-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1056.95', 'ambient_counter': 95, 'ambient_order': 1056, 'ambient_tex': 'D_{22}:C_{24}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 264, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1056.95.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '264.16', 'subgroup_hash': 16, 'subgroup_order': 264, 'subgroup_tex': 'C_{22}:C_{12}', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1056.95', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '880.210', 'aut_weyl_index': 8, 'centralizer': '44.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '12.c1.a1', '44.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4480, 3902, 4525, 3982, 3613, 7169, 3953, 3504], 'generators': [25, 704, 528, 2, 96], 'label': '1056.95.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '88.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '44.3'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [2, 2, 10, 44], 'aut_gens': [[1, 4], [1, 260], [1, 92], [1, 238], [111, 6]], 'aut_group': '1760.1090', 'aut_hash': 1090, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1760, 'aut_permdeg': 46, 'aut_perms': [37981314399962824042483854637618513318874523117244749563, 16339240716040372458759856763467696556178309120000, 36575638725364118806064638754574982027423859307735872719, 2752035464243037835834316911547862205533876894086547217493], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 11, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [11, 2, 5, 1], [12, 11, 8, 1], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 1], [66, 2, 10, 1], [66, 2, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4\\times F_{11}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 11, 4], [6, 1, 6], [11, 2, 5], [12, 11, 8], [22, 2, 15], [33, 2, 10], [66, 2, 30]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '22.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['44.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 11, 2, 2], [6, 1, 2, 3], [11, 2, 5, 1], [12, 11, 4, 2], [22, 2, 5, 3], [33, 2, 10, 1], [66, 2, 10, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 132, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '132.7', 'hash': 16, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 11], 'inner_gens': [[1, 172], [97, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 22, 'inner_split': True, 'inner_tex': 'D_{11}', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 60]], 'label': '264.16', 'linC_count': 480, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 14, 'linR_count': 20, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C22:C12', 'ngens': 5, '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': 14, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 84, 'number_divisions': 20, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 32, 'number_subgroups': 92, 'old_label': None, 'order': 264, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 44], [6, 6], [11, 10], [12, 88], [22, 30], [33, 20], [66, 60]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [2, 2, 20], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1, 260], [135, 260], [135, 142]], 'outer_group': '80.46', 'outer_hash': 46, 'outer_nilpotent': True, 'outer_order': 80, 'outer_permdeg': 11, 'outer_perms': [3669840, 40320, 11612224], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_{10}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2], [10, 4], [20, 4]], 'representations': {'PC': {'code': 18933675603620682900019, 'gens': [1, 3], 'pres': [5, -2, -2, -2, -3, -11, 10, 2582, 42, 1603, 78, 6004]}, 'GLZN': {'d': 2, 'p': 55, 'gens': [166651, 3961541, 5325937, 3493896, 5656784]}, 'Perm': {'d': 20, 'gens': [93884681647, 20922789888000, 128047474114560000, 186810624000, 4364893]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{22}:C_{12}', 'transitive_degree': 264, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.23', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 10, 11], 'aut_gens': [[1, 2, 4], [529, 2, 964], [1, 2, 436], [3, 2, 964], [1, 2, 966], [1, 2, 172], [1, 2, 260], [1, 2, 292], [97, 2, 4]], 'aut_group': None, 'aut_hash': 3808563084807252545, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7040, 'aut_permdeg': 54, 'aut_perms': [43398657250692036612895837113429563263586701016530971432562285629407837, 148576054751616936453313951632324874000767095140257353164676923295582236, 109457087503506015185783347675645949104508303693021039628771800253521728, 148576054751605931208960874922958677597072730454664184873485598623582236, 43398657250708544479308368329286222689303830257388598315413811072991837, 148648988368014141462982013191435080697429617664237092620654810766901422, 111958009223572275102245821324239221667247604205017433699207440132228597, 34928216239410853547248937861947079328431227387605309432762880046940592], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 22, 2, 1], [3, 1, 2, 1], [4, 1, 2, 2], [4, 22, 2, 1], [6, 1, 2, 3], [6, 22, 4, 1], [8, 2, 4, 1], [8, 22, 4, 1], [11, 2, 5, 1], [12, 1, 4, 2], [12, 22, 4, 1], [22, 2, 5, 3], [24, 2, 8, 1], [24, 22, 8, 1], [33, 2, 10, 1], [44, 2, 10, 2], [66, 2, 10, 3], [88, 2, 40, 1], [132, 2, 20, 2], [264, 2, 80, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{11}:C_5.C_2^6.C_2', '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': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 22, 2], [3, 1, 2], [4, 1, 4], [4, 22, 2], [6, 1, 6], [6, 22, 4], [8, 2, 4], [8, 22, 4], [11, 2, 5], [12, 1, 8], [12, 22, 4], [22, 2, 15], [24, 2, 8], [24, 22, 8], [33, 2, 10], [44, 2, 20], [66, 2, 30], [88, 2, 40], [132, 2, 40], [264, 2, 80]], 'center_label': '24.9', 'center_order': 24, 'central_product': True, 'central_quotient': '44.3', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 95, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['352.26', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 22, 1, 2], [3, 1, 2, 1], [4, 1, 2, 2], [4, 22, 2, 1], [6, 1, 2, 3], [6, 22, 2, 2], [8, 2, 4, 1], [8, 22, 4, 1], [11, 2, 5, 1], [12, 1, 4, 2], [12, 22, 4, 1], [22, 2, 5, 3], [24, 2, 8, 1], [24, 22, 8, 1], [33, 2, 10, 1], [44, 2, 10, 2], [66, 2, 10, 3], [88, 2, 40, 1], [132, 2, 20, 2], [264, 2, 80, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 264, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '132.7', 'hash': 95, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 1, 22], 'inner_gens': [[1, 2, 966], [1, 2, 4], [99, 2, 4]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 44, 'inner_split': True, 'inner_tex': 'D_{22}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 252]], 'label': '1056.95', 'linC_count': 2560, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 60, 'linQ_dim': 18, 'linQ_dim_count': 60, 'linR_count': 80, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D22:C24', 'ngens': 7, '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': 34, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 300, 'number_divisions': 36, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 92, 'number_subgroup_classes': 100, 'number_subgroups': 596, 'old_label': None, 'order': 1056, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 48], [6, 94], [8, 96], [11, 10], [12, 96], [22, 30], [24, 192], [33, 20], [44, 40], [66, 60], [88, 80], [132, 80], [264, 160]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 2, 10], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[529, 2, 964], [1, 2, 436], [3, 2, 964], [1, 2, 172], [3, 2, 644]], 'outer_group': '160.238', 'outer_hash': 238, 'outer_nilpotent': True, 'outer_order': 160, 'outer_permdeg': 15, 'outer_perms': [479001600, 87178291200, 720, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 7], [8, 3], [10, 2], [20, 5], [40, 5], [80, 2]], 'representations': {'PC': {'code': 18685344418559270824364860495666520000019, 'gens': [1, 2, 3], 'pres': [7, -2, -2, 2, -2, -2, -3, -11, 20288, 58, 24419, 80, 24084, 102, 13445, 166, 47046]}, 'GLZN': {'d': 2, 'p': 115, 'gens': [141441468, 67919669, 36501024, 430560, 71790637, 131266261, 138399716]}, 'Perm': {'d': 26, 'gens': [621574841786321719296005, 44357887, 93405312000, 91578240, 16, 135732240, 16754359726882706632704000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 24], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{22}:C_{24}', 'transitive_degree': 528, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [3]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', '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': 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], [4, 1, 2]], 'center_label': '4.1', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 4, 'exponents_of_order': [2], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '2.1', '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4]], 'label': '4.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 1], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -2, -2, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [56, 15], 'family': 'CSOPlus'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [21]}, 'Perm': {'d': 4, 'gens': [22, 7]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
