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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.7784', 'ambient_counter': 7784, 'ambient_order': 1344, 'ambient_tex': '(C_2\\times D_{28}):D_6', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 336, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.7784.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.z1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.42', 'subgroup_hash': 42, 'subgroup_order': 336, 'subgroup_tex': 'C_6.D_{28}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.7784', 'aut_centralizer_order': None, 'aut_label': '4.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '336.a1.a1', 'complements': ['336.bc1.a1', '336.bc1.c1', '336.bc1.b1', '336.bc1.d1', '336.bd1.a1', '336.bd1.c1', '336.bd1.d1', '336.bd1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'contains': ['8.e1.a1', '8.j1.a1', '8.n1.a1', '12.z1.a1', '28.bb1.a1'], 'core': '4.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [722, 192, 8, 672, 4, 448], 'label': '1344.7784.4.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.z1.a1', 'normal_contained_in': ['2.f1.a1', '2.j1.a1', '2.l1.a1'], 'normal_contains': ['8.e1.a1', '8.j1.a1', '8.n1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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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': 42, 'aut_gen_orders': [14, 42, 6, 2, 6, 6, 6], 'aut_gens': [[1, 4, 24], [3, 214, 24], [185, 78, 24], [171, 188, 120], [187, 20, 24], [185, 30, 312], [187, 286, 72], [17, 46, 72]], 'aut_group': None, 'aut_hash': 6896085666905541017, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4032, 'aut_permdeg': 40, 'aut_perms': [165226114444121449421449400440700194686703919939, 554921391360580478082346460751105673924877682585, 512204197671714250424837288535504492622537587222, 694065159970761166250097648351216089462223231360, 570727402868831972650829856373075929538663847007, 707227145656872370242104134008625248121452989086, 232736544693379298106781055318075060884351515430], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 14, 2, 1], [3, 2, 1, 1], [4, 6, 2, 1], [4, 42, 2, 1], [6, 2, 1, 3], [6, 14, 4, 1], [7, 2, 3, 1], [14, 2, 3, 3], [21, 4, 3, 1], [28, 6, 12, 1], [42, 4, 3, 3]], 'aut_supersolvable': True, 'aut_tex': 'C_2^4\\times S_3\\times F_7', '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': 42, 'autcentquo_group': '252.26', 'autcentquo_hash': 26, 'autcentquo_nilpotent': False, 'autcentquo_order': 252, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 14, 2], [3, 2, 1], [4, 6, 2], [4, 42, 2], [6, 2, 3], [6, 14, 4], [7, 2, 3], [14, 2, 9], [21, 4, 3], [28, 6, 12], [42, 4, 9]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '84.8', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 42, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 14, 1, 2], [3, 2, 1, 1], [4, 6, 2, 1], [4, 42, 2, 1], [6, 2, 1, 3], [6, 14, 2, 2], [7, 2, 3, 1], [14, 2, 3, 3], [21, 4, 3, 1], [28, 6, 12, 1], [42, 4, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '84.8', 'hash': 42, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 6, 7], 'inner_gens': [[1, 188, 24], [177, 4, 312], [1, 52, 24]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 84, 'inner_split': True, 'inner_tex': 'S_3\\times D_7', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 34], [4, 12]], 'label': '336.42', 'linC_count': 72, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 8, 'linQ_dim': 12, 'linQ_dim_count': 40, 'linR_count': 63, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.D28', 'ngens': 6, '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': 21, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 54, 'number_divisions': 23, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 68, 'number_subgroups': 348, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 2], [4, 96], [6, 62], [7, 6], [14, 18], [21, 12], [28, 72], [42, 36]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 20, 24], [3, 4, 24], [169, 4, 24], [169, 6, 72]], 'outer_group': '48.52', 'outer_hash': 52, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [40320, 3628800, 24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 2], [6, 2], [12, 7]], 'representations': {'PC': {'code': 353241883890009803603813225, 'gens': [1, 3, 5], 'pres': [6, -2, -2, -2, -3, -2, -7, 12, 3386, 50, 387, 2356, 88, 2609]}, 'GLZN': {'d': 2, 'p': 52, 'gens': [3515225, 3833636, 5236617, 4983177, 1327395, 6974867]}, 'Perm': {'d': 18, 'gens': [3669247, 21016674967680, 186810624000, 7983360, 376610217984000, 973]}}, 'schur_multiplier': [2, 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_6.D_{28}', 'transitive_degree': 168, '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, 4, 16], [1, 2, 452, 208], [1, 2, 4, 656], [9, 2, 4, 656], [673, 2, 4, 656], [1, 10, 4, 656], [1, 674, 4, 656], [1, 2, 12, 656], [1, 2, 676, 656], [1, 2, 4, 664], [1, 2, 4, 1328], [1, 2, 4, 976], [1, 194, 4, 16]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 64512, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 2, 1], [2, 6, 2, 1], [2, 14, 2, 1], [2, 28, 1, 2], [2, 84, 1, 1], [3, 2, 1, 1], [4, 4, 1, 2], [4, 6, 2, 2], [4, 12, 1, 1], [4, 28, 1, 1], [4, 42, 2, 1], [4, 84, 1, 2], [6, 2, 1, 3], [6, 4, 2, 1], [6, 28, 2, 2], [6, 56, 1, 1], [7, 2, 3, 1], [12, 8, 1, 2], [12, 56, 1, 1], [14, 2, 3, 3], [14, 4, 6, 1], [14, 12, 6, 1], [21, 4, 3, 1], [28, 4, 6, 2], [28, 6, 12, 1], [28, 12, 6, 2], [42, 4, 3, 3], [42, 8, 6, 1], [84, 8, 6, 2]], '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, 2, 2], [2, 6, 2], [2, 14, 2], [2, 28, 2], [2, 84, 1], [3, 2, 1], [4, 4, 2], [4, 6, 4], [4, 12, 1], [4, 28, 1], [4, 42, 2], [4, 84, 2], [6, 2, 3], [6, 4, 2], [6, 28, 4], [6, 56, 1], [7, 2, 3], [12, 8, 2], [12, 56, 1], [14, 2, 9], [14, 4, 6], [14, 12, 6], [21, 4, 3], [28, 4, 12], [28, 6, 12], [28, 12, 12], [42, 4, 9], [42, 8, 6], [84, 8, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '336.219', 'commutator_count': 1, 'commutator_label': '84.15', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 7784, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 6, 1, 2], [2, 14, 1, 2], [2, 28, 1, 2], [2, 84, 1, 1], [3, 2, 1, 1], [4, 4, 1, 2], [4, 6, 1, 2], [4, 6, 2, 1], [4, 12, 1, 1], [4, 28, 1, 1], [4, 42, 2, 1], [4, 84, 1, 2], [6, 2, 1, 3], [6, 4, 1, 2], [6, 28, 1, 2], [6, 28, 2, 1], [6, 56, 1, 1], [7, 2, 3, 1], [12, 8, 1, 2], [12, 56, 1, 1], [14, 2, 3, 3], [14, 4, 3, 2], [14, 12, 3, 2], [21, 4, 3, 1], [28, 4, 6, 2], [28, 6, 12, 1], [28, 12, 3, 2], [28, 12, 6, 1], [42, 4, 3, 3], [42, 8, 3, 2], [84, 8, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 14938560, 'exponent': 84, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '336.219', 'hash': 7784, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 336, 'inner_split': None, 'inner_tex': 'D_6\\times D_{14}', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 64], [4, 43], [8, 6]], 'label': '1344.7784', '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*D28):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, 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': 48, 'number_characteristic_subgroups': 120, 'number_conjugacy_classes': 129, 'number_divisions': 58, 'number_normal_subgroups': 148, 'number_subgroup_autclasses': 520, 'number_subgroup_classes': 668, 'number_subgroups': 6212, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 187], [3, 2], [4, 324], [6, 182], [7, 6], [12, 72], [14, 114], [21, 12], [28, 264], [42, 84], [84, 96]], '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': '192.1543', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 192, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^5\\times C_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, 12], [4, 7], [6, 8], [8, 1], [12, 8], [24, 6]], 'representations': {'PC': {'code': 18069228781767458373827965519461052168841282347964888075, 'gens': [1, 2, 3, 5], 'pres': [8, -2, -2, -2, -2, 2, -2, -3, -7, 8122, 66, 27844, 17612, 4660, 116, 9997, 11157, 141, 23310, 7190, 222, 36879]}, 'Perm': {'d': 22, 'gens': [2439325305154977144, 87665659465, 12501360, 187289716320, 87657292800, 3719544, 3, 55969571858264064000]}}, '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\\times D_{28}):D_6', 'transitive_degree': 336, '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}
