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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '384.2163', 'ambient_counter': 2163, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_{12}).Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 96, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.2163.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.c1.b1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.163', 'subgroup_hash': 163, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.2163', 'aut_centralizer_order': 192, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '128.2323', 'aut_weyl_index': 384, 'centralizer': '16.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.a1', '2.e1.b1'], 'contains': ['8.a1.a1', '8.h1.b1', '8.m1.b1', '8.m2.a1', '12.b1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7307, 1438, 5114, 802, 2840, 4025, 4253, 3123], 'generators': [123, 208, 216, 212, 192, 128], 'label': '384.2163.4.c1.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.b1.b1', '2.c1.a1', '2.e1.b1'], 'normal_contains': ['8.a1.a1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': '48.43', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 2, 4, 2, 2], 'aut_gens': [[1, 2, 8], [49, 3, 13], [1, 6, 92], [49, 27, 12], [53, 74, 88], [1, 7, 93]], 'aut_group': '1024.dia', 'aut_hash': 5313781939793747337, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 18, 'aut_perms': [2263765394009950, 373760, 1468880480428365, 1847849781657599, 19199983104], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [3, 1, 2, 1], [4, 2, 4, 1], [4, 2, 8, 1], [6, 1, 2, 3], [6, 1, 8, 1], [12, 2, 8, 1], [12, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^7:D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '512.517075', 'autcent_hash': 4817036966848599930, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4.C_2^5', '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], [3, 1, 2], [4, 2, 12], [6, 1, 14], [12, 2, 24]], 'center_label': '24.15', 'center_order': 24, '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', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 163, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.4', 1], ['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 2, 1, 4], [4, 2, 2, 4], [6, 1, 2, 7], [12, 2, 2, 4], [12, 2, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 273, 'exponent': 12, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '24.15', 'hash': 163, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 2, 2], 'inner_gens': [[1, 2, 8], [1, 2, 56], [1, 50, 8]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 12]], 'label': '96.163', 'linC_count': 4992, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 80, 'linQ_dim': 6, 'linQ_dim_count': 32, 'linR_count': 64, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C4:C12', 'ngens': 6, 'nilpotency_class': 2, 'nilpotent': True, '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': 14, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 60, 'number_divisions': 32, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 92, 'number_subgroups': 108, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [6, 14], [12, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 8, 8, 0, 0, 0, 0, 0], 'outer_gens': [[1, 6, 9], [49, 26, 40], [53, 26, 40], [1, 2, 40], [49, 2, 40], [1, 3, 8], [1, 7, 12], [1, 6, 8]], 'outer_group': '256.53380', 'outer_hash': 53380, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 12, 'outer_perms': [1871400, 40682903, 167450536, 40723336, 40723343, 766200, 212340360, 40723320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 8]], 'representations': {'PC': {'code': 238133119682177, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, -2, -2, -3, 31, 681, 69, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [58438769827333370, 125101750005088212, 125101743012388261]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083311105, 2149582850, 237095820, 3253405763, 1087570945, 232080716]}, 'Perm': {'d': 13, 'gens': [83508504, 522637920, 90744, 4, 1037836800, 90720]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4:C_{12}', 'transitive_degree': 96, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 4, 6, 4, 12, 2, 4], 'aut_gens': [[1, 2, 16, 32], [325, 330, 16, 168], [25, 114, 24, 356], [29, 214, 24, 164], [277, 262, 16, 32], [73, 70, 24, 372], [149, 322, 16, 32], [81, 282, 16, 368], [261, 274, 16, 168]], 'aut_group': None, 'aut_hash': 1818465419181993652, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 80, 'aut_perms': [23210123406092424500376933166881262052354386502205507604013980578487391005944729266382723950216990264541763251265979583, 65341597482148718299761578900588803073424133195165732902647379349569471755190159169679333070854687964141360380208968296, 50262756715107004905140391785192730568407135482728620298917766922755737226433169276631809253762972697058584575628134152, 26352366473576755120744540880864907756799407349476470035615848270029889557689941955330583931890740448044356804604152261, 54147947805428835501450961785854337942961018574576617333252993635607989913658132389597709790336989330524188934941110241, 3660341776186011635970338763969250682543788026619825486092074334292883147273983446280326593748291672189889155473030184, 57922759848804703861437215734472026232672519797620018941372569375070269053522184866537330052096269244213626524767051222, 21332606575120013790434659828932842757741369316163759914979843040649636556703683045614237087393206378505307793748250371], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [2, 24, 2, 1], [3, 2, 1, 1], [4, 2, 2, 2], [4, 4, 4, 1], [4, 8, 4, 1], [4, 24, 2, 1], [6, 2, 1, 3], [6, 2, 2, 2], [8, 12, 8, 1], [12, 4, 2, 2], [12, 4, 8, 1], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^9.C_2^5)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '512.10494213', 'autcent_hash': 1718285292446712970, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '96.209', 'autcentquo_hash': 209, 'autcentquo_nilpotent': False, 'autcentquo_order': 96, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 24, 2], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 8, 4], [4, 24, 2], [6, 2, 7], [8, 12, 8], [12, 4, 12], [12, 8, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '48.43', 'commutator_count': 2, 'commutator_label': '48.44', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2163, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 24, 1, 2], [3, 2, 1, 1], [4, 2, 1, 4], [4, 4, 1, 4], [4, 8, 2, 2], [4, 24, 2, 1], [6, 2, 1, 7], [8, 12, 2, 4], [12, 4, 1, 4], [12, 4, 2, 4], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2163, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 1, 6], 'inner_gens': [[1, 214, 16, 176], [221, 2, 16, 368], [1, 2, 16, 32], [273, 82, 16, 32]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': True, 'inner_tex': 'C_6:D_4', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 38], [4, 14]], 'label': '384.2163', 'linC_count': 640, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 32, 'linQ_dim': 10, 'linQ_dim_count': 112, 'linR_count': 312, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2*D12).Q8', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 60, 'number_divisions': 43, 'number_normal_subgroups': 91, 'number_subgroup_autclasses': 150, 'number_subgroup_classes': 290, 'number_subgroups': 1150, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 55], [3, 2], [4, 104], [6, 14], [8, 96], [12, 112]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 4, 2, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[209, 202, 16, 232], [1, 10, 16, 32], [1, 202, 16, 32], [193, 2, 16, 160], [1, 218, 16, 32], [193, 30, 16, 32], [1, 106, 16, 40], [1, 218, 16, 248], [1, 198, 24, 228], [1, 10, 16, 40]], 'outer_group': '1024.dlb', 'outer_hash': 7684842177144052536, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 18, 'outer_perms': [384624, 5329, 40301501, 6267305809, 40279680, 356995102476289, 753226750470910, 39916800, 355693655501305, 5304], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^7:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 19], [8, 4]], 'representations': {'PC': {'code': 236722302568103725750732140289398285133313, 'gens': [1, 2, 5, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 3425, 41, 290, 66, 8453, 8845, 141, 17926, 8974, 166, 16391, 8207]}, 'Perm': {'d': 23, 'gens': [1182646847538562346770, 2401639573065320787242, 214357874047833564856, 2457615882055606272023, 2457615882055786060343, 3535007329255514112023, 3535007329255514112000, 93405312000]}}, 'schur_multiplier': [2, 2, 2], '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_2\\times D_{12}).Q_8', 'transitive_degree': 192, '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}
