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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.772', 'ambient_counter': 772, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.D_8', 'central': False, 'central_factor': True, 'centralizer_order': 84, 'characteristic': True, 'core_order': 192, 'counter': 16, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1344.772.7.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '7.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.138', 'subgroup_hash': 138, 'subgroup_order': 192, 'subgroup_tex': 'C_{12}.D_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1344.772', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '512.10493114', 'aut_weyl_index': 6, 'centralizer': '16.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['14.a1.a1', '14.b1.a1', '14.c1.a1', '21.a1.a1'], 'core': '7.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8285, 3804, 3655, 5988, 4681, 7137, 6926, 7829], 'generators': [1, 680, 336, 2, 672, 448, 348], 'label': '1344.772.7.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['14.a1.a1', '14.c1.a1', '14.b1.a1', '21.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '7.a1.a1', 'projective_image': '112.20', 'quotient_action_image': '1.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '7.a1.a1', 'subgroup_fusion': None, 'weyl_group': '16.3'}
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gps_groups • Show schema
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{'Agroup': False, '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': 4, 'aut_gen_orders': [2, 4, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 16], [1, 6, 16], [5, 2, 16], [1, 106, 16], [97, 2, 16], [1, 150, 112], [61, 2, 112], [1, 2, 80]], 'aut_group': '512.10493114', 'aut_hash': 2216133851576011484, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 34, 'aut_perms': [3695786416542731629507777773672541044, 125369237118155089932589986031681123859, 7119405074906467719416291380508447822, 232647201180195425643561696305549758080, 5292865063864490595708948730328383524, 162587396504279235595970498932845177720, 2450415076490809314868101120000], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [6, 1, 2, 3], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 4, 1], [24, 4, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 2, 4], [4, 4, 1], [4, 8, 2], [6, 1, 6], [8, 4, 8], [12, 2, 8], [12, 4, 2], [12, 8, 4], [24, 4, 16]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '16.3', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 138, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [6, 1, 2, 3], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 2, 2], [24, 4, 8, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '12.5', 'hash': 138, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2], 'inner_gens': [[1, 150, 112], [61, 2, 112], [97, 98, 16]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': True, 'inner_tex': 'C_2^2:C_4', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 30], [4, 3]], 'label': '192.138', 'linC_count': 128, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12.D8', 'ngens': 7, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [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': 24, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 57, 'number_divisions': 26, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 64, 'number_subgroups': 114, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [6, 6], [8, 32], [12, 56], [24, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 4, 0, 0, 0], 'outer_gens': [[1, 6, 16], [5, 2, 16], [1, 106, 16], [97, 2, 16], [1, 2, 80]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 32, 'outer_perms': [8259470424175296574426514081379841, 17774154876782283574170730336362004, 26330869002213901050922466899460658, 34830753587784208264754691194221536, 43328107513216344878530623767946840], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 9], [8, 5]], 'representations': {'PC': {'code': 127579648312838695058256526209, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 56, 2101, 36, 254, 58, 3924, 1971, 102, 124]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [102661, 120406, 80557, 74096, 19311, 37048, 38503]}, 'Perm': {'d': 19, 'gens': [1153381250700960, 7222372716562680, 4, 13917765117696744, 8448744, 20713823523993600, 20713823536535304]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.D_8', 'transitive_degree': 192, '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': '168.39', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 2, 2, 2, 4, 2, 6], 'aut_gens': [[1, 2, 16], [1, 6, 16], [5, 2, 16], [1, 682, 16], [673, 2, 16], [1, 350, 688], [1013, 2, 688], [1, 2, 464], [1, 2, 1168]], 'aut_group': None, 'aut_hash': 5484155219206140901, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 3072, 'aut_permdeg': 40, 'aut_perms': [690559611839853212685755213773307095228848254992, 17279855897767252291119475877082469492601180703, 251489213526094164533627154793693449448752460416, 9438240403387192866162883110137508293632515901, 334932503258578568297757104613916498379897812912, 10479231074669751604002118661087675355707927492, 31658014080, 201875742234393297772666866452007240], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [6, 1, 2, 3], [7, 1, 6, 1], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 4, 1], [14, 1, 6, 3], [21, 1, 12, 1], [24, 4, 8, 2], [28, 2, 6, 4], [28, 4, 6, 1], [28, 8, 12, 1], [42, 1, 12, 3], [56, 4, 24, 2], [84, 2, 12, 4], [84, 4, 12, 1], [84, 8, 24, 1], [168, 4, 48, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times C_6\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '192.1543', 'autcent_hash': 1543, 'autcent_nilpotent': True, 'autcent_order': 192, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5\\times C_6', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 2, 4], [4, 4, 1], [4, 8, 2], [6, 1, 6], [7, 1, 6], [8, 4, 8], [12, 2, 8], [12, 4, 2], [12, 8, 4], [14, 1, 18], [21, 1, 12], [24, 4, 16], [28, 2, 24], [28, 4, 6], [28, 8, 12], [42, 1, 36], [56, 4, 48], [84, 2, 48], [84, 4, 12], [84, 8, 24], [168, 4, 96]], 'center_label': '84.15', 'center_order': 84, 'central_product': True, 'central_quotient': '16.3', 'commutator_count': 1, 'commutator_label': '8.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 772, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.13', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [6, 1, 2, 3], [7, 1, 6, 1], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 2, 2], [14, 1, 6, 3], [21, 1, 12, 1], [24, 4, 8, 2], [28, 2, 6, 4], [28, 4, 6, 1], [28, 8, 6, 2], [42, 1, 12, 3], [56, 4, 24, 2], [84, 2, 12, 4], [84, 4, 12, 1], [84, 8, 12, 2], [168, 4, 48, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 192, 'exponent': 168, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '84.15', 'hash': 772, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2], 'inner_gens': [[1, 350, 688], [1013, 2, 688], [673, 674, 16]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': True, 'inner_tex': 'C_2^2:C_4', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 168], [2, 210], [4, 21]], 'label': '1344.772', 'linC_count': 6144, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 128, 'linQ_dim': 16, 'linQ_dim_count': 32, 'linR_count': 48, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84.D8', 'ngens': 8, 'nilpotency_class': 3, 'nilpotent': True, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 68, 'number_conjugacy_classes': 399, 'number_divisions': 52, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 116, 'number_subgroup_classes': 128, 'number_subgroups': 228, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [6, 6], [7, 6], [8, 32], [12, 56], [14, 18], [21, 12], [24, 64], [28, 168], [42, 36], [56, 192], [84, 336], [168, 384]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 4, 0, 0, 0, 0], 'outer_gens': [[1, 6, 16], [5, 2, 16], [1, 682, 16], [673, 2, 16], [1, 2, 464], [1, 2, 1168]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [87178291200, 479001600, 3628800, 40320, 720, 27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 9], [6, 4], [8, 5], [12, 8], [24, 9], [48, 5]], 'representations': {'PC': {'code': 25617611315116931798144640400181341987262125835, 'gens': [1, 2, 5], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -7, 5376, 5601, 41, 290, 66, 27524, 13772, 116, 141, 222]}, 'Perm': {'d': 26, 'gens': [1967006139794236901606400, 16884790023978593098905600, 32938948375988273574278400, 777120739718400, 49118985076707970744320000, 49118985077865281280979200, 725760, 4320]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 84], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{84}.D_8', 'transitive_degree': 1344, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '7.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 6, 'aut_gen_orders': [6], 'aut_gens': [[1], [3]], 'aut_group': '6.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 6, 'aut_permdeg': 5, 'aut_perms': [27], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [7, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_6', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 6, 'autcent_group': '6.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_6', '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], [7, 1, 6]], 'center_label': '7.1', 'center_order': 7, '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': ['7.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [7, 1, 6, 1]], 'element_repr_type': 'PC', 'elementary': 7, 'eulerian_function': 1, 'exponent': 7, 'exponents_of_order': [1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [7], 'faithful_reps': [[1, 0, 6]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '7.1', 'hash': 1, 'hyperelementary': 7, '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': 6, 'irrQ_dim': 6, 'irrR_degree': 2, 'irrep_stats': [[1, 7]], 'label': '7.1', 'linC_count': 6, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1, 'linQ_dim': 6, 'linQ_dim_count': 1, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C7', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 7, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 7, 'order_factorization_type': 1, 'order_stats': [[1, 1], [7, 6]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '6.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 6, 'outer_permdeg': 5, 'outer_perms': [27], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 7, 'primary_abelian_invariants': [7], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [6, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -7]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [74473229056828135]}, 'Lie': [{'d': 1, 'q': 7, 'gens': [873], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 7, 'gens': [351]}, 'Perm': {'d': 7, 'gens': [4320]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [7], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7', 'transitive_degree': 7, 'wreath_data': None, 'wreath_product': False}
