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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1440.1381', 'ambient_counter': 1381, 'ambient_order': 1440, 'ambient_tex': 'C_5\\times C_6^2.Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 360, 'characteristic': True, 'core_order': 36, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.1381.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1440.1381', 'aut_centralizer_order': 576, 'aut_label': '40.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '96.189', 'aut_weyl_index': 576, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '20.a1', '20.b1', '20.c1'], 'contains': ['80.a1', '120.c1'], 'core': '40.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1525, 7958, 1522, 8249], 'generators': [360, 728, 960, 720], 'label': '1440.1381.40.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1', 'normal_contained_in': ['8.c1', '20.a1', '20.b1', '20.c1'], 'normal_contains': ['80.a1', '120.c1'], 'normalizer': '1.a1', 'old_label': '40.c1', 'projective_image': '720.359', 'quotient_action_image': '4.2', 'quotient_action_kernel': '10.2', 'quotient_action_kernel_order': 10, 'quotient_fusion': None, 'short_label': '40.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '36.8', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [3, 2, 2, 2, 4, 4], 'aut_gens': [[1, 3], [24, 16], [12, 10], [1, 21], [2, 33], [25, 35], [26, 5]], 'aut_group': '96.189', 'aut_hash': 189, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96, 'aut_permdeg': 10, 'aut_perms': [23040, 363168, 368047, 1, 1641001, 2442654], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 8, 1], [4, 1, 2, 1], [6, 1, 8, 1], [12, 1, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '96.189', 'autcent_hash': 189, 'autcent_nilpotent': False, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times \\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], [2, 1, 1], [3, 1, 8], [4, 1, 2], [6, 1, 8], [12, 1, 16]], 'center_label': '36.8', 'center_order': 36, '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', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 2], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [4, 1, 2, 1], [6, 1, 2, 4], [12, 1, 4, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 6, 'exponent': 12, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '18.5', 'hash': 8, '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, 36]], 'label': '36.8', 'linC_count': 288, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 48, 'linQ_dim': 6, 'linQ_dim_count': 48, 'linR_count': 72, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C12', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 36, 'number_divisions': 15, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 18, 'number_subgroups': 18, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 2], [6, 8], [12, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [3, 2, 2, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[24, 16], [12, 10], [1, 21], [2, 33], [25, 35], [26, 5]], 'outer_group': '96.189', 'outer_hash': 189, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 10, 'outer_perms': [23040, 363168, 368047, 1, 1641001, 2442654], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [4, 4]], 'representations': {'PC': {'code': 319593, 'gens': [1, 2], 'pres': [4, -3, -2, -2, -3, 21, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101732552038707, 91655858505665801]}, 'GLFp': {'d': 2, 'p': 13, 'gens': [15381, 6592]}, 'Perm': {'d': 10, 'gens': [1169280, 240, 4, 367920]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 12], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{12}', 'transitive_degree': 36, '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': '40.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 12, 8, 12, 4, 12, 6], 'aut_gens': [[1, 2, 24], [617, 502, 992], [609, 602, 1128], [601, 126, 472], [1, 126, 176], [961, 618, 232], [969, 498, 1040], [369, 1218, 1184]], 'aut_group': None, 'aut_hash': 8094071161320713060, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 55296, 'aut_permdeg': 48, 'aut_perms': [4389970650585292795401352172078235146220747259002059957691284, 11803798526736022537093800650921158240374295640391196329542710, 2675990675342019692928137725478730792183793080899430729935984, 6472379464163884014962821248103680065361072491990664590668079, 9841692466545211022744823490735700697971836219242964548452636, 12230664330108950868367435318800754600924721085166127796946965, 9623857528816334126989489610855966403351247677470364876188326], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 2, 4, 1], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 4, 1], [6, 4, 4, 1], [8, 4, 2, 1], [8, 18, 2, 2], [8, 36, 2, 1], [10, 1, 4, 1], [10, 2, 4, 1], [12, 2, 8, 1], [12, 4, 4, 1], [15, 2, 16, 1], [20, 1, 8, 1], [20, 2, 4, 1], [24, 4, 16, 1], [30, 2, 16, 1], [30, 4, 16, 1], [40, 4, 8, 1], [40, 18, 8, 2], [40, 36, 8, 1], [60, 2, 32, 1], [60, 4, 16, 1], [120, 4, 64, 1]], 'aut_supersolvable': False, 'aut_tex': '\\ASL(2,3).C_2^3.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.45', 'autcent_hash': 45, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '1728.47845', 'autcentquo_hash': 47845, 'autcentquo_nilpotent': False, 'autcentquo_order': 1728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [3, 2, 4], [4, 1, 2], [4, 2, 1], [5, 1, 4], [6, 2, 4], [6, 4, 4], [8, 4, 2], [8, 18, 4], [8, 36, 2], [10, 1, 4], [10, 2, 4], [12, 2, 8], [12, 4, 4], [15, 2, 16], [20, 1, 8], [20, 2, 4], [24, 4, 16], [30, 2, 16], [30, 4, 16], [40, 4, 8], [40, 18, 16], [40, 36, 8], [60, 2, 32], [60, 4, 16], [120, 4, 64]], 'center_label': '20.2', 'center_order': 20, 'central_product': True, 'central_quotient': '72.35', 'commutator_count': 1, 'commutator_label': '36.8', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1381, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['288.297', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [3, 2, 1, 4], [4, 1, 2, 1], [4, 2, 1, 1], [5, 1, 4, 1], [6, 2, 1, 4], [6, 4, 1, 4], [8, 4, 2, 1], [8, 18, 2, 2], [8, 36, 2, 1], [10, 1, 4, 1], [10, 2, 4, 1], [12, 2, 2, 4], [12, 4, 1, 4], [15, 2, 4, 4], [20, 1, 8, 1], [20, 2, 4, 1], [24, 4, 4, 4], [30, 2, 4, 4], [30, 4, 4, 4], [40, 4, 8, 1], [40, 18, 8, 2], [40, 36, 8, 1], [60, 2, 8, 4], [60, 4, 4, 4], [120, 4, 16, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 20832, 'exponent': 120, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '180.35', 'hash': 1381, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [4, 6, 6], 'inner_gens': [[1, 1090, 984], [1097, 2, 744], [481, 722, 24]], 'inner_hash': 35, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_6^2:C_2', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 40], [2, 190], [4, 40]], 'label': '1440.1381', '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': 'C5*C6^2.Q8', '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, 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': 30, 'number_characteristic_subgroups': 38, 'number_conjugacy_classes': 270, 'number_divisions': 66, 'number_normal_subgroups': 94, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 180, 'number_subgroups': 440, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3], [3, 8], [4, 4], [5, 4], [6, 24], [8, 152], [10, 12], [12, 32], [15, 32], [20, 16], [24, 64], [30, 96], [40, 608], [60, 128], [120, 256]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [6, 4, 4, 4], 'outer_gen_pows': [0, 192, 8, 0], 'outer_gens': [[1217, 1214, 944], [1321, 1342, 168], [737, 1082, 1288], [841, 486, 1376]], 'outer_group': '768.1089004', 'outer_hash': 1089004, 'outer_nilpotent': False, 'outer_order': 768, 'outer_permdeg': 128, 'outer_perms': [305856723050182979274300591511193521442683353145021916449462723175821035415361811149658211277336895490087426083687184900022644352706733375142796132026650315024542156395966421178189067719496661599122235399848509254423, 184673131258024103123237135103366405708123964335823845659533995089112336917653737869199375884235028827478364876049380243669958454640162907339733200577949867020732413810735753884443155136320419943327253015871636297519, 61345831636697066184256234477985019702598061389161847277706112467437888414939486773018916415041301712409122116633801803479323503285601424598848533471308190198725785575374025542413173674002524239586136555676287533502, 43792547009056397826035210740188061025238068728554185109376282048949188698619063893777063206208112196898130244291356445477279008594841363755326605158091236314199877255626166697361680155002217439587266025226556598542], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\times C_4\\times \\GL(2,3)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 12], [4, 16], [8, 17], [16, 12], [32, 5]], 'representations': {'PC': {'code': 5672501483672701792227107170414925028820788384876216647943, 'gens': [1, 2, 5], 'pres': [8, -2, -2, -2, -3, -2, -2, -3, -5, 2880, 17441, 41, 482, 66, 23555, 2907, 39364, 14892, 116, 25349, 141, 59142, 222]}, 'Perm': {'d': 27, 'gens': [15512334044060385230192130, 3067916261725, 2561305169719296000, 4504061280061, 5897117537101, 7300107214540, 418829647187403284152320000, 26976017466662584320000]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_6^2.Q_8', 'transitive_degree': 720, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '40.9', '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, 4], 'aut_gens': [[1, 2], [21, 2], [1, 14], [21, 19]], 'aut_group': '32.25', 'aut_hash': 25, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 32, 'aut_permdeg': 8, 'aut_perms': [11527, 17, 11647], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 4, 1], [5, 1, 4, 1], [10, 1, 4, 1], [10, 1, 8, 1], [20, 1, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.25', 'autcent_hash': 25, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times D_4', '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], [4, 1, 4], [5, 1, 4], [10, 1, 12], [20, 1, 16]], 'center_label': '40.9', 'center_order': 40, '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', '2.1', '5.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [5, 1, 4, 1], [10, 1, 4, 3], [20, 1, 8, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 18, 'exponent': 20, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '20.5', 'hash': 9, '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, 40]], 'label': '40.9', 'linC_count': 288, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 4, 'linQ_dim': 6, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C20', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_conjugacy_classes': 40, 'number_divisions': 12, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 40, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 3], [4, 4], [5, 4], [10, 12], [20, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 4], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[21, 2], [1, 14], [21, 19]], 'outer_group': '32.25', 'outer_hash': 25, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 8, 'outer_perms': [11527, 17, 11647], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [8, 2]], 'representations': {'PC': {'code': 5899779, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -5, 21, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125101729074815868, 91655853488337157]}, 'GLFp': {'d': 2, 'p': 41, 'gens': [1585222, 2756880]}, 'Perm': {'d': 11, 'gens': [131040, 3628800, 96, 41040]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], '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_{20}', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}
