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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2904', 'ambient_counter': 2904, 'ambient_order': 1296, 'ambient_tex': '\\SU(3,2):S_3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 9, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2904.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.182', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 182, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_9:C_2', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1296.2904', 'aut_centralizer_order': 648, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 648, 'centralizer': '2.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '72.a1.a1', '72.f1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.b1.b1', '432.b1.c1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2322, 5115, 4095, 4733, 6592, 5602, 3663, 5614], 'generators': [16, 432], 'label': '1296.2904.144.a1.a1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['432.b1.b1', '432.b1.c1', '432.b1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '1296.2904', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.41', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '9.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 3], [1, 7], [4, 3]], 'aut_group': '48.29', 'aut_hash': 29, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 8, 'aut_perms': [31834, 28334], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '48.29', 'autcent_hash': 29, 'autcent_nilpotent': False, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(2,3)', '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], [3, 1, 8]], 'center_label': '9.2', 'center_order': 9, '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': ['3.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '9.2', 'hash': 2, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 9]], 'label': '9.2', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 6, 'linQ_dim': 4, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3^2', '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': 9, 'number_divisions': 5, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 9, 'order_factorization_type': 2, 'order_stats': [[1, 1], [3, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 7], [4, 3]], 'outer_group': '48.29', 'outer_hash': 29, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 8, 'outer_perms': [31834, 28334], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 6, 'pgroup': 3, 'primary_abelian_invariants': [3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -3, 3]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16858733, 35931237]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [687, 1374]}, 'Perm': {'d': 6, 'gens': [240, 4]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2', 'transitive_degree': 9, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 12, 12, 24], 'aut_gens': [[1, 2, 16, 48, 144, 432], [537, 806, 464, 288, 480, 432], [721, 294, 448, 192, 336, 432], [1105, 966, 896, 1056, 1200, 432], [1109, 850, 880, 384, 96, 864]], 'aut_group': None, 'aut_hash': 2213538631687328649, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7776, 'aut_permdeg': 144, 'aut_perms': [3192981550204459594220335019268478304250873967799497893400774381321757482991136611669841922949282588305809423992828868718573691613389593297528751596250058018339546721057504565632247777865428593038416984219446177579641066911674551846669641577839111101, 2266829890241921719147935063464777664047703413547059799267041933772960643747524341987243883505665287791442280964641493604157394050476126655429814077731068352097842359531027739419625562760248189829320659546991606760719950056965581050235521049763768206, 3683064416370515878160524293445848564151556102410657799173195221695100131645288548924631447232537103912560493784771691858758783145681316566815079667956217258087031776169193258464729523939640677204315980223139133531541665363340638512724987762936605692, 3415547835054920859075788665971168438514785979964421303752576476627558758836393227661380504602325378167350359857700389037691756141601854989887419025731493649927653979826604149982706394664481027655172109238873119969121172090801868821955768862113288665], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 108, 1, 1], [3, 2, 1, 1], [3, 2, 3, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 18, 1, 1], [6, 18, 3, 1], [6, 216, 1, 1], [8, 162, 1, 2], [12, 36, 1, 3], [12, 36, 3, 1], [12, 36, 6, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_3.C_4:S_3^2.C_2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 2213538631687328649, 'autcentquo_nilpotent': False, 'autcentquo_order': 7776, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_3.C_4:S_3^2.C_2', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 108, 1], [3, 2, 4], [3, 24, 1], [3, 48, 1], [4, 18, 1], [4, 36, 1], [6, 18, 4], [6, 216, 1], [8, 162, 2], [12, 36, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1296.2904', 'commutator_count': 1, 'commutator_label': '324.110', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2904, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 108, 1, 1], [3, 2, 1, 4], [3, 24, 1, 1], [3, 48, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 18, 1, 4], [6, 216, 1, 1], [8, 162, 2, 1], [12, 36, 1, 4], [12, 36, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 24, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '432.739', 'hash': 2904, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [4, 8, 3, 3, 3, 3], 'inner_gens': [[1, 6, 16, 1056, 768, 432], [13, 2, 32, 288, 672, 864], [1, 34, 16, 48, 144, 432], [721, 626, 16, 48, 576, 432], [817, 482, 16, 912, 144, 432], [1, 866, 16, 48, 144, 432]], 'inner_hash': 2904, 'inner_nilpotent': False, 'inner_order': 1296, 'inner_split': True, 'inner_tex': '\\SU(3,2):S_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 7], [4, 1], [6, 12], [8, 2], [12, 3], [16, 1]], 'label': '1296.2904', 'linC_count': 48, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 12, 'linQ_dim': 8, 'linQ_dim_count': 12, 'linR_count': 12, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SU(3,2):S3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 30, 'number_divisions': 25, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 86, 'number_subgroup_classes': 116, 'number_subgroups': 2770, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 117], [3, 80], [4, 54], [6, 288], [8, 324], [12, 432]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 2, 32, 48, 144, 432], [1, 2, 880, 48, 144, 432]], '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': 6, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 3], [6, 6], [8, 2], [12, 6], [16, 1]], 'representations': {'PC': {'code': 430894858464092923157181655982052872395967909045831170885391, 'gens': [1, 2, 5, 6, 7, 8], 'pres': [8, -2, -2, -2, -2, -3, -3, 3, -3, 64, 97, 41, 290, 66, 652, 50693, 6925, 9237, 605, 43014, 18830, 17494, 2046, 718, 27663]}, 'Perm': {'d': 30, 'gens': [1340572076885649679655321991625, 1623286101263528208518410056600, 1960838609834270030025961837464, 2276619634729489572414222288480, 11437083195776210982930129141360, 20487773315199994009651963818720, 29738721948408851790406194310563, 38840638737587731943636346553680]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SU(3,2):S_3', 'transitive_degree': 81, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [8, 2, 4, 2, 3, 3], 'aut_gens': [[23802, 5306, 37817, 5515, 276480, 80884], [23802, 37727, 37817, 5515, 80884, 321987], [27320, 5306, 20073, 5515, 321987, 45507], [23802, 598, 37817, 5515, 321987, 184197], [23802, 5306, 37817, 5515, 138690, 45507], [285730, 85801, 112583, 143305, 276480, 80884], [188355, 40349, 298904, 40892, 276480, 80884]], 'aut_group': '144.182', 'aut_hash': 182, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 144, 'aut_permdeg': 9, 'aut_perms': [12443, 3295, 6781, 18498, 296735, 257496], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 12, 1, 1], [3, 8, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 24, 1, 1], [8, 18, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'F_9:C_2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '144.182', 'autcentquo_hash': 182, 'autcentquo_nilpotent': False, 'autcentquo_order': 144, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:C_2', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 12, 1], [3, 8, 1], [4, 18, 1], [4, 36, 1], [6, 24, 1], [8, 18, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '144.182', 'commutator_count': 1, 'commutator_label': '36.9', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 182, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 12, 1, 1], [3, 8, 1, 1], [4, 18, 1, 1], [4, 36, 1, 1], [6, 24, 1, 1], [8, 18, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 48, 'exponent': 24, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '144.182', 'hash': 182, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 2, 4, 2, 3, 3], 'inner_gens': [[23802, 37727, 37817, 5515, 80884, 321987], [27320, 5306, 20073, 5515, 321987, 45507], [23802, 598, 37817, 5515, 321987, 184197], [23802, 5306, 37817, 5515, 138690, 45507], [285730, 85801, 112583, 143305, 276480, 80884], [188355, 40349, 298904, 40892, 276480, 80884]], 'inner_hash': 182, 'inner_nilpotent': False, 'inner_order': 144, 'inner_split': True, 'inner_tex': 'F_9:C_2', 'inner_used': [1, 2, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 3], [8, 2]], 'label': '144.182', 'linC_count': 2, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'F9:C2', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 9, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 25, 'number_subgroup_classes': 25, 'number_subgroups': 162, 'old_label': None, 'order': 144, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 21], [3, 8], [4, 54], [6, 24], [8, 36]], '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': 4, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 1], [8, 2]], 'representations': {'PC': {'code': 37830836297451535842285202495875, 'gens': [1, 2, 5, 6], 'pres': [6, -2, -2, -2, -2, -3, 3, 73, 31, 218, 50, 964, 1210, 976, 142, 2885, 299, 737, 455]}, 'Lie': [{'d': 1, 'q': 9, 'gens': [62619, 1930, 5913], 'family': 'AGammaL'}], 'GLFp': {'d': 3, 'p': 3, 'gens': [11017, 14041, 16990, 8101, 15342, 8183]}, 'Perm': {'d': 9, 'gens': [23802, 5306, 37817, 5515, 276480, 80884]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'F_9:C_2', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
