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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1344.9827', 'ambient_counter': 9827, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1344.9827.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.9827', 'aut_centralizer_order': 8064, 'aut_label': '32.a1', 'aut_quo_index': 128, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 8064, 'centralizer': '4.g1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.d1', '16.e1', '16.f1', '16.g1'], 'contains': ['64.a1', '96.a1', '224.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8136, 5953, 2087, 5131], 'generators': [672, 16, 448], 'label': '1344.9827.32.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['64.a1', '96.a1', '224.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '672.1172', 'quotient_action_image': '4.2', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '42.6', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [2, 6], 'aut_gens': [[1], [13], [11]], 'aut_group': '12.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 12, 'aut_permdeg': 7, 'aut_perms': [24, 723], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [21, 1, 12, 1], [42, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', '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], [3, 1, 2], [6, 1, 2], [7, 1, 6], [14, 1, 6], [21, 1, 12], [42, 1, 12]], 'center_label': '42.6', 'center_order': 42, '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', '3.1', '7.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [7, 1, 6, 1], [14, 1, 6, 1], [21, 1, 12, 1], [42, 1, 12, 1]], 'element_repr_type': 'PC', 'elementary': 42, 'eulerian_function': 1, 'exponent': 42, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[1, 0, 12]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '42.6', 'hash': 6, 'hyperelementary': 42, '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': 12, 'irrQ_dim': 12, 'irrR_degree': 2, 'irrep_stats': [[1, 42]], 'label': '42.6', 'linC_count': 12, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 3, 'linQ_dim': 8, 'linQ_dim_count': 3, 'linR_count': 6, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C42', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 42, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 42, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2], [7, 6], [14, 6], [21, 12], [42, 12]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[13], [11]], 'outer_group': '12.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [24, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [6, 2], [12, 2]], 'representations': {'PC': {'code': 339347, 'gens': [1], 'pres': [3, -2, -3, -7, 6, 22]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [351, 2064, 1032]}, 'Perm': {'d': 12, 'gens': [39916800, 725760, 4320]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [42], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{42}', 'transitive_degree': 42, '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': 84, 'aut_gen_orders': [6, 12, 6, 6, 6, 12, 12], 'aut_gens': [[1, 2, 8, 112], [49, 674, 1060, 620], [53, 1122, 24, 1292], [709, 230, 696, 560], [677, 1126, 436, 172], [721, 450, 88, 560], [677, 230, 356, 956], [757, 674, 388, 620]], 'aut_group': None, 'aut_hash': 7051851194349206198, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96768, 'aut_permdeg': 46, 'aut_perms': [638881304812013605077721345306219725844008829497805796095, 5289325927106019875531847612675023499509275749736460826320, 2009429917190396401013594020724661842171962447379201682554, 3204460980097971763885437736805394103219192581110713331288, 4771220472604210885281362020301414842338388620174974607176, 3186017724290819919538708921232057025653873746850484902551, 2305314613255401631334919230421731256044154292770749330833], 'aut_phi_ratio': 252.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 28, 1, 1], [2, 84, 3, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 2, 3, 1], [4, 28, 3, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 3, 1], [6, 28, 2, 1], [7, 2, 3, 1], [8, 6, 2, 1], [8, 12, 3, 1], [12, 4, 1, 1], [12, 4, 3, 1], [12, 28, 6, 1], [14, 2, 3, 1], [14, 4, 9, 1], [21, 4, 3, 1], [28, 2, 6, 1], [28, 4, 9, 1], [42, 4, 3, 1], [42, 8, 9, 1], [56, 6, 12, 1], [56, 12, 18, 1], [84, 4, 6, 1], [84, 8, 9, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{42}\\times A_4).C_6.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': 42, 'autcentquo_group': None, 'autcentquo_hash': 4137113322461592796, 'autcentquo_nilpotent': False, 'autcentquo_order': 6048, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times S_3^2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 28, 1], [2, 84, 3], [3, 2, 1], [4, 2, 4], [4, 28, 3], [4, 84, 1], [6, 2, 1], [6, 4, 3], [6, 28, 2], [7, 2, 3], [8, 6, 2], [8, 12, 3], [12, 4, 4], [12, 28, 6], [14, 2, 3], [14, 4, 9], [21, 4, 3], [28, 2, 6], [28, 4, 9], [42, 4, 3], [42, 8, 9], [56, 6, 12], [56, 12, 18], [84, 4, 6], [84, 8, 9]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '672.1172', 'commutator_count': 1, 'commutator_label': '84.6', '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': 9827, '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, 28, 1, 1], [2, 84, 1, 3], [3, 2, 1, 1], [4, 2, 1, 4], [4, 28, 1, 3], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 3], [6, 28, 2, 1], [7, 2, 3, 1], [8, 6, 2, 1], [8, 12, 1, 3], [12, 4, 1, 4], [12, 28, 2, 3], [14, 2, 3, 1], [14, 4, 3, 3], [21, 4, 3, 1], [28, 2, 6, 1], [28, 4, 3, 3], [42, 4, 3, 1], [42, 8, 3, 3], [56, 6, 12, 1], [56, 12, 6, 3], [84, 4, 6, 1], [84, 8, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9959040, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '336.219', 'hash': 9827, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 4, 14, 6], 'inner_gens': [[1, 6, 776, 112], [677, 2, 8, 560], [689, 2, 8, 784], [1, 898, 680, 112]], 'inner_hash': 1172, 'inner_nilpotent': False, 'inner_order': 672, 'inner_split': True, 'inner_tex': 'D_{42}:C_2^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 68], [4, 38], [8, 7]], 'label': '1344.9827', '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': 'C84.C2^4', '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': 30, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 129, 'number_divisions': 56, 'number_normal_subgroups': 152, 'number_subgroup_autclasses': 216, 'number_subgroup_classes': 516, 'number_subgroups': 4772, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 287], [3, 2], [4, 176], [6, 70], [7, 6], [8, 48], [12, 184], [14, 42], [21, 12], [28, 48], [42, 84], [56, 288], [84, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6, 6], 'outer_gen_pows': [0, 336, 0, 0], 'outer_gens': [[1, 2, 8, 560], [1, 674, 344, 112], [1, 678, 24, 112], [1, 6, 404, 172]], 'outer_group': '144.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 12, 'outer_perms': [126, 40284846, 128177569, 168018768], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6^2:C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 26, '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, 4], [6, 8], [8, 2], [12, 12], [48, 2]], 'representations': {'PC': {'code': 8020324940482114554518688159483986295271455365176930873, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -7, -2, -2, -3, 97, 41, 16226, 4050, 24835, 91, 3844, 13453, 4733, 141, 31374, 166, 28687]}, 'Perm': {'d': 26, 'gens': [621574835364392082572401, 358853980172015, 4579695696049, 5994942718867, 7217571701309, 8707980666344, 6758061133824000, 16754357281155028254720000]}}, '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_{84}.C_2^4', 'transitive_degree': 336, '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': 4, 'aut_exponent': 24, 'aut_gen_orders': [12, 4], 'aut_gens': [[2565, 517, 1537, 2577], [517, 2593, 1553, 529], [2597, 2561, 1569, 529]], 'aut_group': '3072.dx', 'aut_hash': 2019763691454065160, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 16, 'aut_perms': [11404422904581, 2678277315556], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 2, 8, 1], [4, 2, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6:(C_2\\times S_4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '1536.408640869', 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_4', '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, 8], [4, 2, 4]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 46, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 8], [4, 2, 1, 4]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 105, 'exponent': 4, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '16.14', 'hash': 46, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 1, 2, 2], 'inner_gens': [[2565, 517, 1537, 2577], [2565, 517, 1537, 2577], [2565, 517, 1537, 2609], [2565, 517, 1569, 2577]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4]], 'label': '32.46', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 192, 'linQ_dim': 4, 'linQ_dim_count': 192, 'linR_count': 192, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*D4', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 20, 'number_divisions': 20, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 118, 'number_subgroups': 158, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 23], [4, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [513, 2577, 513, 513, 513, 513, 513, 513, 513], 'outer_gens': [[2561, 517, 1537, 2577], [2565, 517, 3601, 2577], [2561, 2565, 1537, 2577], [2597, 549, 3585, 2577], [2597, 517, 1541, 2577], [2597, 549, 1537, 529], [2597, 517, 1537, 2581], [2565, 517, 3585, 2577], [2565, 517, 1541, 2577]], 'outer_group': '768.1090070', 'outer_hash': 1090070, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [41909165, 41141520, 727204, 182610863, 138989536, 135359400, 101693640, 182610840, 138989520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5:S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4]], 'representations': {'PC': {'code': 542728, 'gens': [1, 2, 3, 4], 'pres': [5, -2, 2, 2, 2, -2, 133, 58]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931074, 7233746, 7233586, 7115160]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [34876415, 29555524, 28816400, 14811013, 28233362]}, 'GLZq': {'d': 2, 'q': 8, 'gens': [2561, 529, 2565, 1537, 545]}, 'Perm': {'d': 8, 'gens': [1567, 5160, 11536, 23, 11520]}}, '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\\times D_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
