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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '4200.b', 'ambient_counter': 2, 'ambient_order': 4200, 'ambient_tex': 'D_{210}:C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 2100, 'characteristic': True, 'core_order': 12, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4200.b.350.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '350.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '350.7', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 350, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5\\times D_{35}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4200.b', 'aut_centralizer_order': 20160, 'aut_label': '350.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 20160, 'centralizer': '2.a1.a1', 'complements': ['12.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['50.a1.a1', '70.a1.a1', '70.b1.a1', '70.c1.a1', '70.c1.b1', '175.a1.a1'], 'contains': ['700.a1.a1', '700.b1.a1', '1050.a1.a1'], 'core': '350.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4397, 8249, 5029, 7486, 6666, 8241, 4649, 8241], 'generators': [1972725720, 1972725511, 131515230], 'label': '4200.b.350.a1.a1', 'mobius_quo': 0, 'mobius_sub': 35, 'normal_closure': '350.a1.a1', 'normal_contained_in': ['50.a1.a1', '70.a1.a1', '70.b1.a1'], 'normal_contains': ['700.a1.a1', '1050.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '350.a1.a1', 'projective_image': '2100.a', 'quotient_action_image': '2.1', 'quotient_action_kernel': '175.2', 'quotient_action_kernel_order': 175, 'quotient_fusion': None, 'short_label': '350.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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 6], 'aut_gens': [[1, 2], [6, 9], [6, 11]], 'aut_group': '12.4', 'aut_hash': 4, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12, 'aut_permdeg': 5, 'aut_perms': [6, 31], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [3, 1, 2, 1], [6, 1, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.4', 'autcent_hash': 4, 'autcent_nilpotent': False, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_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], [2, 1, 3], [3, 1, 2], [6, 1, 6]], 'center_label': '12.5', 'center_order': 12, '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': ['2.1', '2.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [6, 1, 2, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 4, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 12]], 'label': '12.5', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 6, 'linQ_dim': 3, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C6', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 12, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [3, 2], [6, 6]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[6, 9], [6, 11]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4]], 'representations': {'PC': {'code': 273, 'gens': [1, 2], 'pres': [3, -2, -2, -3, 16]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [3362, 16507]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [1030, 2064]}, 'Perm': {'d': 7, 'gens': [720, 24, 4]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_6', 'transitive_degree': 12, '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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [4, 6, 4, 12, 12, 84, 12], 'aut_gens': [[44732, 216060414, 995756688], [4917144, 1315150395, 18787968], [8729070, 1766059238, 159696976], [4778728, 1315150341, 535454241], [1913348, 1315150341, 385151346], [4718804, 666969124, 206666530], [8059778, 1972725617, 1324544274], [1378674, 1005150773, 1427877630]], 'aut_group': None, 'aut_hash': 5292214774166627756, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 80640, 'aut_permdeg': 216, 'aut_perms': 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1027369314281487206901008705778344459037012911864747983263510826810765190646752723190179180104568364083499413315986820071232594231098952556358589628082382578083307438592962534608008919764510462836355615135378815754844069869666106074649411569916529889024273424525562645647760399114974399615227084138421959378081445347514547947865154622129729724894146823660289155298208503024149656946276976804612608112092727806636], 'aut_phi_ratio': 84.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 210, 1, 1], [3, 2, 1, 1], [4, 210, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [6, 2, 1, 1], [6, 2, 2, 1], [7, 2, 3, 1], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 2], [10, 2, 8, 1], [10, 2, 16, 1], [10, 210, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [15, 2, 4, 2], [15, 2, 16, 1], [20, 210, 4, 1], [21, 2, 6, 1], [30, 2, 4, 2], [30, 2, 8, 2], [30, 2, 16, 1], [30, 2, 32, 1], [35, 2, 12, 2], [35, 2, 48, 1], [42, 2, 6, 1], [42, 2, 12, 1], [70, 2, 12, 2], [70, 2, 24, 2], [70, 2, 48, 1], [70, 2, 96, 1], [105, 2, 24, 2], [105, 2, 96, 1], [210, 2, 24, 2], [210, 2, 48, 2], [210, 2, 96, 1], [210, 2, 192, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_4\\times C_{105}.C_6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.10', 'autcent_hash': 10, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '5040.bh', 'autcentquo_hash': 3346192685167362256, 'autcentquo_nilpotent': False, 'autcentquo_order': 5040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 210, 1], [3, 2, 1], [4, 210, 1], [5, 1, 4], [5, 2, 10], [6, 2, 3], [7, 2, 3], [10, 1, 4], [10, 2, 34], [10, 210, 4], [14, 2, 9], [15, 2, 24], [20, 210, 4], [21, 2, 6], [30, 2, 72], [35, 2, 72], [42, 2, 18], [70, 2, 216], [105, 2, 144], [210, 2, 432]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '420.40', 'commutator_count': 1, 'commutator_label': '210.12', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '5.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['840.130', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 210, 1, 1], [3, 2, 1, 1], [4, 210, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [6, 2, 1, 1], [6, 2, 2, 1], [7, 2, 3, 1], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 8], [10, 210, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [15, 2, 4, 2], [15, 2, 8, 2], [20, 210, 4, 1], [21, 2, 6, 1], [30, 2, 4, 2], [30, 2, 8, 8], [35, 2, 12, 2], [35, 2, 24, 2], [42, 2, 6, 1], [42, 2, 12, 1], [70, 2, 12, 2], [70, 2, 24, 8], [105, 2, 24, 2], [105, 2, 48, 2], [210, 2, 24, 2], [210, 2, 48, 8]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 36, 'exponent': 420, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': [[2, 0, 192]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2100.a', 'hash': 3359083014773249027, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 10, 105], 'inner_gens': [[44732, 9393954, 18787968], [6950129, 216060414, 995756688], [189267, 216060414, 995756688]], 'inner_hash': 40, 'inner_nilpotent': False, 'inner_order': 420, 'inner_split': True, 'inner_tex': 'D_{210}', 'inner_used': [1, 2, 3], 'irrC_degree': 2, 'irrQ_degree': 96, 'irrQ_dim': 96, 'irrR_degree': None, 'irrep_stats': [[1, 20], [2, 1045]], 'label': '4200.b', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'D210:C10', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 52, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 1065, 'number_divisions': 72, 'number_normal_subgroups': 54, 'number_subgroup_autclasses': 144, 'number_subgroup_classes': 168, 'number_subgroups': 2080, 'old_label': None, 'order': 4200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 213], [3, 2], [4, 210], [5, 24], [6, 6], [7, 6], [10, 912], [14, 18], [15, 48], [20, 840], [21, 12], [30, 144], [35, 144], [42, 36], [70, 432], [105, 288], [210, 864]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 12], 'outer_gen_pows': [9393932, 9393932, 9393932, 9393932], 'outer_gens': [[44732, 216060414, 65757698], [44732, 216060414, 1794240937], [44732, 1465453343, 1559392621], [44732, 976968825, 854847881]], 'outer_group': '192.1400', 'outer_hash': 1400, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [87178291200, 479002344, 2400, 87661326507], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4\\times C_{12}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 7], [6, 2], [8, 14], [12, 3], [16, 10], [24, 5], [48, 14], [96, 10]], 'representations': {'PC': {'code': '43365680413020353969293007077124413662543', 'gens': [1, 2, 6], 'pres': [7, -2, -2, -3, -5, -7, -2, -5, 58773, 36, 79298, 79, 58467, 164, 12604, 124]}, 'GLFp': {'d': 2, 'p': 211, 'gens': [44732, 216060414, 995756688]}, 'Perm': {'d': 24, 'gens': [51097344545418837856, 25903235728530847895794, 53952034955649038208071]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{210}:C_{10}', 'transitive_degree': 420, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [60, 30, 28, 12], 'aut_gens': [[1, 10], [327, 110], [311, 260], [151, 220], [223, 230]], 'aut_group': None, 'aut_hash': 6689779008057805882, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3360, 'aut_permdeg': 39, 'aut_perms': [12276634611259940266075176873975331271664283490, 19221019525894338726674953538768658820018229872, 19779225335434016187892073765821497684583046432, 1165022133730743137378744179309508987377555714], 'aut_phi_ratio': 28.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 35, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 8, 1], [7, 2, 3, 1], [10, 35, 4, 1], [35, 2, 12, 2], [35, 2, 48, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times F_5\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '840.139', 'autcentquo_hash': 139, 'autcentquo_nilpotent': False, 'autcentquo_order': 840, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 35, 1], [5, 1, 4], [5, 2, 10], [7, 2, 3], [10, 35, 4], [35, 2, 72]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '70.3', 'commutator_count': 1, 'commutator_label': '35.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '5.1', '7.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['5.1', 1], ['70.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 35, 1, 1], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [7, 2, 3, 1], [10, 35, 4, 1], [35, 2, 12, 2], [35, 2, 24, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 70, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7], 'faithful_reps': [[2, 0, 48]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '350.7', 'hash': 7, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 35], 'inner_gens': [[1, 340], [21, 10]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 70, 'inner_split': True, 'inner_tex': 'D_{35}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 4, 'irrep_stats': [[1, 10], [2, 85]], 'label': '350.7', 'linC_count': 48, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 72, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5*D35', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 95, 'number_divisions': 12, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 20, 'number_subgroups': 112, 'old_label': None, 'order': 350, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 35], [5, 24], [7, 6], [10, 140], [35, 144]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [4, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 80], [3, 160]], 'outer_group': '48.20', 'outer_hash': 20, 'outer_nilpotent': True, 'outer_order': 48, 'outer_permdeg': 11, 'outer_perms': [864, 4032003], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 3], [6, 1], [8, 2], [24, 2], [48, 2]], 'representations': {'PC': {'code': 144443913776339, 'gens': [1, 3], 'pres': [4, -2, -5, -5, -7, 8, 4082, 70, 4803]}, 'GLFp': {'d': 2, 'p': 71, 'gens': [19327195, 10379468, 5112]}, 'Perm': {'d': 17, 'gens': [21115948009087, 46032173550720, 66718256814720, 973]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times D_{35}', 'transitive_degree': 70, 'wreath_data': None, 'wreath_product': False}
