8.h1.a1', '8.j1.a1', '8.q1.a1', '12.bh1.a1'], 'core': '4.bb1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6115, 2772, 6367, 6689, 7004, 6483, 7247, 6489], 'generators': [35, 128, 16, 36, 216, 192], 'label': '384.13721.4.bb1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.bb1.a1', 'normal_contained_in': ['2.b1.a1', '2.n1.a1', '2.l1.a1'], 'normal_contains': ['8.h1.a1', '8.j1.a1', '8.q1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.bb1.a1', 'projective_image': '96.209', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '96.209'}
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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': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 2, 12], 'aut_gens': [[1, 2, 16], [1, 10, 16], [57, 2, 16], [1, 50, 16], [1, 62, 16], [1, 2, 80], [53, 34, 16]], 'aut_group': '384.20133', 'aut_hash': 20133, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 13, 'aut_perms': [1, 126, 288, 3628926, 5041, 1041510960], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 2, 1], [4, 12, 2, 1], [6, 2, 1, 3], [8, 6, 4, 1], [12, 4, 1, 2], [12, 4, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{12}:C_2^5', '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': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 2, 2], [4, 4, 2], [4, 12, 2], [6, 2, 3], [8, 6, 4], [12, 4, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 2, 1], [4, 12, 1, 2], [6, 2, 1, 3], [8, 6, 4, 1], [12, 4, 1, 2], [12, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 24, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '12.4', 'hash': 17, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 54, 16], [61, 2, 80], [1, 34, 16]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [4, 2]], 'label': '96.17', 'linC_count': 16, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 6, 'linQ_dim': 8, 'linQ_dim_count': 8, 'linR_count': 6, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4.D12', 'ngens': 6, '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': 16, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 24, 'number_divisions': 17, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 38, 'number_subgroup_classes': 42, 'number_subgroups': 90, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 36], [6, 6], [8, 24], [12, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 4, 0, 0], 'outer_gens': [[1, 10, 16], [53, 2, 16], [49, 2, 16], [1, 50, 16]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 7]], 'representations': {'PC': {'code': 5151313018440513232321, 'gens': [1, 2, 5], 'pres': [6, -2, -2, -2, -2, -2, -3, 288, 649, 31, 218, 50, 1210, 88, 1163]}, 'GLZN': {'d': 2, 'p': 15, 'gens': [4044, 5458, 46133, 13504, 37136, 38326]}, 'Perm': {'d': 15, 'gens': [87657662492, 174835586813, 274467916800, 274467930107, 19342, 3991680]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4.D_{12}', 'transitive_degree': 96, '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': 12, 'aut_gen_orders': [2, 12, 6, 2, 6, 12, 2, 6, 4, 2, 6], 'aut_gens': [[1, 2, 4, 32], [193, 2, 212, 240], [201, 258, 276, 224], [193, 322, 332, 32], [209, 194, 196, 240], [17, 82, 284, 48], [201, 82, 84, 224], [25, 146, 156, 160], [193, 146, 156, 32], [217, 18, 212, 368], [209, 18, 20, 240], [209, 258, 84, 48]], 'aut_group': None, 'aut_hash': 2404398907887337476, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 32, 'aut_perms': [1536572109773150244677585626704, 20301949765872344856376585407083225, 8604833472767952334537582123013367, 216218606011079788328550347061054727, 40363722710674252689302124944710504, 254908979055907699425897355242600930, 152009436521045901172327338456908670, 155970763811233431980623493472944005, 239596214019792566919523376813144227, 240303838121552857354067282406359610, 20302571640064105386896384751949649], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 2, 1], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 6, 2, 2], [4, 8, 1, 2], [4, 12, 1, 1], [4, 12, 2, 2], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 2, 1], [8, 4, 2, 1], [8, 8, 1, 1], [8, 12, 2, 1], [8, 24, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 1], [12, 16, 1, 2], [24, 8, 2, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^3.C_2^6.C_2^2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 2], [2, 12, 1], [3, 2, 1], [4, 2, 2], [4, 4, 4], [4, 6, 4], [4, 8, 2], [4, 12, 5], [4, 24, 2], [6, 2, 3], [6, 8, 2], [8, 4, 2], [8, 8, 1], [8, 12, 2], [8, 24, 1], [12, 4, 4], [12, 8, 3], [12, 16, 2], [24, 8, 4]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.209', 'commutator_count': 1, 'commutator_label': '24.9', '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', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 13721, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 2], [2, 12, 1, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 4, 2, 1], [4, 6, 2, 2], [4, 8, 1, 2], [4, 12, 1, 3], [4, 12, 2, 1], [4, 24, 1, 2], [6, 2, 1, 3], [6, 8, 1, 2], [8, 4, 2, 1], [8, 8, 1, 1], [8, 12, 2, 1], [8, 24, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 8, 1, 1], [12, 8, 2, 1], [12, 16, 1, 2], [24, 8, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1048320, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '48.51', 'hash': 13721, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 4, 6], 'inner_gens': [[1, 2, 12, 32], [1, 2, 4, 176], [25, 2, 4, 352], [1, 274, 68, 32]], 'inner_hash': 209, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': None, 'inner_tex': 'D_4\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 20], [4, 14], [8, 1]], 'label': '384.13721', 'linC_count': 32, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 10, 'linQ_dim': 14, 'linQ_dim_count': 32, 'linR_count': 30, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C4*D4).D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 109, 'number_conjugacy_classes': 51, 'number_divisions': 41, 'number_normal_subgroups': 115, 'number_subgroup_autclasses': 338, 'number_subgroup_classes': 372, 'number_subgroups': 1110, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 23], [3, 2], [4, 168], [6, 22], [8, 64], [12, 72], [24, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 264, 128, 0, 264, 256], 'outer_gens': [[193, 2, 212, 240], [201, 258, 276, 224], [193, 322, 332, 32], [209, 194, 196, 240], [201, 82, 84, 224], [209, 258, 84, 48]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1986736653611805572127286873536947066319250840854104201700743011418544733947514671441768, 4248473297564191751083406974048467761233919819854070242389359854110385789664105501027017, 6264556666921829552188280992571796524248572730719809401346541701292297443463163578366856, 8284840794291001210136325287161314524830038015281662860335425187218051290618868960348207, 12313555714353916482624769204531964951635690915729736249471635856317484891492819079990508, 18357332328741003960976796697653736907850535733714369523988208812031864371409197465600000], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 8], [8, 4], [16, 1]], 'representations': {'PC': {'code': 90894005787658698375853854586611532575239681, 'gens': [1, 2, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 1545, 290, 66, 771, 91, 4237, 4245, 141, 8974, 4502, 166, 8207, 4119]}, 'Perm': {'d': 27, 'gens': [451768756378589506346646985, 870651234558726603050401465, 78385920770286960863155200, 868789633897037315063399281, 12136560, 1307370618174645277864934400, 1726915190629220826012979200, 3]}}, '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_4\\times D_4).D_6', 'transitive_degree': 192, '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': '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}
