-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.4010', 'ambient_counter': 4010, 'ambient_order': 864, 'ambient_tex': 'C_6^2.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '864.4010.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.4010', 'subgroup_hash': 4010, 'subgroup_order': 864, 'subgroup_tex': 'C_6^2.S_4', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '864.4010', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.a1', 'complements': ['864.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1', '3.b1', '4.c1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3876, 3924, 1740, 4455], 'generators': [793169, 1591333, 47521, 545461, 1167265, 70633, 887131, 886483], 'label': '864.4010.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '216.90', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 4, 12], 'aut_gens': [[793169, 1664773, 346894, 909811, 70633], [1632995, 1665205, 541136, 909811, 70633], [886483, 1458449, 952751, 887131, 70633], [1632995, 1217374, 137153, 909811, 887131]], 'aut_group': None, 'aut_hash': 7963030017670136781, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 72, 'aut_perms': [42801001033821747631249064993335892595292584926133763718161217152561875269306687652731011912201167474461, 13198022655074581250455586475418438167313274752835516822158888126123871645580283805770728861711593955555, 14066556122884654603730765194177570697118834417478608719171522289747705807292391763465034532335482160005], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 1, 1], [2, 3, 3, 1], [2, 18, 4, 1], [3, 2, 1, 1], [3, 3, 1, 2], [4, 18, 4, 1], [6, 2, 3, 1], [6, 3, 1, 2], [6, 3, 3, 4], [6, 6, 1, 3], [6, 6, 3, 3], [6, 18, 4, 2], [9, 24, 1, 3], [12, 18, 4, 2], [18, 24, 3, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2.S_4\\times S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '216.90', 'autcentquo_hash': 90, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2.S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 18, 4], [3, 2, 1], [3, 3, 2], [4, 18, 4], [6, 2, 3], [6, 3, 14], [6, 6, 12], [6, 18, 8], [9, 24, 3], [12, 18, 8], [18, 24, 9]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '216.90', 'commutator_count': 1, 'commutator_label': '36.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4010, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['216.90', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 18, 1, 4], [3, 2, 1, 1], [3, 3, 2, 1], [4, 18, 1, 4], [6, 2, 1, 3], [6, 3, 2, 7], [6, 6, 1, 4], [6, 6, 2, 4], [6, 18, 2, 4], [9, 24, 1, 1], [9, 24, 2, 1], [12, 18, 2, 4], [18, 24, 1, 3], [18, 24, 2, 3]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 32760, 'exponent': 36, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '288.1033', 'hash': 4010, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [1, 6, 9, 2, 2], 'inner_gens': [[793169, 1664773, 346894, 909811, 70633], [793169, 1664773, 1614427, 70633, 909811], [793169, 1240918, 346894, 887131, 909811], [793169, 824947, 1210012, 909811, 70633], [793169, 824947, 369574, 909811, 70633]], 'inner_hash': 90, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2.S_4', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 12], [3, 24], [6, 16]], 'label': '864.4010', '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': True, 'name': 'C6^2.S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 76, 'number_divisions': 52, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': 157, 'number_subgroup_classes': 489, 'number_subgroups': 2796, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 87], [3, 8], [4, 72], [6, 264], [9, 72], [12, 144], [18, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [46657, 46657, 46657, 46657], 'outer_gens': [[793169, 1664773, 518222, 909811, 70633], [1632995, 824299, 1380710, 909811, 70633], [793169, 62831, 346894, 909811, 70633], [793169, 824299, 346894, 909811, 70633]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 8], [4, 4], [6, 16], [12, 4]], 'representations': {'PC': {'code': 2634830382324408270877392177797474151686517070764588, 'gens': [1, 2, 4, 7, 8], 'pres': [8, -2, -2, -3, -2, -3, -3, -2, 2, 41, 2123, 1267, 91, 972, 980, 156, 3469, 12110, 3054, 1046, 6927, 1183, 1767]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 793169, 909811, 1166401, 521467, 47305, 70633, 1310731]}, 'Perm': {'d': 17, 'gens': [1308157011415, 482630400, 1037836800, 16199, 1394852721874, 99229, 21009968179200, 44460928512000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 4, 12], 'aut_gens': [[793169, 1664773, 346894, 909811, 70633], [1632995, 1665205, 541136, 909811, 70633], [886483, 1458449, 952751, 887131, 70633], [1632995, 1217374, 137153, 909811, 887131]], 'aut_group': None, 'aut_hash': 7963030017670136781, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5184, 'aut_permdeg': 72, 'aut_perms': [42801001033821747631249064993335892595292584926133763718161217152561875269306687652731011912201167474461, 13198022655074581250455586475418438167313274752835516822158888126123871645580283805770728861711593955555, 14066556122884654603730765194177570697118834417478608719171522289747705807292391763465034532335482160005], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 3, 1, 1], [2, 3, 3, 1], [2, 18, 4, 1], [3, 2, 1, 1], [3, 3, 1, 2], [4, 18, 4, 1], [6, 2, 3, 1], [6, 3, 1, 2], [6, 3, 3, 4], [6, 6, 1, 3], [6, 6, 3, 3], [6, 18, 4, 2], [9, 24, 1, 3], [12, 18, 4, 2], [18, 24, 3, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2.S_4\\times S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.12', 'autcent_hash': 12, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '216.90', 'autcentquo_hash': 90, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2.S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 18, 4], [3, 2, 1], [3, 3, 2], [4, 18, 4], [6, 2, 3], [6, 3, 14], [6, 6, 12], [6, 18, 8], [9, 24, 3], [12, 18, 8], [18, 24, 9]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '216.90', 'commutator_count': 1, 'commutator_label': '36.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4010, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['216.90', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 18, 1, 4], [3, 2, 1, 1], [3, 3, 2, 1], [4, 18, 1, 4], [6, 2, 1, 3], [6, 3, 2, 7], [6, 6, 1, 4], [6, 6, 2, 4], [6, 18, 2, 4], [9, 24, 1, 1], [9, 24, 2, 1], [12, 18, 2, 4], [18, 24, 1, 3], [18, 24, 2, 3]], 'element_repr_type': 'GLZN', 'elementary': 1, 'eulerian_function': 32760, 'exponent': 36, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '288.1033', 'hash': 4010, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [1, 6, 9, 2, 2], 'inner_gens': [[793169, 1664773, 346894, 909811, 70633], [793169, 1664773, 1614427, 70633, 909811], [793169, 1240918, 346894, 887131, 909811], [793169, 824947, 1210012, 909811, 70633], [793169, 824947, 369574, 909811, 70633]], 'inner_hash': 90, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2.S_4', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 12], [3, 24], [6, 16]], 'label': '864.4010', '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': True, 'name': 'C6^2.S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 32, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 76, 'number_divisions': 52, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': 157, 'number_subgroup_classes': 489, 'number_subgroups': 2796, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 87], [3, 8], [4, 72], [6, 264], [9, 72], [12, 144], [18, 216]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [46657, 46657, 46657, 46657], 'outer_gens': [[793169, 1664773, 518222, 909811, 70633], [1632995, 824299, 1380710, 909811, 70633], [793169, 62831, 346894, 909811, 70633], [793169, 824299, 346894, 909811, 70633]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 8], [4, 4], [6, 16], [12, 4]], 'representations': {'PC': {'code': 2634830382324408270877392177797474151686517070764588, 'gens': [1, 2, 4, 7, 8], 'pres': [8, -2, -2, -3, -2, -3, -3, -2, 2, 41, 2123, 1267, 91, 972, 980, 156, 3469, 12110, 3054, 1046, 6927, 1183, 1767]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 793169, 909811, 1166401, 521467, 47305, 70633, 1310731]}, 'Perm': {'d': 17, 'gens': [1308157011415, 482630400, 1037836800, 16199, 1394852721874, 99229, 21009968179200, 44460928512000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
