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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.10114', 'ambient_counter': 10114, 'ambient_order': 1600, 'ambient_tex': 'C_2^2\\times C_{20}:F_5', 'central': False, 'central_factor': False, 'centralizer_order': 400, 'characteristic': False, 'core_order': 5, 'counter': 130, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.10114.320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '320.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '320.1591', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1591, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 320, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{10}.C_2^4', 'simple': True, 'solvable': True, 'special_labels': ['C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1600.10114', 'aut_centralizer_order': 307200, 'aut_label': '320.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 614400, 'centralizer': '4.e1', 'complements': ['5.a1'], 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '160.a1', '160.b1', '160.e1', '160.g1', '160.i1'], 'contains': ['1600.a1'], 'core': '320.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [679, 4727, 2801, 3694], 'generators': [320], 'label': '1600.10114.320.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '320.a1', 'normal_contained_in': ['64.a1', '160.a1', '160.b1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '320.a1', 'projective_image': '1600.10114', 'quotient_action_image': '4.1', 'quotient_action_kernel': '80.45', 'quotient_action_kernel_order': 80, 'quotient_fusion': None, 'short_label': '320.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [2]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', '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': 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], [5, 1, 4]], 'center_label': '5.1', 'center_order': 5, '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': ['5.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 1, 'exponent': 5, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5.1', 'hash': 1, 'hyperelementary': 5, '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, 5]], 'label': '5.1', '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': 'C5', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 5, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 5, 'order_factorization_type': 1, 'order_stats': [[1, 1], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 5, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -5]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26329372]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131]}, 'Perm': {'d': 5, 'gens': [96]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [5], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5', 'transitive_degree': 5, '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': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 120, 'aut_gen_orders': [60, 8, 8, 4, 8], 'aut_gens': [[1, 2, 8, 80], [41, 546, 49, 560], [841, 487, 520, 1257], [41, 126, 360, 1217], [40, 715, 65, 721], [801, 594, 825, 1080]], 'aut_group': None, 'aut_hash': 903259633507885408, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2457600, 'aut_permdeg': 800, 'aut_perms': 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'aut_phi_ratio': 3840.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 25, 1, 2], [2, 25, 6, 1], [4, 2, 4, 1], [4, 50, 4, 1], [4, 50, 16, 1], [5, 4, 2, 1], [5, 4, 4, 1], [10, 4, 2, 1], [10, 4, 4, 1], [10, 4, 12, 1], [10, 4, 24, 1], [20, 4, 16, 1], [20, 4, 32, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{10}^2.C_2^6.C_{12}.C_2.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4.C_2^4.S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': None, 'autcentquo_hash': 10254, 'autcentquo_nilpotent': False, 'autcentquo_order': 1600, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5^2.C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 25, 8], [4, 2, 4], [4, 50, 20], [5, 4, 6], [10, 4, 42], [20, 4, 48]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '200.48', 'commutator_count': 1, 'commutator_label': '50.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 10114, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['400.159', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 25, 1, 8], [4, 2, 1, 4], [4, 50, 1, 4], [4, 50, 2, 8], [5, 4, 1, 2], [5, 4, 2, 2], [10, 4, 1, 14], [10, 4, 2, 14], [20, 4, 2, 8], [20, 4, 4, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 807240, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '800.1206', 'hash': 10114, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [1, 4, 5, 10], 'inner_gens': [[1, 2, 8, 80], [1, 2, 56, 240], [1, 34, 8, 80], [1, 1442, 8, 80]], 'inner_hash': 48, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'C_{10}:F_5', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 96]], 'label': '1600.10114', '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': 'C2^2*C20:F5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 136, 'number_divisions': 80, 'number_normal_subgroups': 250, 'number_subgroup_autclasses': 147, 'number_subgroup_classes': 1072, 'number_subgroups': 10028, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 207], [4, 1008], [5, 24], [10, 168], [20, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [12, 4, 4, 4, 4], 'outer_gen_pows': [32, 996, 1300, 0, 400], 'outer_gens': [[41, 546, 49, 560], [841, 487, 520, 1257], [41, 126, 360, 1217], [40, 715, 65, 721], [801, 594, 825, 1080]], 'outer_group': None, 'outer_hash': 2344437273852571667, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 128, 'outer_perms': [3132040021508802927290269141570017422857330610671891354553566641039637464402080576138684591249920663426037382124505111153183243768833527067275224016116457536465203329156010655890757625195161321067596594665233227696, 6169364629371319899755151898881083788298654028346707871761536469177509373782261576737311687857680425328409426777232513766239155014632270354730962870411445244661396702959791208346656577568035874347299915799297171171, 9205936166363081301780858153393229230684411824316496454106022942306972704075666064999925615488354822023767062974601570917810771466024574249828326570758081965613897047819153727720975181907674495650051149248281063857, 12242507703354842703805881744463049061479108027061598797626361906958168685160122627291683937118911740542720732204103661908481996702160829786556225597264530992260629745067894582260618220991691119868027797596686483732, 15279079240331077769413962336919678282484802373724633899067864127023365610082439349663594010204575718831809897884624410978249109658620250724257654749479671937309217662894520353555404307364105683316548587558731889514], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^5.A_4.C_2^4.C_2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 16], [8, 24], [16, 8]], 'representations': {'PC': {'code': 3044897548897492230344640933393952742542178913312530104515, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -5, -2, -2, -5, 41, 907, 595, 91, 652, 660, 5773, 8661, 141, 13454, 20182, 166, 30735, 20503]}, 'GLZN': {'d': 2, 'p': 100, 'gens': [1007249, 1006343, 49000049, 1005001, 81208021, 1002001, 1002501, 99000099]}, 'Perm': {'d': 18, 'gens': [359804574219007, 16, 5183, 11656, 5606234726400, 5160, 777140346124800, 1157666954129280]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_{20}:F_5', 'transitive_degree': 160, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 120, 'aut_gen_orders': [2, 4, 2, 5, 4, 2, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 8, 16], [169, 10, 8, 144], [1, 2, 8, 272], [161, 170, 8, 144], [1, 130, 8, 16], [1, 251, 8, 144], [161, 171, 168, 304], [1, 2, 8, 153], [1, 162, 8, 144], [1, 162, 8, 304], [8, 162, 1, 144], [1, 11, 8, 144]], 'aut_group': '61440.em', 'aut_hash': 5907412864111550192, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 61440, 'aut_permdeg': 80, 'aut_perms': [5594800199753698094584207757572722539964085204190530852146612122702993900178460505002435004828549318359225558596089842, 68851923750974802716263448293933692482687165113097724521852473440832781786562662607499268713163381834348783286854346240, 16184585276369329221734354900823932319009179047434760936316596063352870419590493377055970504387433429858417645929561709, 7248716704173495525314976137649241214375934829555037409689330589946464425793483170907107476565415864401443898517346560, 57072023638460676751995659883046236043340967401980937427582340289689476813037694038493097496811142305636239422206519039, 6457170821260400442273872841380054963878165564677821450180403488789815231254640259303354268493948146972463521618669539, 7247834141831606432759521472568323921526638270522544616928246172250319522724345875139126121127181799469640669128293984, 18120909197443868393909271234554392357764915068178928901208705677137537843013037787396944592051082728239856414218852784, 18120909197443868393909271234554392357764914661757175663780033243188217570986443300482379334642907049625111905747913264, 17226292869860394149717470855359069007437667227009993108073820756755492136473795238953235334628878451447029793167818008, 6331006711149799453743905293012873782238369273040049414709876767695017073289031784481156777171792160092036880328294399], 'aut_phi_ratio': 480.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 5, 1, 2], [2, 5, 6, 1], [4, 2, 4, 1], [4, 10, 4, 1], [4, 10, 8, 2], [5, 4, 1, 1], [10, 4, 1, 1], [10, 4, 6, 1], [20, 4, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5\\times C_2^6:(C_2\\times S_4)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '1536.408640869', 'autcent_hash': 4599629986281706675, 'autcent_nilpotent': False, 'autcent_order': 1536, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^6:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '40.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 40, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 5, 8], [4, 2, 4], [4, 10, 20], [5, 4, 1], [10, 4, 7], [20, 4, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '40.12', 'commutator_count': 1, 'commutator_label': '10.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1591, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['80.31', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 5, 1, 8], [4, 2, 1, 4], [4, 10, 1, 4], [4, 10, 2, 8], [5, 4, 1, 1], [10, 4, 1, 7], [20, 4, 2, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 52080, 'exponent': 20, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '160.236', 'hash': 1591, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [1, 4, 1, 10], 'inner_gens': [[1, 2, 8, 16], [1, 2, 8, 48], [1, 2, 8, 16], [1, 290, 8, 16]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 40, 'inner_split': False, 'inner_tex': 'C_2\\times F_5', 'inner_used': [2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 8], [4, 16]], 'label': '320.1591', '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': 'D10.C2^4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 14, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 56, 'number_divisions': 44, 'number_normal_subgroups': 196, 'number_subgroup_autclasses': 78, 'number_subgroup_classes': 418, 'number_subgroups': 1386, 'old_label': None, 'order': 320, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 47], [4, 208], [5, 4], [10, 28], [20, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 80, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[9, 10, 8, 176], [8, 11, 9, 17], [1, 90, 8, 16], [1, 163, 168, 176], [161, 10, 8, 16], [161, 11, 168, 25], [161, 10, 8, 184], [1, 2, 8, 176], [1, 3, 8, 16], [1, 10, 8, 16]], 'outer_group': '1536.408632661', 'outer_hash': 6321312703651895429, 'outer_nilpotent': False, 'outer_order': 1536, 'outer_permdeg': 16, 'outer_perms': [4296764107855, 262017867456, 4302991486080, 7, 126, 2877842004342, 5413204742273, 5167, 2878807236480, 1321086775680], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^6:S_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 8], [8, 4]], 'representations': {'PC': {'code': 728382543465111153222064060268547, 'gens': [1, 2, 4, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -5, 36, 851, 1278, 102, 2028, 3043, 124, 4717, 3156]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [8009, 8201, 28219, 72009, 24069, 8081, 152019]}, 'Perm': {'d': 13, 'gens': [482671449, 1037927520, 1037968560, 1437136560, 16, 1037836800, 34]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{10}.C_2^4', 'transitive_degree': 80, 'wreath_data': None, 'wreath_product': False}
