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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.9828', 'ambient_counter': 9828, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 84, 'characteristic': True, 'core_order': 168, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.9828.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.41', 'subgroup_hash': 41, 'subgroup_order': 168, 'subgroup_tex': 'Q_8\\times C_{21}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.9828', 'aut_centralizer_order': 336, 'aut_label': '8.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '288.1033', 'aut_weyl_index': 336, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1', '4.o1', '4.p1'], 'contains': ['16.c1', '24.e1', '56.e1'], 'core': '8.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [634, 9699, 1471, 9704], 'generators': [169, 448, 32, 840, 112], 'label': '1344.9828.8.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': ['4.g1'], 'normal_contains': ['16.c1', '24.e1', '56.e1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '672.1172', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '84.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 2, 2, 2], 'aut_gens': [[1, 2], [85, 35], [43, 125], [85, 2], [1, 58], [1, 86]], 'aut_group': '288.1033', 'aut_hash': 1033, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 288, 'aut_permdeg': 11, 'aut_perms': [40323, 726504, 7983360, 1680, 3669120], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 2, 3, 1], [6, 1, 2, 1], [7, 1, 6, 1], [12, 2, 6, 1], [14, 1, 6, 1], [21, 1, 12, 1], [28, 2, 18, 1], [42, 1, 12, 1], [84, 2, 36, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', '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], [3, 1, 2], [4, 2, 3], [6, 1, 2], [7, 1, 6], [12, 2, 6], [14, 1, 6], [21, 1, 12], [28, 2, 18], [42, 1, 12], [84, 2, 36]], 'center_label': '42.6', 'center_order': 42, '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', '3.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 41, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['7.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [4, 2, 1, 3], [6, 1, 2, 1], [7, 1, 6, 1], [12, 2, 2, 3], [14, 1, 6, 1], [21, 1, 12, 1], [28, 2, 6, 3], [42, 1, 12, 1], [84, 2, 12, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 32, 'exponent': 84, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[2, 0, 12]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '84.15', 'hash': 41, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 86], [85, 2]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 4, 'irrep_stats': [[1, 84], [2, 21]], 'label': '168.41', 'linC_count': 12, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 20, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'Q8*C21', 'ngens': 5, 'nilpotency_class': 2, 'nilpotent': True, '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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 105, 'number_divisions': 20, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 24, 'number_subgroups': 24, 'old_label': None, 'order': 168, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 2], [4, 6], [6, 2], [7, 6], [12, 12], [14, 6], [21, 12], [28, 36], [42, 12], [84, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [0, 2, 0], 'outer_gens': [[1, 58], [43, 50], [127, 153]], 'outer_group': '72.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [367920, 368065, 806403], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 1], [6, 4], [12, 5], [24, 1]], 'representations': {'PC': {'code': 3146747749725875627, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -3, -7, 420, 861, 26, 42, 78]}, 'GLFp': {'d': 2, 'p': 43, 'gens': [77400, 1659350]}, 'Perm': {'d': 18, 'gens': [1869015385036800, 1108921316025600, 725760, 4320, 357001369401600]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 42], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8\\times C_{21}', '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': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [4, 12, 6, 28, 6, 6, 6], 'aut_gens': [[1, 2, 4, 224], [113, 83, 53, 1177], [784, 674, 205, 1177], [1, 34, 492, 1232], [113, 163, 901, 1289], [784, 810, 613, 281], [1, 43, 21, 1289], [113, 18, 652, 1120]], 'aut_group': None, 'aut_hash': 7051851194349206198, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96768, 'aut_permdeg': 46, 'aut_perms': [3688341667176169128275825133370899381739808971822021173717, 1653906307646216700147784047734323963397994581726083309372, 3832677824903119268597542599895551817747824890956143072157, 4182039674100789802255800396425500815284870138429088849574, 5205374834962771433016312178527037827623414258397167413965, 4889835750235661969866601510371700425217615064291683581269, 5153898098472853216051455028197755360146665833644949711005], 'aut_phi_ratio': 252.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 28, 3, 1], [2, 84, 3, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 2, 3, 1], [4, 28, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 3, 1], [6, 28, 6, 1], [7, 2, 3, 1], [8, 6, 2, 1], [8, 12, 3, 1], [12, 4, 1, 1], [12, 4, 3, 1], [12, 28, 2, 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_3^2\\times F_7).C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 3], [2, 28, 3], [2, 84, 3], [3, 2, 1], [4, 2, 4], [4, 28, 1], [4, 84, 1], [6, 2, 1], [6, 4, 3], [6, 28, 6], [7, 2, 3], [8, 6, 2], [8, 12, 3], [12, 4, 4], [12, 28, 2], [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': 9828, '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, 3], [2, 84, 1, 3], [3, 2, 1, 1], [4, 2, 1, 4], [4, 28, 1, 1], [4, 84, 1, 1], [6, 2, 1, 1], [6, 4, 1, 3], [6, 28, 2, 3], [7, 2, 3, 1], [8, 6, 2, 1], [8, 12, 1, 3], [12, 4, 1, 4], [12, 28, 2, 1], [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': 9828, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [2, 2, 28, 6], 'inner_gens': [[1, 2, 116, 336], [1, 2, 220, 224], [113, 10, 4, 1120], [113, 2, 452, 224]], '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': 96, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 68], [4, 38], [8, 7]], 'label': '1344.9828', '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': 220, 'number_subgroup_classes': 536, 'number_subgroups': 5284, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 343], [3, 2], [4, 120], [6, 182], [7, 6], [8, 48], [12, 72], [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, 672, 0, 0], 'outer_gens': [[1, 2, 4, 1120], [841, 674, 4, 1120], [1, 2, 12, 224], [672, 842, 5, 1289]], 'outer_group': '144.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 12, 'outer_perms': [127, 40284720, 128177406, 168018894], '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': 1493842485832376865047223613080878875444873219464373, 'gens': [1, 2, 3, 7], 'pres': [8, 2, 2, 2, 2, 2, 7, 2, 3, 2786, 2650, 66, 3467, 91, 4172, 116, 4621, 18822, 15702, 166, 14359]}, 'Perm': {'d': 26, 'gens': [621574835364385413030019, 358761571485572, 4504465898119, 64273922472, 5914910361881, 7300903509315, 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': '4.2', '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, 6], [3, 2]], 'aut_group': '8.3', 'aut_hash': 3, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 4, 'aut_perms': [5, 9], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [4, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_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': 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, 1], [2, 2, 2], [4, 2, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, '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'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [4, 2, 1, 1]], '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': [[2, 1, 1]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '4.2', 'hash': 3, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 6], [5, 2]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 1]], 'label': '8.3', 'linC_count': 1, 'linC_degree': 2, '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': 'D4', 'ngens': 2, 'nilpotency_class': 2, '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': 5, 'number_divisions': 5, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 8, 'number_subgroups': 10, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 5], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [2], 'outer_gens': [[3, 2]], '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': 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], [2, 1]], 'representations': {'PC': {'code': 294, 'gens': [1, 2], 'pres': [3, -2, 2, -2, 37, 16]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [29, 56, 24], 'family': 'COPlus'}, {'d': 1, 'q': 4, 'gens': [7, 16, 1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [12, 55, 56]}, 'Perm': {'d': 4, 'gens': [6, 16, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4', 'transitive_degree': 4, 'wreath_data': ['C_2', 'C_2', '2T1'], 'wreath_product': True}
