-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '8736.c', 'ambient_counter': 3, 'ambient_order': 8736, 'ambient_tex': 'C_8.\\PSL(2,13)', 'central': True, 'central_factor': False, 'centralizer_order': 8736, 'characteristic': True, 'core_order': 8, 'counter': 69, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '8736.c.1092.a1.a1', 'maximal': False, 'maximal_normal': True, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1092.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1092.25', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 25, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1092, 'quotient_simple': True, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': '\\PSL(2,13)', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '8736.c', 'aut_centralizer_order': None, 'aut_label': '1092.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['84.b1.a1', '156.b1.a1', '364.e1.a1', '546.a1.a1'], 'contains': ['2184.a1.a1'], 'core': '1092.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8728, 1227, 7739, 1227, 7440, 1137, 6996, 1137], 'generators': [545429530, 57921720, 24134050], 'label': '8736.c.1092.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1092, 'normal_closure': '1092.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['2184.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1092.a1.a1', 'projective_image': '1092.25', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1092.25', 'quotient_action_kernel_order': 1092, 'quotient_fusion': None, 'short_label': '1092.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2], 'aut_gens': [[1], [5], [3]], 'aut_group': '4.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [1, 6], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', '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], [8, 1, 4]], 'center_label': '8.1', 'center_order': 8, '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', '2.1'], 'composition_length': 3, '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], [8, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 8, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '4.1', '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 8]], 'label': '8.1', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C8', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 1], [4, 2], [8, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5], [3]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1]], 'representations': {'PC': {'code': 323, 'gens': [1], 'pres': [3, -2, -2, -2, 6, 16]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26315074]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [77]}, 'Perm': {'d': 8, 'gens': [40176, 16582, 5167]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_8', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [14, 4, 2, 6], 'aut_gens': [[545429530, 57921720, 437680179, 613374539, 24134050], [786770030, 57921720, 676099076, 721764582, 38614480], [786770030, 57921720, 234480029, 627517526, 38614480], [91709390, 57921720, 201979308, 625202008, 38614480], [786770030, 57921720, 11476294, 645794366, 38614480]], 'aut_group': None, 'aut_hash': 4331851435958396675, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8736, 'aut_permdeg': 160, 'aut_perms': [173717497388006549534744836916124829253289432752740343852408737019751646715001300991793252138863307079107173584134165864719115663414675186080856969319365194107432271716493062361493273280446849697290392820097535406253108297439268583505153160495143922879257807280943933069193660006387826, 305899260520530948096695072171599284671614759484686607406427839697252237849331853433533707887375280072276055272013652014680293712760798178651153703678475149065800371534959001240753733234735349409246448951370726949715825756360608738282997114756903894431473498721097079509321140453620260, 412766839547560050414686788225278284844874421981784007083835556571114847617297768010605182878385244767093276809585736715970136808394938762673886987890246553388657561872178825769286711465116874751814093123279392610313472438951798007581644259062334366236783957466762444457906306344923414, 335438341705520058128298324243827694292586306820441052957348639856573683955492468682896027925975152611898951805816960658756543935449943675480257415028705071359695677521733938838633540905763448808485853025832094092291594297689712904568083911795318015681722998966943299440788164134743381], 'aut_phi_ratio': 3.7916666666666665, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 156, 1, 3], [8, 1, 4, 1], [8, 182, 2, 1], [12, 182, 1, 2], [12, 182, 2, 1], [13, 84, 2, 1], [14, 156, 1, 3], [24, 182, 4, 2], [26, 84, 2, 1], [28, 156, 2, 3], [52, 84, 4, 1], [56, 156, 4, 3], [104, 84, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times \\PSL(2,13).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 182, 1], [3, 182, 1], [4, 1, 2], [4, 182, 1], [6, 182, 3], [7, 156, 3], [8, 1, 4], [8, 182, 2], [12, 182, 4], [13, 84, 2], [14, 156, 3], [24, 182, 8], [26, 84, 2], [28, 156, 6], [52, 84, 4], [56, 156, 12], [104, 84, 8]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '2184.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '1092.25'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 156, 3, 1], [8, 1, 4, 1], [8, 182, 2, 1], [12, 182, 2, 2], [13, 84, 2, 1], [14, 156, 3, 1], [24, 182, 4, 2], [26, 84, 2, 1], [28, 156, 6, 1], [52, 84, 4, 1], [56, 156, 12, 1], [104, 84, 8, 1]], 'element_repr_type': 'GLFq', 'elementary': 1, 'eulerian_function': 5940, 'exponent': 2184, 'exponents_of_order': [5, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[6, 0, 8], [12, 0, 12], [14, 0, 12]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '2184.o', 'hash': 1266776031419148375, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [1, 1, 2, 13, 1], 'inner_gens': [[545429530, 57921720, 437680179, 613374539, 24134050], [545429530, 57921720, 437680179, 613374539, 24134050], [545429530, 57921720, 437680179, 404186708, 24134050], [545429530, 57921720, 430680031, 613374539, 24134050], [545429530, 57921720, 437680179, 613374539, 24134050]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [3, 4], 'irrC_degree': 6, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [6, 8], [7, 8], [12, 24], [13, 4], [14, 20]], 'label': '8736.c', 'linC_count': 8, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 48, 'linQ_degree_count': 1, 'linQ_dim': 48, 'linQ_dim_count': 1, 'linR_count': 4, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C8.PSL(2,13)', '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, 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': 31, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 68, 'number_divisions': 22, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 74, 'number_subgroup_classes': 85, 'number_subgroups': 5996, 'old_label': None, 'order': 8736, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 183], [3, 182], [4, 184], [6, 546], [7, 468], [8, 368], [12, 728], [13, 168], [14, 468], [24, 1456], [26, 168], [28, 936], [52, 336], [56, 1872], [104, 672]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [4826810, 4826810, 4826810], 'outer_gens': [[545429530, 57921720, 262525404, 416933699, 24134050], [91709390, 57921720, 437680179, 429833316, 38614480], [333049890, 57921720, 437680179, 265506932, 24134050]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 112, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [13, 2], [14, 6], [26, 1], [28, 3], [36, 2], [48, 1], [56, 1], [72, 1], [112, 1], [144, 1]], 'representations': {'GLFq': {'d': 2, 'q': 169, 'gens': [545429530, 57921720, 437680179, 613374539, 24134050]}, 'Perm': {'d': 112, 'gens': [1826924877283244963059662761157197231704002146885323420823962266291077739968917027402395206199118358719241521228514885103800886122352352107279456265813146082177018467222464142337453, 3573557767455205938080027920357296613169692244080732861627284407516798638592780184482368648542537192496970537768272719005830443337476025715400686240011192044467333644888694963322376, 5432668803825595195362873846150637505698904226790286193211302974193245067960695277307143538177317210273066064360978445581228418910869935050338319119969113562239205880552655361275549, 7179026192558219555650271996806056227755385030613234854739048284102376706939880869859931971737718265113079154899613941974651914377483804408593113622691074754442525969921557483036061, 8926963953040712745646524287002850104561187403879360940898066699485698683286651199942865623499335270808473570855890714469563648358819182370831776040016719216412526407098076260932488]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_8.\\PSL(2,13)', 'transitive_degree': 112, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [12, 3], 'aut_gens': [[15381, 2053], [5753, 3703], [15753, 14334]], 'aut_group': '2184.b', 'aut_hash': 7763277135502868404, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2184, 'aut_permdeg': 91, 'aut_perms': [15685624209542281043180093832356955359558084980787576118939763356894651589906212972242836233730372715269387981677749662727246705895496015546, 88904264646742496335384702563170983777880925500795965825705028509132871588844625292831170146632406414409051897144147289726343368975320434687], 'aut_phi_ratio': 7.583333333333333, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 91, 1, 1], [3, 182, 1, 1], [6, 182, 1, 1], [7, 156, 1, 3], [13, 84, 2, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PGL(2,13)', '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': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 91, 1], [3, 182, 1], [6, 182, 1], [7, 156, 3], [13, 84, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '1092.25', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['1092.25'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 25, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 91, 1, 1], [3, 182, 1, 1], [6, 182, 1, 1], [7, 156, 3, 1], [13, 84, 2, 1]], 'element_repr_type': 'Lie', 'elementary': 1, 'eulerian_function': 495, 'exponent': 546, 'exponents_of_order': [2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[7, 1, 2], [12, 1, 3], [13, 1, 1], [14, 1, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1092.25', 'hash': 25, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [6, 3], 'inner_gens': [[15381, 1663], [5246, 2053]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [1, 2], 'irrC_degree': 7, 'irrQ_degree': 13, 'irrQ_dim': 13, 'irrR_degree': 7, 'irrep_stats': [[1, 1], [7, 2], [12, 3], [13, 1], [14, 2]], 'label': '1092.25', 'linC_count': 2, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 13, 'linQ_degree_count': 1, 'linQ_dim': 13, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'PSL(2,13)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 9, 'number_divisions': 6, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 15, 'number_subgroup_classes': 16, 'number_subgroups': 942, 'old_label': None, 'order': 1092, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 91], [3, 182], [6, 182], [7, 468], [13, 168]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [1807], 'outer_gens': [[4604, 6652]], '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': True, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [13, 1], [14, 3], [36, 1]], 'representations': {'Lie': [{'d': 2, 'q': 13, 'gens': [2053, 15381], 'family': 'PSL'}, {'d': 2, 'q': 13, 'gens': [33787665, 1272582], 'family': 'PSU'}, {'d': 3, 'q': 13, 'gens': [58292859, 3262951455], 'family': 'Omega'}, {'d': 3, 'q': 13, 'gens': [58292859, 3262951455], 'family': 'POmega'}, {'d': 2, 'q': 13, 'gens': [2053, 15381], 'family': 'PSigmaL'}], 'GLFp': {'d': 3, 'p': 13, 'gens': [8354693709, 7376835470]}, 'Perm': {'d': 14, 'gens': [560517275, 132642186, 6268172431]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\PSL(2,13)', 'transitive_degree': 14, 'wreath_data': None, 'wreath_product': False}
