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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.13282', 'ambient_counter': 13282, 'ambient_order': 384, 'ambient_tex': '(C_2\\times D_8).D_6', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 96, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.13282.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1.a1', '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': '96.176', 'subgroup_hash': 176, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.13282', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.h1.a1', '8.i1.a1', '8.y1.a1', '12.b1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [2, 192, 4, 16, 96, 128], 'label': '384.13282.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.i1.a1', '8.h1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '96.176', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [3, 2, 92], [1, 2, 44], [1, 2, 28], [2, 3, 4], [1, 2, 5], [1, 2, 6], [1, 50, 4], [49, 2, 4], [1, 2, 52]], 'aut_group': '768.1090213', 'aut_hash': 1090213, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 768, 'aut_permdeg': 12, 'aut_perms': [1508400, 40723327, 40723336, 495360, 85800, 766200, 90842400, 135732240, 40723320], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 1, 6, 1], [6, 1, 2, 1], [6, 1, 12, 1], [8, 1, 16, 1], [12, 1, 4, 1], [12, 1, 12, 1], [24, 1, 32, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^5:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '768.1090213', 'autcent_hash': 1090213, 'autcent_nilpotent': False, 'autcent_order': 768, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^5:S_4', '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, 7], [3, 1, 2], [4, 1, 8], [6, 1, 14], [8, 1, 16], [12, 1, 16], [24, 1, 32]], 'center_label': '96.176', 'center_order': 96, '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', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 176, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 4], [6, 1, 2, 7], [8, 1, 4, 4], [12, 1, 4, 4], [24, 1, 8, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 364, 'exponent': 24, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '24.15', 'hash': 176, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 96]], 'label': '96.176', 'linC_count': 46592, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 96, 'linQ_dim': 7, 'linQ_dim_count': 96, 'linR_count': 192, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C24', 'ngens': 6, 'nilpotency_class': 1, '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': 12, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 96, 'number_divisions': 32, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 28, 'number_subgroup_classes': 76, 'number_subgroups': 76, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 8], [6, 14], [8, 16], [12, 16], [24, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 92], [1, 2, 44], [1, 2, 28], [2, 3, 4], [1, 2, 5], [1, 2, 6], [1, 50, 4], [49, 2, 4], [1, 2, 52]], 'outer_group': '768.1090213', 'outer_hash': 1090213, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 12, 'outer_perms': [1508400, 40723327, 40723336, 495360, 85800, 766200, 90842400, 135732240, 40723320], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 8, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 8], [8, 4]], 'representations': {'PC': {'code': 638205298433, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -2, -3, 50, 69, 88]}, 'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 75598583751, 34426082502, 14591950001, 71529966879, 123802874376]}, 'Perm': {'d': 15, 'gens': [27760320, 479001600, 87178291200, 4, 11614560, 3669864]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 24], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_{24}', '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 24, 'aut_gen_orders': [24, 6, 4, 6, 4, 6, 4, 8], 'aut_gens': [[1, 2, 8, 32], [195, 210, 168, 240], [5, 6, 264, 240], [23, 6, 120, 352], [1, 18, 152, 224], [215, 22, 232, 368], [213, 22, 152, 48], [213, 2, 264, 368], [195, 2, 296, 368]], 'aut_group': None, 'aut_hash': 1723455815902563418, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 40, 'aut_perms': [569736749111036908666595744765750116589427282482, 226037444159747826817916538007675953708809823308, 565154993620359212805305234643625582686334636343, 385563624962870176855961467557761464977760935323, 46516594200694775784659757791502645141502507718, 620802557336675564789991853203570957262965323088, 368232944042356628919549992168111087275316803126, 558229961809195783777370681072484690420844876349], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 4, 1, 1], [2, 8, 2, 1], [2, 24, 2, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 8, 2, 1], [4, 12, 2, 2], [4, 24, 2, 1], [6, 2, 1, 3], [6, 4, 2, 1], [6, 16, 2, 1], [8, 4, 2, 2], [8, 24, 2, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 16, 2, 1], [24, 4, 4, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^2.C_2^6.C_2^4)', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.38', 'autcentquo_hash': 38, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 4, 1], [2, 8, 2], [2, 24, 2], [3, 2, 1], [4, 2, 2], [4, 4, 1], [4, 8, 2], [4, 12, 4], [4, 24, 2], [6, 2, 3], [6, 4, 2], [6, 16, 2], [8, 4, 4], [8, 24, 2], [12, 4, 4], [12, 16, 2], [24, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '96.209', 'commutator_count': 1, 'commutator_label': '24.9', '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': 13282, '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, 8, 1, 2], [2, 24, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 4, 1, 1], [4, 8, 1, 2], [4, 12, 1, 4], [4, 24, 1, 2], [6, 2, 1, 3], [6, 4, 2, 1], [6, 16, 1, 2], [8, 4, 2, 2], [8, 24, 1, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 16, 1, 2], [24, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 524160, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '48.51', 'hash': 13282, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 2, 6], 'inner_gens': [[1, 198, 8, 48], [5, 2, 24, 32], [1, 18, 8, 352], [17, 2, 72, 32]], 'inner_hash': 209, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': None, 'inner_tex': 'D_4\\times D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 20]], 'label': '384.13282', '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': '(C2*D8).D6', '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': 29, 'number_characteristic_subgroups': 43, 'number_conjugacy_classes': 48, 'number_divisions': 38, 'number_normal_subgroups': 109, 'number_subgroup_autclasses': 224, 'number_subgroup_classes': 370, 'number_subgroups': 1430, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 71], [3, 2], [4, 120], [6, 46], [8, 64], [12, 48], [24, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [4, 0, 0, 0, 0, 4], 'outer_gens': [[213, 210, 264, 352], [193, 194, 72, 160], [5, 214, 152, 352], [193, 214, 72, 176], [1, 214, 24, 368], [211, 194, 120, 48]], 'outer_group': '128.2163', 'outer_hash': 2163, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 32, 'outer_perms': [118914921966453230635690807124993850, 55875202784656482372427229640129840, 1777968526953894803359776396605808, 115660445338188135545808318680471470, 108945930653142584281032657409671339, 33988083303939678171151103959499530], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 27, '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], [8, 4], [16, 2]], 'representations': {'PC': {'code': 236703185923877706424428538641176762904065, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -2, -3, 3169, 41, 4706, 1170, 395, 91, 2309, 2141, 141, 2270, 166, 2079]}, 'Perm': {'d': 27, 'gens': [405880136984561850311665012, 65201036649827064418800594, 884219951613211328686703419, 1242812202888852395720415666, 1678416337188270231552000000, 4485159970600, 5713560422706, 6758061133824000]}}, 'schur_multiplier': [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_2\\times D_8).D_6', '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}
