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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '16128.bb', 'ambient_counter': 28, 'ambient_order': 16128, 'ambient_tex': 'C_3\\times \\SL(2,7).D_8', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 336, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '16128.bb.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '672.1048', 'subgroup_hash': 1048, 'subgroup_order': 672, 'subgroup_tex': 'C_2\\times \\SL(2,7)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '16128.bb', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1344.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1'], 'contains': ['48.a1.a1', '168.f1.a1', '168.f1.a2', '192.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6927191804567, 32462063879538, 19491026353169, 28487064012000], 'label': '16128.bb.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '336.209'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 168, 'aut_gen_orders': [3, 6, 2], 'aut_gens': [[8176132, 34603218, 13568049, 31897574], [2094042, 34603218, 3785138, 31897574], [23288847, 15061583, 28289446, 31897574], [27348207, 34603218, 39764490, 31897574]], 'aut_group': '672.1254', 'aut_hash': 1254, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 672, 'aut_permdeg': 44, 'aut_perms': [1364201776141002038935754124982016274471392419546152, 60472782585283864422937398258113522597819221389272328, 583769131622531417787940593977453461614182574691901], 'aut_phi_ratio': 3.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 56, 1, 1], [4, 42, 1, 2], [6, 56, 1, 1], [6, 56, 2, 1], [7, 24, 2, 1], [8, 42, 1, 2], [8, 42, 2, 1], [14, 24, 2, 1], [14, 24, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\PGL(2,7)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 168, 'autcentquo_group': '336.208', 'autcentquo_hash': 208, 'autcentquo_nilpotent': False, 'autcentquo_order': 336, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,7)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 56, 1], [4, 42, 2], [6, 56, 3], [7, 24, 2], [8, 42, 4], [14, 24, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '168.42', 'commutator_count': 1, 'commutator_label': '336.114', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '168.42'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1048, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['336.114', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 56, 1, 1], [4, 42, 1, 2], [6, 56, 1, 3], [7, 24, 2, 1], [8, 42, 2, 2], [14, 24, 2, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 342, 'exponent': 168, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.209', 'hash': 1048, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [4, 1, 2, 1], 'inner_gens': [[8176132, 34603218, 2183463, 31897574], [8176132, 34603218, 13568049, 31897574], [26496389, 34603218, 13568049, 31897574], [8176132, 34603218, 13568049, 31897574]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': '\\PSL(2,7)', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [3, 4], [4, 4], [6, 6], [7, 2], [8, 4]], 'label': '672.1048', 'linC_count': 4, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 4, 'linQ_dim': 9, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2*SL(2,7)', 'ngens': 4, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 22, 'number_divisions': 16, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 39, 'number_subgroup_classes': 52, 'number_subgroups': 682, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 56], [4, 84], [6, 168], [7, 48], [8, 168], [14, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [35496934, 5767203], 'outer_gens': [[33519643, 34603218, 29430250, 31897574], [2078704, 15061583, 13568049, 31897574]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 4], [7, 2], [8, 6], [12, 2]], 'representations': {'GLFp': {'d': 3, 'p': 7, 'gens': [8176132, 34603218, 13568049, 31897574]}, 'Perm': {'d': 18, 'gens': [2438381165698975, 5541463280954544]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times \\SL(2,7)', 'transitive_degree': 32, '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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 168, 'aut_gen_orders': [4, 8, 2, 6, 8, 4], 'aut_gens': [[32462063879538, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [32462063879538, 28487064012000, 12191951780412, 12736206817243, 9495688004000, 18160723818440, 18845087665259, 33086642344516], [32462063879538, 28487064012000, 26579518075539, 26736608836248, 18991376008000, 9586798696970, 3777280734582, 14097243663259], [8140372662367, 28487064012000, 12191951780412, 22504121239083, 18991376008000, 30911906936064, 25498501117369, 5682850184692], [8140372662367, 28487064012000, 12191951780412, 24116233846758, 9495688004000, 7762950617520, 21685662457662, 5682850184692], [14736183681012, 28487064012000, 26579518075539, 906675979685, 18991376008000, 15311205152566, 7590119394289, 24674226075043], [14736183681012, 28487064012000, 12191951780412, 29116079561622, 18991376008000, 8494812263222, 12337963396289, 33086642344516]], 'aut_group': None, 'aut_hash': 4660582895174876950, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 43008, 'aut_permdeg': 60, 'aut_perms': [10364074258859140388930521246993570365125026479401696082636226487715550003724224, 6960419551462355307688203316320019137071712370620950377104203168757721698074692213, 5878843314255489107732071993367602791671155694326332796453392761870069524115167926, 5387711816367427519142231894530210168798708144863723367223363650201576919495848008, 8281966916461532925941223343268401111061853594312451758868231582507921049245759741, 6319408150211680272003247189133948652833111925697435685570213455907153788745270918], 'aut_phi_ratio': 9.333333333333334, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 8, 1, 1], [2, 42, 1, 1], [2, 168, 1, 1], [3, 1, 2, 1], [3, 56, 1, 1], [3, 56, 2, 1], [4, 2, 1, 1], [4, 8, 1, 1], [4, 42, 1, 1], [4, 84, 2, 1], [4, 168, 1, 1], [6, 1, 2, 1], [6, 8, 2, 1], [6, 42, 2, 1], [6, 56, 1, 1], [6, 56, 2, 1], [6, 168, 2, 1], [6, 448, 1, 1], [6, 448, 2, 1], [7, 24, 2, 1], [8, 2, 2, 1], [8, 42, 1, 2], [8, 84, 1, 2], [8, 336, 1, 2], [12, 2, 2, 1], [12, 8, 2, 1], [12, 42, 2, 1], [12, 84, 4, 1], [12, 112, 1, 1], [12, 112, 2, 1], [12, 168, 2, 1], [12, 448, 1, 1], [12, 448, 2, 1], [14, 24, 2, 1], [14, 192, 2, 1], [16, 2, 4, 1], [16, 84, 2, 1], [16, 84, 4, 1], [21, 24, 4, 1], [24, 2, 4, 1], [24, 42, 2, 2], [24, 84, 2, 2], [24, 112, 2, 1], [24, 112, 4, 1], [24, 336, 2, 2], [28, 48, 2, 1], [28, 192, 2, 1], [42, 24, 4, 1], [42, 192, 4, 1], [48, 2, 8, 1], [48, 84, 4, 1], [48, 84, 8, 1], [48, 112, 4, 1], [48, 112, 8, 1], [56, 48, 4, 1], [84, 48, 4, 1], [84, 192, 4, 1], [112, 48, 8, 1], [168, 48, 8, 1], [336, 48, 16, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2\\times C_4).C_2^4.\\SO(3,7)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 168, 'autcentquo_group': '5376.cr', 'autcentquo_hash': 7124868893884309361, 'autcentquo_nilpotent': False, 'autcentquo_order': 5376, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times D_4\\times \\PGL(2,7)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 8, 1], [2, 42, 1], [2, 168, 1], [3, 1, 2], [3, 56, 3], [4, 2, 1], [4, 8, 1], [4, 42, 1], [4, 84, 2], [4, 168, 1], [6, 1, 2], [6, 8, 2], [6, 42, 2], [6, 56, 3], [6, 168, 2], [6, 448, 3], [7, 24, 2], [8, 2, 2], [8, 42, 2], [8, 84, 2], [8, 336, 2], [12, 2, 2], [12, 8, 2], [12, 42, 2], [12, 84, 4], [12, 112, 3], [12, 168, 2], [12, 448, 3], [14, 24, 2], [14, 192, 2], [16, 2, 4], [16, 84, 6], [21, 24, 4], [24, 2, 4], [24, 42, 4], [24, 84, 4], [24, 112, 6], [24, 336, 4], [28, 48, 2], [28, 192, 2], [42, 24, 4], [42, 192, 4], [48, 2, 8], [48, 84, 12], [48, 112, 12], [56, 48, 4], [84, 48, 4], [84, 192, 4], [112, 48, 8], [168, 48, 8], [336, 48, 16]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '2688.ds', 'commutator_count': 1, 'commutator_label': '1344.6315', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '168.42'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 28, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['5376.bh', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 8, 1, 1], [2, 42, 1, 1], [2, 168, 1, 1], [3, 1, 2, 1], [3, 56, 1, 1], [3, 56, 2, 1], [4, 2, 1, 1], [4, 8, 1, 1], [4, 42, 1, 1], [4, 84, 1, 2], [4, 168, 1, 1], [6, 1, 2, 1], [6, 8, 2, 1], [6, 42, 2, 1], [6, 56, 1, 1], [6, 56, 2, 1], [6, 168, 2, 1], [6, 448, 1, 1], [6, 448, 2, 1], [7, 24, 2, 1], [8, 2, 2, 1], [8, 42, 2, 1], [8, 84, 1, 2], [8, 336, 1, 2], [12, 2, 2, 1], [12, 8, 2, 1], [12, 42, 2, 1], [12, 84, 2, 2], [12, 112, 1, 1], [12, 112, 2, 1], [12, 168, 2, 1], [12, 448, 1, 1], [12, 448, 2, 1], [14, 24, 2, 1], [14, 192, 2, 1], [16, 2, 4, 1], [16, 84, 2, 1], [16, 84, 4, 1], [21, 24, 4, 1], [24, 2, 4, 1], [24, 42, 4, 1], [24, 84, 2, 2], [24, 112, 2, 1], [24, 112, 4, 1], [24, 336, 2, 2], [28, 48, 2, 1], [28, 192, 2, 1], [42, 24, 4, 1], [42, 192, 4, 1], [48, 2, 8, 1], [48, 84, 4, 1], [48, 84, 8, 1], [48, 112, 4, 1], [48, 112, 8, 1], [56, 48, 4, 1], [84, 48, 4, 1], [84, 192, 4, 1], [112, 48, 8, 1], [168, 48, 8, 1], [336, 48, 16, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 1368, 'exponent': 336, 'exponents_of_order': [8, 2, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 0, 16], [12, 0, 16], [16, 0, 8]], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '2016.de', 'hash': 6474831304702359576, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 168, 'inner_gen_orders': [2, 1, 2, 8, 1, 8, 8, 4], 'inner_gens': [[32462063879538, 28487064012000, 12191951780412, 318043883633, 9495688004000, 30499378636940, 17085807398282, 5682850184692], [32462063879538, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [6212516140062, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [14736183681012, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 17226677806540, 2696263894061, 14097243663259], [32462063879538, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [4561705163974, 28487064012000, 26579518075539, 24326831373044, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [14736183681012, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259], [8140372662367, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259]], 'inner_hash': 5326254461264611855, 'inner_nilpotent': False, 'inner_order': 2688, 'inner_split': True, 'inner_tex': 'D_8\\times \\GL(3,2)', 'inner_used': [1, 3, 4, 6], 'irrC_degree': 8, 'irrQ_degree': 96, 'irrQ_dim': 96, 'irrR_degree': 16, 'irrep_stats': [[1, 12], [2, 9], [3, 24], [6, 30], [7, 12], [8, 36], [12, 33], [14, 9], [16, 21]], 'label': '16128.bb', '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': False, 'metacyclic': False, 'monomial': False, 'name': 'C3*SL(2,7).D8', '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, 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': 68, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 186, 'number_divisions': 68, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 597, 'number_subgroup_classes': 815, 'number_subgroups': 30208, 'old_label': None, 'order': 16128, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 219], [3, 170], [4, 388], [6, 1950], [7, 48], [8, 928], [12, 2456], [14, 432], [16, 512], [21, 96], [24, 2528], [28, 480], [42, 864], [48, 2368], [56, 192], [84, 960], [112, 384], [168, 384], [336, 768]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [4747844002000, 20991864020747, 4747844002000], 'outer_gens': [[32462063879538, 28487064012000, 26579518075539, 834303313200, 18991376008000, 9450481347175, 3777280734582, 14097243663259], [32462063879538, 28487064012000, 26579518075539, 19462333899513, 9495688004000, 31788461251876, 2696263894061, 14097243663259], [32462063879538, 28487064012000, 26579518075539, 1813063582463, 9495688004000, 27476238949449, 10430694186692, 24674226075043]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 131, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 5], [4, 2], [6, 8], [7, 4], [8, 5], [12, 10], [14, 5], [16, 5], [24, 4], [28, 2], [32, 2], [48, 4], [56, 1], [64, 3], [96, 2], [128, 2]], 'representations': {'GLFp': {'d': 4, 'p': 7, 'gens': [32462063879538, 28487064012000, 26579518075539, 1569693347250, 9495688004000, 9450481347175, 2696263894061, 14097243663259]}, 'Perm': {'d': 131, 'gens': [6470389677569132057379586876449590213268695831143949512349743732362127879480284586384879424248593858895577850625819877924069510608874457785720387175125932553917594105492542421998800865590203435221715278018279450749060184, 13482883130264823817332678548086489852684433369436619266803468835893683380060946565571568538963583105542051192328498102930995539020531344455248581240689796385513535099437399523680119155840787908214221795250763863977224624, 3, 20004129469649827187099307680569493170370994775269155558707705470245313698695750779922505423892104593165637166559351431639428268303917970106082006606055281017288707533444911933839354205024571549236416396588764389377169680, 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'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times \\SL(2,7).D_8', 'transitive_degree': 384, 'wreath_data': None, 'wreath_product': False}
