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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '124500.a', 'ambient_counter': 1, 'ambient_order': 124500, 'ambient_tex': 'C_{249}\\times D_{250}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 30, 'counter': 61, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '124500.a.4150._.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4150.A', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4150.b', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 4150, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{25}\\times C_{83}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': None, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '124500.a', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [62250, 49800, 41500], 'label': '124500.a.4150._.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4150.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4150._.A', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '30.4', '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], [7]], '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], [3, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [15, 1, 8, 1], [30, 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], [3, 1, 2], [5, 1, 4], [6, 1, 2], [10, 1, 4], [15, 1, 8], [30, 1, 8]], 'center_label': '30.4', 'center_order': 30, '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', '3.1', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [5, 1, 4, 1], [6, 1, 2, 1], [10, 1, 4, 1], [15, 1, 8, 1], [30, 1, 8, 1]], 'element_repr_type': 'PC', 'elementary': 30, 'eulerian_function': 1, 'exponent': 30, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[1, 0, 8]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '30.4', 'hash': 4, 'hyperelementary': 30, '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, 30]], 'label': '30.4', 'linC_count': 8, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 3, 'linQ_dim': 6, 'linQ_dim_count': 3, 'linR_count': 4, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C30', 'ngens': 3, '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': 30, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 30, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [5, 4], [6, 2], [10, 4], [15, 8], [30, 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], [7]], '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': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [4, 2], [8, 2]], 'representations': {'PC': {'code': 71879, 'gens': [1], 'pres': [3, -2, -3, -5, 6, 22]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [58415888370979138]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [11393]}, 'Perm': {'d': 10, 'gens': [362880, 10080, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [30], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{30}', 'transitive_degree': 30, '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': '996.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20500, 'aut_gen_orders': [10250, 4100, 4100, 4100, 4100], 'aut_gens': [[1, 2], [68227, 54242], [50299, 62174], [122509, 103274], [24403, 37654], [51295, 24806]], 'aut_group': None, 'aut_hash': 5836021023641505038, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4100000, 'aut_permdeg': 334, 'aut_perms': 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456407533660018489556329676461442847883961317310197369338099219053178065772405049066519536219841502914698725908459015292328332554980541492700798101650602048477513330154730625237344483645759329254494924042044532705573303768031123344106182836320001154300456625468548105220653278559899366367306731625542742556052432022175640477304116562099182326288077189471913285178637720407177366878098357466256101572887403085257079627741931617337797975081852529717913090747936372682900204024760395380357938182376590174915264734161240064791178872735437468693490915373761334596804408194178302388662605745579077330652268765774017815200506258375306713611871392648688757045528589087582623749399514772111923847482346050068], 'aut_phi_ratio': 125.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 125, 2, 1], [3, 1, 2, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 125, 4, 1], [10, 2, 2, 1], [15, 2, 4, 1], [25, 2, 10, 1], [30, 2, 4, 1], [50, 2, 10, 1], [75, 2, 20, 1], [83, 1, 82, 1], [125, 2, 50, 1], [150, 2, 20, 1], [166, 1, 82, 1], [166, 125, 164, 1], [249, 1, 164, 1], [250, 2, 50, 1], [375, 2, 100, 1], [415, 2, 164, 1], [498, 1, 164, 1], [498, 125, 328, 1], [750, 2, 100, 1], [830, 2, 164, 1], [1245, 2, 328, 1], [2075, 2, 820, 1], [2490, 2, 328, 1], [4150, 2, 820, 1], [6225, 2, 1640, 1], [10375, 2, 4100, 1], [12450, 2, 1640, 1], [20750, 2, 4100, 1], [31125, 2, 8200, 1], [62250, 2, 8200, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_{82}\\times (C_{25}.C_{25}.C_5):C_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 82, 'autcent_group': '328.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 328, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{82}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 500, 'autcentquo_group': '12500.e', 'autcentquo_hash': 6914754566746293549, 'autcentquo_nilpotent': False, 'autcentquo_order': 12500, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{125}:C_{100}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 125, 2], [3, 1, 2], [5, 2, 2], [6, 1, 2], [6, 125, 4], [10, 2, 2], [15, 2, 4], [25, 2, 10], [30, 2, 4], [50, 2, 10], [75, 2, 20], [83, 1, 82], [125, 2, 50], [150, 2, 20], [166, 1, 82], [166, 125, 164], [249, 1, 164], [250, 2, 50], [375, 2, 100], [415, 2, 164], [498, 1, 164], [498, 125, 328], [750, 2, 100], [830, 2, 164], [1245, 2, 328], [2075, 2, 820], [2490, 2, 328], [4150, 2, 820], [6225, 2, 1640], [10375, 2, 4100], [12450, 2, 1640], [20750, 2, 4100], [31125, 2, 8200], [62250, 2, 8200]], 'center_label': '498.4', 'center_order': 498, 'central_product': None, 'central_quotient': '250.1', 'commutator_count': None, 'commutator_label': '125.1', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '5.1', '5.1', '83.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 125, 1, 2], [3, 1, 2, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 125, 2, 2], [10, 2, 2, 1], [15, 2, 4, 1], [25, 2, 10, 1], [30, 2, 4, 1], [50, 2, 10, 1], [75, 2, 20, 1], [83, 1, 82, 1], [125, 2, 50, 1], [150, 2, 20, 1], [166, 1, 82, 1], [166, 125, 82, 2], [249, 1, 164, 1], [250, 2, 50, 1], [375, 2, 100, 1], [415, 2, 164, 1], [498, 1, 164, 1], [498, 125, 164, 2], [750, 2, 100, 1], [830, 2, 164, 1], [1245, 2, 328, 1], [2075, 2, 820, 1], [2490, 2, 328, 1], [4150, 2, 820, 1], [6225, 2, 1640, 1], [10375, 2, 4100, 1], [12450, 2, 1640, 1], [20750, 2, 4100, 1], [31125, 2, 8200, 1], [62250, 2, 8200, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 62250, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 5, 41], 'factors_of_order': [2, 3, 5, 83], 'faithful_reps': None, 'familial': False, 'frattini_label': '25.1', 'frattini_quotient': '4980.d', 'hash': 665558448552374996, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 250, 'inner_gen_orders': [2, 125], 'inner_gens': [[1, 998], [123505, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 250, 'inner_split': False, 'inner_tex': 'D_{125}', 'inner_used': [1, 2], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '124500.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': True, 'metacyclic': True, 'monomial': True, 'name': 'C249*D250', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 3, 0, 0, 1, 1, 1, 1, 3, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 3, 0, 1, 1, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 31872, 'number_divisions': 40, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': None, 'number_subgroup_classes': 80, 'number_subgroups': 1904, 'old_label': None, 'order': 124500, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 251], [3, 2], [5, 4], [6, 502], [10, 4], [15, 8], [25, 20], [30, 8], [50, 20], [75, 40], [83, 82], [125, 100], [150, 40], [166, 20582], [249, 164], [250, 100], [375, 200], [415, 328], [498, 41164], [750, 200], [830, 328], [1245, 656], [2075, 1640], [2490, 656], [4150, 1640], [6225, 3280], [10375, 8200], [12450, 3280], [20750, 8200], [31125, 16400], [62250, 16400]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2050, 'outer_gen_orders': [410, 50, 2050, 2050, 2050], 'outer_gen_pows': [1, 0, 0, 21, 21], 'outer_gens': [[1, 18086], [67231, 110558], [4981, 113678], [4981, 14854], [4981, 114454]], 'outer_group': None, 'outer_hash': 1709335650994229279, 'outer_nilpotent': True, 'outer_order': 16400, 'outer_permdeg': 74, 'outer_perms': [171122577953407480787637943117164930788430605504029060487505987590673153830785334233112137262820930, 850649747691274295629237507414968323459989779913175192927607926776665823372701019061631320064000000000, 171158957560876044698415418469687710148981210677870985361807403043708553371190003006913682525640960, 4470115632635170790849113151252219720667905384836948058374342228915462888263082240487674703128673683761216, 4470115632635229553631804323813440556795725530748318595180467672913314899997984572401491528263777683761216], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{2050}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 213, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 83], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '6372324679266810872284735140182647424210801730510068964527728319338107', 'gens': [1, 2], 'pres': [7, -2, -2, -3, -5, -5, -5, -83, 13973, 36, 41918, 79, 167667, 164, 1047904, 207, 1058405, 250]}, 'GLFp': {'d': 2, 'p': 499, 'gens': [61877246503, 42925861575]}, 'Perm': {'d': 213, 'gens': [23721744575914321484456334960156148986589180822413055260276434597576771602734896121576747475926266028451591926773742186593018671045188997642525314538741519991529670055759434012907916156357821972446144565047636452, 4756137296759039716662154561026181570299584239081422977982183361989343657475678356551084823755618454706653515821085882226326150863922255464437239686581845691637811659669184816595208769032787394187045518291699324881422567573750598281205357457823185238542805289371657256936853181513267149664679468404395803005163666653047313682368550312957337773849849841976215104598408281616551380823074107747267810197116]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 498], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{249}\\times D_{250}', 'transitive_degree': 62250, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '166.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4100, 'aut_gen_orders': [164, 82, 410], 'aut_gens': [[1, 2], [3155, 186], [3985, 98], [2325, 3978]], 'aut_group': None, 'aut_hash': 12222580631130517, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41000, 'aut_permdeg': 107, 'aut_perms': [6194090453340830805221210776193148317984010286602441386955378593271796531168490379263461227100178202781679155332107261892372385059393218469382616818841074538169814264205989, 1849560675628026658582271631060831192394317796090361994165349344463745533071545542925873336328811499554649765614889834050968016883086380767670123994965010876078563060031891, 1834287208443596099806602450439988911649124767593936912873752245299362941798916539098145022101629587459252681751830322782425696185518840359944791367507240538830381493058659], 'aut_phi_ratio': 25.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [5, 2, 2, 1], [25, 2, 10, 1], [83, 1, 82, 1], [166, 25, 82, 1], [415, 2, 164, 1], [2075, 2, 820, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{82}\\times D_{25}.C_{10}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 82, 'autcent_group': '82.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 82, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{82}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 100, 'autcentquo_group': '500.18', 'autcentquo_hash': 18, 'autcentquo_nilpotent': False, 'autcentquo_order': 500, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_{25}:C_{20}', 'cc_stats': [[1, 1, 1], [2, 25, 1], [5, 2, 2], [25, 2, 10], [83, 1, 82], [166, 25, 82], [415, 2, 164], [2075, 2, 820]], 'center_label': '83.1', 'center_order': 83, 'central_product': True, 'central_quotient': '50.1', 'commutator_count': 1, 'commutator_label': '25.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '5.1', '5.1', '83.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['50.1', 1], ['83.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [5, 2, 2, 1], [25, 2, 10, 1], [83, 1, 82, 1], [166, 25, 82, 1], [415, 2, 164, 1], [2075, 2, 820, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 252, 'exponent': 4150, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 5, 41], 'factors_of_order': [2, 5, 83], 'faithful_reps': [[2, 0, 820]], 'familial': False, 'frattini_label': '5.1', 'frattini_quotient': '830.1', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 50, 'inner_gen_orders': [2, 25], 'inner_gens': [[1, 998], [3155, 2]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 50, 'inner_split': False, 'inner_tex': 'D_{25}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 1640, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 166], [2, 996]], 'label': '4150.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': True, 'monomial': True, 'name': 'D25*C83', '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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 1162, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 12, 'number_subgroups': 68, 'old_label': None, 'order': 4150, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 25], [5, 4], [25, 20], [83, 82], [166, 2050], [415, 328], [2075, 1640]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 410, 'outer_gen_orders': [2, 410], 'outer_gen_pows': [1, 0], 'outer_gens': [[1, 1164], [1, 1372]], 'outer_group': '820.20', 'outer_hash': 20, 'outer_nilpotent': True, 'outer_order': 820, 'outer_permdeg': 50, 'outer_perms': [258623241511168180642964355153611979969197632389120000000000, 608540612336810912965817692809489337748525225254846464000000000], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{410}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 108, 'pgroup': 0, 'primary_abelian_invariants': [2, 83], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [4, 1], [20, 1], [82, 2], [328, 1], [1640, 1]], 'representations': {'PC': {'code': '439081705905739340901875', 'gens': [1, 2], 'pres': [4, -2, -5, -5, -83, 7985, 45, 10082, 70]}, 'GLFp': {'d': 2, 'p': 499, 'gens': [2394616189, 61877246503]}, 'Perm': {'d': 108, 'gens': [56213055407243470421616, 12380921884109809718625918504485969512169560791333763137415761458481668540468257551551837625132581751459691578892934601249531595513914854274274549436397754221728366592000000, 701391835124898593479300, 1350198335266800302106816]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [166], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{25}\\times C_{83}', 'transitive_degree': 2075, 'wreath_data': None, 'wreath_product': False}
