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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '28894769971200000000.a', 'ambient_counter': 1, 'ambient_order': 28894769971200000000, 'ambient_tex': 'A_5^8.C_2^4.C_2^6.\\PSL(2,7)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 335923200000000, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '28894769971200000000.a.168._.LJ', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '168.LJ', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '171992678400000000.cu', 'subgroup_hash': None, 'subgroup_order': 171992678400000000, 'subgroup_tex': 'A_5^8.C_4.C_2^4.C_2^4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '28894769971200000000.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': 84, 'diagramx': None, 'generators': [18720979200, 45360, 958003200, 1269047912603090780160000, 590465598079208281695237219287040000000, 1181202549834004434843459382149120000000, 267761894400, 523022913225688372701056607253229571603899613, 21457691078431478366242604274978590523227835460, 20920909852217130754791560697299162214829532186, 4, 9767719188486388493844480000000, 925553903285559933665280000000, 271353675587871452984943575040000000, 27527506182452690092631959163161804800000000, 550922116975843703070107182711386931200000000, 1060180981351218469783798427229880320000000000, 1492560, 1134720, 894381714737624309038374023331840000000, 26313083693369353016721801216000000000, 77607141158826639360000, 8946448455745580025685412413440000000, 42365207345757997578297692415645211521729448394, 38, 711374856192000, 12804747411456000, 1175091669949317120000, 354835667978617665509919398644488646007928980490, 10080, 174356582400, 15, 11292160911544957796352000000, 82128315303451197030842895560702486213037086648, 250048261951488000, 12972960000, 21981085680015262940184087391232851968000000000], 'label': '28894769971200000000.a.168._.LJ', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '168.LJ', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168._.LJ', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[440681735352936824597888487913586762962622487617, 334451551180667919731118532439191894478301065631, 815887376457117927941258174066151611734120443588, 145498546158876638166986101769741039792787661378, 145994040679958319062870821250925440322479264585], [440681735352936824597888487913574292979849239662, 334451551180667919731119747535069564243912585605, 773536308195414464233743904893627175049320443513, 145498546158876655566996192077141187064467661322, 145994040679958336126132541517609881881519264556], [440681735352936824597888487913702005689325591609, 334451551180667919731119154011594355495348105639, 814841331222184725717738159617951463151720443584, 145498546158876647008344804048316388700819661369, 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145994040679958319062870821250925440322479264585], [334960810322638095488464493258582702377258424496, 500829336960753100732099099082341665225909643451, 733772825819040817974922982414173108803956659898, 186803941778648883997428766091050821977294163048, 104675627082774994906915068678353476884978294378], [397200129208951053308298337896053336588233289531, 690842141514436188916130212777639824235605916197, 230808580274668480564162741770723571651405058541, 61193647425058019904806650322742870484829781223, 210424089953498595655001539966663458392974190085]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 687970713600000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': None, 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '171992678400000000.cu', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '60.5', '60.5', '60.5', '60.5', '60.5', '60.5', '60.5', '60.5'], 'composition_length': 18, 'conjugacy_classes_known': False, 'counter': 73, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': None, 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 240, 'exponents_of_order': [26, 8, 8], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '171992678400000000.cu', 'hash': 2038849062537429938, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'A_5^8.C_4.C_2^4.C_2^4', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '171992678400000000.cu', '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': 'A5^8.C4.C2^4.C2^4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 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, 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-
gps_groups • Show schema
Hide schema
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