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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '105600.a', 'ambient_counter': 1, 'ambient_order': 105600, 'ambient_tex': '\\GL(2,11):D_4', 'central': False, 'central_factor': False, 'centralizer_order': 52800, 'characteristic': True, 'core_order': 20, 'counter': 1192, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '105600.a.5280.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '5280.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1422479616026575418, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 5280, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2\\times \\PSL(2,11).C_2', 'simple': False, 'solvable': True, 'special_labels': ['U1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '105600.a', 'aut_centralizer_order': None, 'aut_label': '5280.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.E', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['480.J', '1056.H', '1760.H', '2640.A', '2640.B', '2640.C', '2640.V', '2640.BK', '2640.BY', '2640.CG', '2640.CP', '2640.CR', '2640.CV', '2640.CW'], 'contains': ['10560.A', '26400.A'], 'core': '5280.A', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [5809717384314194, 37595466963011736, 41772741070013040], 'label': '105600.a.5280.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5280.A', 'normal_contained_in': ['8.A', '2640.A', '2640.B', '2640.C'], 'normal_contains': ['10560.A', '26400.A'], 'normalizer': '1.a1', 'old_label': '5280.a1', 'projective_image': None, 'quotient_action_image': '2.1', 'quotient_action_kernel': '2640.a', 'quotient_action_kernel_order': 2640, 'quotient_fusion': None, 'short_label': '5280.A', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '20.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1], [11], [17]], 'aut_group': '8.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 6, 'aut_perms': [120, 9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [10, 1, 4, 1], [20, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_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, 1], [4, 1, 2], [5, 1, 4], [10, 1, 4], [20, 1, 8]], 'center_label': '20.2', 'center_order': 20, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [5, 1, 4, 1], [10, 1, 4, 1], [20, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 20, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 8, 'irrQ_dim': 8, 'irrR_degree': 2, 'irrep_stats': [[1, 20]], 'label': '20.2', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C20', '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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 20, 'number_divisions': 6, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [4, 2], [5, 4], [10, 4], [20, 8]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[11], [17]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [4, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 2], [8, 1]], 'representations': {'PC': {'code': 51395, 'gens': [1], 'pres': [3, -2, -2, -5, 6, 16]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [58438750843733785]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504, 252]}, 'Perm': {'d': 9, 'gens': [131040, 96, 41040]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [20], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{20}', 'transitive_degree': 20, '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': '40.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [20, 12, 12, 10, 2, 10, 4], 'aut_gens': [[12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432], [12531822321003912, 26963794547688323, 33162634604281934, 35355820177512131, 5575705262007556, 11619123519371993, 33418192856010432], [20886370535006520, 1002586243376696, 6812520979007886, 2657345645368334, 24845211363424313, 13251566580699389, 25063644642007824], [16709096428005216, 42152542971882507, 5090196937856381, 15188882652930063, 27198377566141584, 26088572945892121, 29240918749009128], [16709096428005216, 3247703876939126, 24434618089256293, 15188882652930063, 42631924163734921, 26088572945892121, 29240918749009128], [16709096428005216, 1312435126905562, 9974737107365391, 2657345645368334, 14266618358533385, 24456129884550084, 29240918749009128], [12531822321003912, 1625422438811270, 27742683572964519, 2657345645368334, 40136699154465490, 38925579311070212, 33418192856010432], [37595466963011736, 2624867681504552, 13017774803048826, 35355820177512131, 2428799927753494, 31897979080935279, 8354548214002608]], 'aut_group': None, 'aut_hash': 5154683195178725553, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 168960, 'aut_permdeg': 144, 'aut_perms': [28120375007189282270298066239425490011650188272178392843882484895741002422284397225301745147439710685177418859184357632442295227087696532167956837018027959427362305873125241817778497152168860705019421278596797729060261774865010827963278635820845591, 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1129441716755356690440489802495783306833799676980555518681015220187602882024931283230177291615198358129599312958078650826148736182171119313721812646634068741876799124109172573320330121046164773600096071883666450078951140730444662326225989473723049341, 1119103819258460772980632501265643344701328959424485951399771379781365341662445525199087025464592477386966332136762086877643984154229179651080511514666313237220883505906331403482149051605834500676739108788443941101606214007987667805821420738038335926, 30520984566444768746877344192841148581846316039699988297248666265094346592885304377817967520207022406862669529100891776156868890473317232303485455574167690349057627282858980794242663638194902971593617686952538741548903879043393089763952484280344668], 'aut_phi_ratio': 6.6, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 110, 1, 1], [2, 132, 1, 1], [2, 220, 1, 1], [2, 264, 1, 1], [3, 110, 1, 1], [4, 2, 1, 1], [4, 4, 1, 1], [4, 110, 1, 1], [4, 132, 1, 1], [4, 220, 1, 1], [4, 220, 2, 1], [4, 264, 1, 1], [5, 1, 4, 1], [5, 132, 1, 2], [5, 132, 4, 2], [6, 110, 1, 1], [6, 220, 1, 1], [6, 440, 1, 2], [8, 2, 2, 1], [8, 110, 2, 1], [8, 220, 1, 2], [8, 264, 1, 1], [8, 440, 1, 2], [10, 1, 4, 1], [10, 4, 4, 1], [10, 110, 4, 1], [10, 132, 1, 2], [10, 132, 2, 2], [10, 132, 4, 3], [10, 132, 8, 2], [10, 220, 4, 1], [10, 264, 4, 1], [10, 528, 1, 4], [10, 528, 4, 4], [11, 120, 1, 1], [12, 110, 1, 2], [12, 220, 1, 1], [12, 220, 2, 2], [12, 440, 1, 2], [15, 110, 4, 1], [20, 2, 4, 1], [20, 4, 4, 1], [20, 110, 4, 1], [20, 132, 4, 1], [20, 220, 4, 1], [20, 220, 8, 1], [20, 264, 1, 4], [20, 264, 4, 5], [20, 528, 1, 4], [20, 528, 4, 4], [22, 120, 1, 1], [22, 480, 1, 1], [24, 110, 2, 2], [24, 220, 1, 2], [24, 220, 2, 2], [24, 440, 1, 4], [30, 110, 4, 1], [30, 220, 4, 1], [30, 440, 4, 2], [40, 2, 8, 1], [40, 110, 8, 1], [40, 220, 4, 2], [40, 264, 2, 4], [40, 264, 4, 1], [40, 264, 8, 4], [40, 440, 4, 2], [44, 240, 1, 1], [44, 480, 1, 1], [55, 120, 4, 1], [60, 110, 4, 2], [60, 220, 4, 1], [60, 220, 8, 2], [60, 440, 4, 2], [88, 240, 2, 1], [110, 120, 4, 1], [110, 480, 4, 1], [120, 110, 8, 2], [120, 220, 4, 2], [120, 220, 8, 2], [120, 440, 4, 4], [220, 240, 4, 1], [220, 480, 4, 1], [440, 240, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2.C_2^5.\\PSL(2,11).C_2', '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': 660, 'autcentquo_group': None, 'autcentquo_hash': 1422479616026575418, 'autcentquo_nilpotent': False, 'autcentquo_order': 5280, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^2\\times \\PSL(2,11).C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 1], [2, 110, 1], [2, 132, 1], [2, 220, 1], [2, 264, 1], [3, 110, 1], [4, 2, 1], [4, 4, 1], [4, 110, 1], [4, 132, 1], [4, 220, 3], [4, 264, 1], [5, 1, 4], [5, 132, 10], [6, 110, 1], [6, 220, 1], [6, 440, 2], [8, 2, 2], [8, 110, 2], [8, 220, 2], [8, 264, 1], [8, 440, 2], [10, 1, 4], [10, 4, 4], [10, 110, 4], [10, 132, 34], [10, 220, 4], [10, 264, 4], [10, 528, 20], [11, 120, 1], [12, 110, 2], [12, 220, 5], [12, 440, 2], [15, 110, 4], [20, 2, 4], [20, 4, 4], [20, 110, 4], [20, 132, 4], [20, 220, 12], [20, 264, 24], [20, 528, 20], [22, 120, 1], [22, 480, 1], [24, 110, 4], [24, 220, 6], [24, 440, 4], [30, 110, 4], [30, 220, 4], [30, 440, 8], [40, 2, 8], [40, 110, 8], [40, 220, 8], [40, 264, 44], [40, 440, 8], [44, 240, 1], [44, 480, 1], [55, 120, 4], [60, 110, 8], [60, 220, 20], [60, 440, 8], [88, 240, 2], [110, 120, 4], [110, 480, 4], [120, 110, 16], [120, 220, 24], [120, 440, 16], [220, 240, 4], [220, 480, 4], [440, 240, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '2640.l', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '660.13'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['21120.a', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 1], [2, 110, 1, 1], [2, 132, 1, 1], [2, 220, 1, 1], [2, 264, 1, 1], [3, 110, 1, 1], [4, 2, 1, 1], [4, 4, 1, 1], [4, 110, 1, 1], [4, 132, 1, 1], [4, 220, 1, 3], [4, 264, 1, 1], [5, 1, 4, 1], [5, 132, 2, 1], [5, 132, 4, 2], [6, 110, 1, 1], [6, 220, 1, 1], [6, 440, 1, 2], [8, 2, 2, 1], [8, 110, 2, 1], [8, 220, 1, 2], [8, 264, 1, 1], [8, 440, 1, 2], [10, 1, 4, 1], [10, 4, 4, 1], [10, 110, 4, 1], [10, 132, 2, 1], [10, 132, 4, 8], [10, 220, 4, 1], [10, 264, 4, 1], [10, 528, 2, 2], [10, 528, 4, 4], [11, 120, 1, 1], [12, 110, 2, 1], [12, 220, 1, 1], [12, 220, 2, 2], [12, 440, 1, 2], [15, 110, 4, 1], [20, 2, 4, 1], [20, 4, 4, 1], [20, 110, 4, 1], [20, 132, 4, 1], [20, 220, 4, 3], [20, 264, 2, 2], [20, 264, 4, 5], [20, 528, 2, 2], [20, 528, 4, 4], [22, 120, 1, 1], [22, 480, 1, 1], [24, 110, 4, 1], [24, 220, 2, 3], [24, 440, 2, 2], [30, 110, 4, 1], [30, 220, 4, 1], [30, 440, 4, 2], [40, 2, 8, 1], [40, 110, 8, 1], [40, 220, 4, 2], [40, 264, 4, 3], [40, 264, 8, 4], [40, 440, 4, 2], [44, 240, 1, 1], [44, 480, 1, 1], [55, 120, 4, 1], [60, 110, 8, 1], [60, 220, 4, 1], [60, 220, 8, 2], [60, 440, 4, 2], [88, 240, 2, 1], [110, 120, 4, 1], [110, 480, 4, 1], [120, 110, 16, 1], [120, 220, 8, 3], [120, 440, 8, 2], [220, 240, 4, 1], [220, 480, 4, 1], [440, 240, 8, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 2251105920, 'exponent': 1320, 'exponents_of_order': [7, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[20, 0, 48], [24, 0, 40]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': None, 'hash': 4837461391576516431, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 660, 'inner_gen_orders': [1, 2, 2, 4, 4, 2, 1], 'inner_gens': [[12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 24867356193276130, 2657345645368334, 5714653507147733, 38925579311070212, 33418192856010432], [12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 26774775945834116, 11619123519371993, 33418192856010432], [12531822321003912, 26963794547688323, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432], [12531822321003912, 1625422438811270, 25044875356667964, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432], [12531822321003912, 1625422438811270, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432]], 'inner_hash': 5932200999968897442, 'inner_nilpotent': False, 'inner_order': 10560, 'inner_split': True, 'inner_tex': 'D_4.\\PSL(2,11).C_2', 'inner_used': [2, 3, 4, 5], 'irrC_degree': 20, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 40, 'irrep_stats': [[1, 40], [2, 10], [10, 100], [11, 40], [12, 80], [20, 85], [22, 10], [24, 70]], 'label': '105600.a', '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': 'GL(2,11):D4', 'ngens': 7, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 142, 'number_characteristic_subgroups': 52, 'number_conjugacy_classes': 435, 'number_divisions': 125, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 1412, 'number_subgroup_classes': 1568, 'number_subgroups': 186388, 'old_label': None, 'order': 105600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 731], [3, 110], [4, 1172], [5, 1324], [6, 1210], [8, 1808], [10, 17444], [11, 120], [12, 2200], [15, 440], [20, 20528], [22, 600], [24, 3520], [30, 4840], [40, 17792], [44, 720], [55, 480], [60, 8800], [88, 480], [110, 2400], [120, 14080], [220, 2880], [440, 1920]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [4177274107001304, 4177274107001304, 4177274107001304], 'outer_gens': [[12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 5714653507147733, 11619123519371993, 33418192856010432], [12531822321003912, 2934716565033418, 24867356193276130, 15188882652930063, 44450299487939670, 11619123519371993, 33418192856010432], [37595466963011736, 2624867681504552, 14927453047325706, 35355820177512131, 25851164911543430, 31897979080935279, 8354548214002608]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 101, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 8], [8, 2], [10, 12], [11, 8], [20, 7], [22, 2], [24, 8], [40, 15], [44, 8], [48, 19], [80, 9], [88, 2], [96, 4], [160, 3], [192, 6], [320, 2]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 2934716565033418, 24867356193276130, 35355820177512131, 44450299487939670, 11619123519371993, 33418192856010432]}, 'Perm': {'d': 101, 'gens': [94297581965649749136723868670837234653047912706494995507337185164725228079152520491579529134919509853395528996005658807342791455290115051602790915784461951237, 52, 191319518216227721274419705986593788406215965023218783266807088271529861494772417331717063322424944262442353024374306962604439017539815097697719637851446705972, 285663262677083049164869832717306356240472421456074682396120704345715086925588521295292220987856631897957866642102392645143151957131011906952245554774569325613, 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