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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '82575360.q', 'ambient_counter': 17, 'ambient_order': 82575360, 'ambient_tex': 'C_2^{14}.A_7.C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 16384, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '82575360.q.5040._.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '5040.A', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5040.w', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5040, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'S_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 16384, 'subgroup_tex': 'C_2^{14}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '82575360.q', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [121645106635857967, 8841777504949866930630008837161, 20397882081205666208183354965277360379735228721, 8852650863190241951804832753846, 15511261134273157693807927, 25903107682370587468800, 8841777530852853322273714544047, 368046, 8691540457481575679470548815508556926, 10333156198066561101380383604901814634887, 15511261134628851348556800, 13763761774543963858202475099775303680005041, 10888869501509294332477802881, 33452526613163815339850478251006379027622856448000], 'label': '82575360.q.5040._.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '5040.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5040._.A', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 840, 'aut_gen_orders': [4, 20, 12], 'aut_gens': [[145993617038529502657822308691181813878995172135, 1335779055992319234622113785233987674228720110935687], [307787883478730113689344333553217838518125507298423, 1028179263286568306840151369360040062165101464001158], [788027929225360739784294960603205362797993886877296, 582144585024124601045109097357542319488710037161662], [1302703133999056676337884585976383845594867258539576, 1061652201428869302693717388614044035644826432302136]], 'aut_group': None, 'aut_hash': 565277917155204324, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 165150720, 'aut_permdeg': 672, 'aut_perms': 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'aut_phi_ratio': 8.75, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 21, 1, 1], [2, 35, 1, 1], [2, 70, 1, 1], [2, 105, 1, 4], [2, 210, 1, 1], [2, 252, 1, 1], [2, 315, 1, 1], [2, 336, 2, 1], [2, 360, 1, 1], [2, 420, 1, 3], [2, 630, 1, 4], [2, 840, 1, 1], [2, 1260, 1, 6], [2, 2520, 1, 1], [2, 3360, 2, 1], [2, 4032, 1, 1], [2, 5040, 2, 1], [2, 6720, 1, 1], [2, 6720, 2, 1], [2, 13440, 1, 1], [2, 20160, 1, 1], [3, 17920, 1, 1], [3, 286720, 1, 1], [4, 1680, 2, 1], [4, 3360, 2, 2], [4, 5040, 2, 1], [4, 6720, 1, 1], [4, 6720, 2, 2], [4, 10080, 2, 3], [4, 13440, 1, 1], [4, 13440, 2, 1], [4, 20160, 1, 6], [4, 20160, 2, 7], [4, 26880, 1, 3], [4, 40320, 1, 8], [4, 40320, 2, 7], [4, 80640, 1, 15], [4, 80640, 2, 3], [4, 161280, 1, 3], [4, 215040, 2, 1], [4, 645120, 2, 1], [5, 2064384, 1, 1], [6, 17920, 1, 1], [6, 53760, 1, 2], [6, 71680, 1, 2], [6, 107520, 1, 2], [6, 215040, 1, 3], [6, 215040, 2, 1], [6, 286720, 1, 1], [6, 430080, 1, 1], [6, 430080, 2, 2], [6, 573440, 1, 1], [6, 860160, 1, 2], [6, 1720320, 1, 1], [6, 3440640, 1, 1], [7, 2949120, 1, 1], [8, 215040, 2, 1], [8, 645120, 2, 5], [8, 1290240, 2, 2], [10, 2064384, 1, 3], [10, 2064384, 2, 2], [12, 215040, 2, 1], [12, 430080, 1, 1], [12, 430080, 2, 3], [12, 860160, 1, 1], [12, 860160, 2, 2], [12, 1720320, 2, 1], [12, 3440640, 1, 3], [14, 2949120, 1, 3], [24, 1720320, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^{15}.A_7.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': 840, 'autcentquo_group': None, 'autcentquo_hash': 565277917155204324, 'autcentquo_nilpotent': False, 'autcentquo_order': 165150720, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^{15}.A_7.C_2', 'cc_stats': [[1, 1, 1], [2, 21, 1], [2, 35, 1], [2, 70, 1], [2, 105, 4], [2, 210, 1], [2, 252, 1], [2, 315, 1], [2, 336, 2], [2, 360, 1], [2, 420, 3], [2, 630, 4], [2, 840, 1], [2, 1260, 6], [2, 2520, 1], [2, 3360, 2], [2, 4032, 1], [2, 5040, 2], [2, 6720, 3], [2, 13440, 1], [2, 20160, 1], [3, 17920, 1], [3, 286720, 1], [4, 1680, 2], [4, 3360, 4], [4, 5040, 2], [4, 6720, 5], [4, 10080, 6], [4, 13440, 3], [4, 20160, 20], [4, 26880, 3], [4, 40320, 22], [4, 80640, 21], [4, 161280, 3], [4, 215040, 2], [4, 645120, 2], [5, 2064384, 1], [6, 17920, 1], [6, 53760, 2], [6, 71680, 2], [6, 107520, 2], [6, 215040, 5], [6, 286720, 1], [6, 430080, 5], [6, 573440, 1], [6, 860160, 2], [6, 1720320, 1], [6, 3440640, 1], [7, 2949120, 1], [8, 215040, 2], [8, 645120, 10], [8, 1290240, 4], [10, 2064384, 7], [12, 215040, 2], [12, 430080, 7], [12, 860160, 5], [12, 1720320, 2], [12, 3440640, 3], [14, 2949120, 3], [24, 1720320, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '82575360.q', 'commutator_count': 1, 'commutator_label': '41287680.r', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2520.a'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 21, 1, 1], [2, 35, 1, 1], [2, 70, 1, 1], [2, 105, 1, 4], [2, 210, 1, 1], [2, 252, 1, 1], [2, 315, 1, 1], [2, 336, 1, 2], [2, 360, 1, 1], [2, 420, 1, 3], [2, 630, 1, 4], [2, 840, 1, 1], [2, 1260, 1, 6], [2, 2520, 1, 1], [2, 3360, 1, 2], [2, 4032, 1, 1], [2, 5040, 1, 2], [2, 6720, 1, 3], [2, 13440, 1, 1], [2, 20160, 1, 1], [3, 17920, 1, 1], [3, 286720, 1, 1], [4, 1680, 1, 2], [4, 3360, 1, 4], [4, 5040, 1, 2], [4, 6720, 1, 5], [4, 10080, 1, 6], [4, 13440, 1, 3], [4, 20160, 1, 20], [4, 26880, 1, 3], [4, 40320, 1, 22], [4, 80640, 1, 21], [4, 161280, 1, 3], [4, 215040, 1, 2], [4, 645120, 1, 2], [5, 2064384, 1, 1], [6, 17920, 1, 1], [6, 53760, 1, 2], [6, 71680, 1, 2], [6, 107520, 1, 2], [6, 215040, 1, 5], [6, 286720, 1, 1], [6, 430080, 1, 5], [6, 573440, 1, 1], [6, 860160, 1, 2], [6, 1720320, 1, 1], [6, 3440640, 1, 1], [7, 2949120, 1, 1], [8, 215040, 1, 2], [8, 645120, 1, 10], [8, 1290240, 1, 4], [10, 2064384, 1, 3], [10, 2064384, 2, 2], [12, 215040, 1, 2], [12, 430080, 1, 7], [12, 860160, 1, 5], [12, 1720320, 1, 2], [12, 3440640, 1, 3], [14, 2949120, 3, 1], [24, 1720320, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 840, 'exponents_of_order': [18, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[21, 1, 4], [35, 1, 4], [70, 1, 8], [84, 1, 4], [105, 1, 32], [126, 1, 2], [140, 1, 2], [210, 1, 26], [252, 1, 4], [280, 1, 4], [315, 1, 16], [360, 1, 2], [420, 1, 18], [504, 1, 4], [630, 1, 22], [720, 1, 3], [840, 1, 8], [1260, 1, 27], [1680, 1, 1], [2520, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '82575360.q', 'hash': 787774024793549320, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 840, 'inner_gen_orders': [5, 24], 'inner_gens': [[145993617038529502657822308691181813878995172135, 754408176583059873810184895292111935224645979821577], [787442341804456057801873457389391609481458043860416, 1335779055992319234622113785233987674228720110935687]], 'inner_hash': 787774024793549320, 'inner_nilpotent': False, 'inner_order': 82575360, 'inner_split': True, 'inner_tex': 'C_2^{14}.A_7.C_2', 'inner_used': [1, 2], 'irrC_degree': 21, 'irrQ_degree': 21, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 2], [6, 2], [14, 4], [15, 2], [20, 1], [21, 6], [35, 6], [70, 8], [84, 4], [105, 32], [126, 2], [140, 2], [210, 26], [252, 4], [280, 4], [315, 16], [360, 2], [420, 18], [504, 4], [630, 22], [720, 3], [840, 8], [1260, 27], [1680, 1], [2520, 2]], 'label': '82575360.q', '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': False, 'name': 'C2^14.A7.C2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 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, 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, 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, 0, 1, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 154, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 208, 'number_divisions': 204, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 82575360, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 91647], [3, 304640], [4, 5429760], [5, 2064384], [6, 11450880], [7, 2949120], [8, 12042240], [10, 14450688], [12, 21504000], [14, 8847360], [24, 3440640]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[125581981537380567659864468924738052178731405768, 1335799453874400440297163730556840636804752257777847]], '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': None, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [6, 2], [14, 4], [15, 2], [20, 1], [21, 6], [35, 6], [70, 8], [84, 4], [105, 32], [126, 2], [140, 2], [210, 26], [252, 4], [280, 4], [315, 16], [360, 2], [420, 18], [630, 22], [840, 8], [1008, 2], [1260, 27], [1680, 1], [2160, 1], [2520, 2]], 'representations': {'Perm': {'d': 42, 'gens': [1335779055992319234622113785233987674228720110935687, 145993617038529502657822308691181813878995172135]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 768, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_2^{14}.A_7.C_2', 'transitive_degree': 42, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 420, 'aut_gen_orders': [7, 2], 'aut_gens': [[873, 720], [1975, 5], [1017, 720]], 'aut_group': '5040.w', 'aut_hash': 6283920599749723413, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5040, 'aut_permdeg': 21, 'aut_perms': [33353925871431967814, 494845084239614645], 'aut_phi_ratio': 4.375, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 21, 1, 1], [2, 105, 1, 2], [3, 70, 1, 1], [3, 280, 1, 1], [4, 210, 1, 1], [4, 630, 1, 1], [5, 504, 1, 1], [6, 210, 1, 1], [6, 420, 1, 1], [6, 840, 1, 1], [7, 720, 1, 1], [10, 504, 1, 1], [12, 420, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_7', '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': 420, 'autcentquo_group': '5040.w', 'autcentquo_hash': 6283920599749723413, 'autcentquo_nilpotent': False, 'autcentquo_order': 5040, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_7', 'cc_stats': [[1, 1, 1], [2, 21, 1], [2, 105, 2], [3, 70, 1], [3, 280, 1], [4, 210, 1], [4, 630, 1], [5, 504, 1], [6, 210, 1], [6, 420, 1], [6, 840, 1], [7, 720, 1], [10, 504, 1], [12, 420, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5040.w', 'commutator_count': 1, 'commutator_label': '2520.a', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2520.a'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 23, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 21, 1, 1], [2, 105, 1, 2], [3, 70, 1, 1], [3, 280, 1, 1], [4, 210, 1, 1], [4, 630, 1, 1], [5, 504, 1, 1], [6, 210, 1, 1], [6, 420, 1, 1], [6, 840, 1, 1], [7, 720, 1, 1], [10, 504, 1, 1], [12, 420, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3090, 'exponent': 420, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[6, 1, 2], [14, 1, 4], [15, 1, 2], [20, 1, 1], [21, 1, 2], [35, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5040.w', 'hash': 6283920599749723413, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 420, 'inner_gen_orders': [7, 2], 'inner_gens': [[873, 120], [1473, 720]], 'inner_hash': 6283920599749723413, 'inner_nilpotent': False, 'inner_order': 5040, 'inner_split': True, 'inner_tex': 'S_7', 'inner_used': [1, 2], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 2], [6, 2], [14, 4], [15, 2], [20, 1], [21, 2], [35, 2]], 'label': '5040.w', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'S7', 'ngens': 2, '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, 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, 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': 15, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 15, 'number_divisions': 15, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 96, 'number_subgroups': 11300, 'old_label': None, 'order': 5040, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 231], [3, 350], [4, 840], [5, 504], [6, 1470], [7, 720], [10, 504], [12, 420]], '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': None, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2], [14, 4], [15, 2], [20, 1], [21, 2], [35, 2]], 'representations': {'GLZ': {'b': 3, 'd': 6, 'gens': [125079720501303932, 110572326332023]}, 'Perm': {'d': 7, 'gens': [873, 720]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_7', 'transitive_degree': 7, 'wreath_data': None, 'wreath_product': False}
