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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '448.1086', 'ambient_counter': 1086, 'ambient_order': 448, 'ambient_tex': '(Q_8\\times D_{14}):C_2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 224, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '448.1086.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '224.142', 'subgroup_hash': 142, 'subgroup_order': 224, 'subgroup_tex': 'C_{28}.D_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '448.1086', 'aut_centralizer_order': 4, 'aut_label': '2.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '5376.cw', 'aut_weyl_index': 4, 'centralizer': '112.a1.a1', 'complements': ['224.e1.a1', '224.e1.b1', '224.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.l1.b1', '4.m1.a1', '4.m1.b1', '4.n1.a1', '4.p1.a1', '4.r1.a1', '14.j1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4773, 5529, 3537, 8510, 4219, 4215, 3074, 4369], 'generators': [85, 16, 112, 280, 6, 224], 'label': '448.1086.2.j1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.a1', '4.l1.b1', '4.m1.a1', '4.m1.b1', '4.n1.a1', '4.p1.a1', '4.r1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': '112.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': '112.42'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [6, 14, 4, 4, 2, 2, 2], 'aut_gens': [[1, 2, 8], [1, 2, 40], [113, 222, 8], [173, 6, 124], [57, 170, 8], [1, 118, 8], [1, 114, 8], [5, 2, 120]], 'aut_group': '10752.bz', 'aut_hash': 8736525885294042750, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10752, 'aut_permdeg': 19, 'aut_perms': [13516309078272604, 40637475482249427, 40281695116225920, 19207382663669760, 3628800, 3669120, 186810664320], 'aut_phi_ratio': 112.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 28, 2, 1], [4, 2, 2, 1], [4, 4, 2, 1], [4, 14, 4, 1], [7, 2, 3, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 4, 6, 1], [28, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_7\\times C_2^5:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '168.47', 'autcentquo_hash': 47, 'autcentquo_nilpotent': False, 'autcentquo_order': 168, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 28, 2], [4, 2, 2], [4, 4, 2], [4, 14, 4], [7, 2, 3], [14, 2, 9], [28, 4, 18]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '56.12', 'commutator_count': 1, 'commutator_label': '28.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 142, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 28, 1, 2], [4, 2, 1, 2], [4, 4, 1, 2], [4, 14, 2, 2], [7, 2, 3, 1], [14, 2, 3, 3], [28, 4, 3, 2], [28, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 28, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '56.12', 'hash': 142, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 14], 'inner_gens': [[1, 118, 120], [117, 2, 104], [113, 130, 8]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 56, 'inner_split': False, 'inner_tex': 'C_2\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 30], [4, 6]], 'label': '224.142', 'linC_count': 48, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 16, 'linQ_dim': 12, 'linQ_dim_count': 16, 'linR_count': 12, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.D4', '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': 12, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 44, 'number_divisions': 20, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 42, 'number_subgroup_classes': 76, 'number_subgroups': 350, 'old_label': None, 'order': 224, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 59], [4, 68], [7, 6], [14, 18], [28, 72]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[117, 6, 124], [117, 6, 8], [1, 58, 8], [169, 118, 156]], 'outer_group': '192.1434', 'outer_hash': 1434, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 11, 'outer_perms': [766080, 744, 1464, 4032004], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times D_4^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 2], [6, 4], [12, 4]], 'representations': {'PC': {'code': 1558788446317942070515182280901, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, -2, -2, -7, 672, 1417, 31, 2883, 1257, 69, 3130, 88, 3467]}, 'GLZN': {'d': 2, 'p': 105, 'gens': [74088064, 112521163, 1861784, 82191446, 1159201, 9417337]}, 'Perm': {'d': 19, 'gens': [6423483307006207, 14291847635788800, 20004977320917120, 7983360, 27497789064345600, 973]}}, 'schur_multiplier': [2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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_{28}.D_4', 'transitive_degree': 112, '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': 84, 'aut_gen_orders': [28, 2, 6, 12, 4, 12, 6, 6, 6], 'aut_gens': [[1, 2, 4, 112], [225, 42, 116, 392], [57, 2, 52, 392], [1, 82, 300, 168], [57, 2, 372, 392], [281, 82, 388, 168], [225, 314, 212, 112], [225, 26, 100, 336], [57, 242, 260, 392], [281, 66, 244, 392]], 'aut_group': None, 'aut_hash': 6386081533423645612, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21504, 'aut_permdeg': 40, 'aut_perms': [190606553892155262194394287737557010943143061676, 510938976515848472237181277895153998446213086909, 14669166826220241247608340332930386070080374212, 510796095524163580069582646814932031682475372390, 668240371631870215037923718635281599604189411355, 194240745709358658734587742810348940903953716199, 187779668436973448201544346777438685407237811989, 529592664322433957907252959539335008342684818547, 665234490015823542142736233059578922524001392746], 'aut_phi_ratio': 112.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 14, 2, 1], [2, 28, 2, 1], [4, 2, 2, 2], [4, 4, 2, 2], [4, 14, 2, 1], [4, 14, 4, 1], [4, 28, 1, 2], [7, 2, 3, 1], [14, 2, 3, 3], [14, 4, 6, 1], [28, 4, 6, 2], [28, 8, 6, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{14}.(C_6\\times D_4).C_2^5', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '84.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 84, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 14, 2], [2, 28, 2], [4, 2, 4], [4, 4, 4], [4, 14, 6], [4, 28, 2], [7, 2, 3], [14, 2, 9], [14, 4, 6], [28, 4, 12], [28, 8, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '112.42', 'commutator_count': 1, 'commutator_label': '28.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1086, '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, 1], [2, 14, 1, 2], [2, 28, 1, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 1, 4], [4, 14, 1, 4], [4, 14, 2, 1], [4, 28, 1, 2], [7, 2, 3, 1], [14, 2, 3, 3], [14, 4, 6, 1], [28, 4, 3, 2], [28, 4, 6, 1], [28, 8, 3, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 574560, 'exponent': 28, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '112.42', 'hash': 1086, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 14, 2], 'inner_gens': [[1, 58, 284, 112], [57, 2, 108, 112], [281, 10, 4, 336], [1, 2, 228, 112]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': True, 'inner_tex': 'C_2^2\\times D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 32], [4, 19]], 'label': '448.1086', 'linC_count': 480, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 96, 'linQ_dim': 12, 'linQ_dim_count': 64, 'linR_count': 204, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(Q8*D14):C2', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 24, 'number_characteristic_subgroups': 43, 'number_conjugacy_classes': 67, 'number_divisions': 35, 'number_normal_subgroups': 105, 'number_subgroup_autclasses': 168, 'number_subgroup_classes': 290, 'number_subgroups': 1404, 'old_label': None, 'order': 448, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 91], [4, 164], [7, 6], [14, 42], [28, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 12], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[57, 2, 4, 112], [225, 2, 4, 112], [57, 226, 4, 112], [1, 2, 4, 168], [57, 2, 124, 168]], 'outer_group': '192.1531', 'outer_hash': 1531, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 13, 'outer_perms': [1037877120, 482630400, 1520467200, 482670984, 482671587], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}:C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [4, 3], [6, 8], [12, 2], [24, 2]], 'representations': {'PC': {'code': 63695762051874856600011908694151860, 'gens': [1, 2, 3, 6], 'pres': [7, -2, -2, -2, -2, -7, -2, -2, 813, 5966, 1143, 58, 1466, 80, 1691, 3547, 124]}, 'GLZN': {'d': 2, 'p': 105, 'gens': [74088064, 112521163, 82191446, 1159201, 112915193, 71780197, 34352359]}, 'Perm': {'d': 19, 'gens': [6446835116910847, 13897975637145600, 20715131681032320, 20734746793649280, 6446835113241600, 6446835121224960, 973]}}, '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': '(Q_8\\times D_{14}):C_2', 'transitive_degree': 224, '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': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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]], 'center_label': '2.1', 'center_order': 2, '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'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
