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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '63281250.b', 'ambient_counter': 2, 'ambient_order': 63281250, 'ambient_tex': 'C_5^8.\\He_3.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1171875, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '63281250.b.27._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.B', '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': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 2343750, 'subgroup_tex': 'C_5^8.C_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '63281250.b', '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': 9, 'diagramx': None, 'generators': [1294848838399897972406880, 1451553, 9157944981056567706079446192480, 119438130795612676358113624306515060135518811468969564184, 81591528933148268425262507607603474186469987713, 608358530357749898499151219330475435520, 608358494990701380647863460487168000000, 8156060513555468722791311119575887296687879844433984064, 8213052031189615879803252741439236153690, 280216752480], 'label': '63281250.b.27._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '27.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27._.B', 'subgroup_fusion': None, 'weyl_group': None}
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label None does not appear in gps_groups
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '6.2', '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': [[54402522457579950554991253719627201804017088937007030944, 100644598208479656597602084971198966329461359573448765433], [92236870362312190894537382103630163648276876143429529056, 37834347653554071682220038942354765376613175743104131864], [32641445084167096969469784787332886818288541091280076864, 78636239632816866777037996512629659453324630707410054464], [32641445084167099062981218837102301970548694780038711064, 84323909317826914164904154761845196903940948953019596896], [65035608838325276993832886266883902195040409403608631096, 37834347653554071682220057257433180980281510154880131800], [57122647754076139506548901474131673331819499310443568513, 97924539796143316208604333168842807980209676297153709970], [59842706187388439033221741445153046459452125180562668896, 97924539796143317085348077275263988366078813531385052120], [62558583033898132462026329960077458359762431525310507520, 95204414478712831979532964105283423581307326930995581496], [57122647816838853905930908184960783055067649840409648570, 95204414520540505361260198543748696073779885088821033010], [62558583033898133338770081993594951276249767728380364833, 105837500838523113750483974783949778318368024178514531250], [65035608777668785768060356503481755852914160291147193664, 97924539817036694008646813747531859408011447848308136984], [57122647775011179647459946692042702587326679231203379200, 103360475052924787401100746029312852640046525711366205496], [54402522457579950554991279928733864444632667610000000064, 105837500819694300702617540043878681091946235023739670456], [54402522539171478879781027154188328763500254279874880090, 100644598187586279405120493190891309324621549824092769144], [59842706166454142843976114641187516463073106299616101856, 97924539835865507325696120847614240853862648602212020313], [54402522539171478575593556820185074019795523229235520090, 97924539754273979000906321203945699296918823484067036120], [54402522539171481277463494984718116450062056306882880090, 70723278630159261569001287334849166407053779687101110880]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 4050000000, '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': [[1, 1, 1], [2, 1125, 1], [3, 75, 2], [3, 1875, 2], [3, 3750, 1], [3, 15625, 2], [3, 46875, 2], [3, 281250, 1], [5, 3, 4], [5, 6, 2], [5, 9, 40], [5, 18, 80], [5, 27, 48], [5, 54, 780], [5, 81, 312], [5, 162, 1976], [6, 28125, 4], [6, 703125, 4], [9, 7031250, 2], [10, 1125, 4], [10, 3375, 80], [10, 10125, 320], [15, 75, 8], [15, 150, 20], [15, 450, 400], [15, 675, 80], [15, 1350, 1560], [15, 1875, 8], [15, 3750, 44], [15, 5625, 80], [15, 11250, 360], [15, 46875, 16], [15, 93750, 24], [15, 843750, 8], [30, 28125, 16], [30, 84375, 160], [30, 703125, 16]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '63281250.b', 'commutator_count': None, 'commutator_label': '10546875.b', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 13, 'conjugacy_classes_known': False, 'counter': 2, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1125, 1, 1], [3, 75, 2, 1], [3, 1875, 2, 1], [3, 3750, 1, 1], [3, 15625, 2, 1], [3, 46875, 2, 1], [3, 281250, 1, 1], [5, 3, 4, 1], [5, 6, 2, 1], [5, 9, 4, 10], [5, 18, 4, 20], [5, 27, 4, 12], [5, 54, 2, 10], [5, 54, 4, 190], [5, 81, 4, 78], [5, 162, 4, 494], [6, 28125, 2, 2], [6, 703125, 2, 2], [9, 7031250, 2, 1], [10, 1125, 4, 1], [10, 3375, 4, 20], [10, 10125, 4, 80], [15, 75, 8, 1], [15, 150, 4, 1], [15, 150, 8, 2], [15, 450, 8, 50], [15, 675, 8, 10], [15, 1350, 4, 10], [15, 1350, 8, 190], [15, 1875, 8, 1], [15, 3750, 4, 3], [15, 3750, 8, 4], [15, 5625, 8, 10], [15, 11250, 4, 10], [15, 11250, 8, 40], [15, 46875, 8, 2], [15, 93750, 4, 2], [15, 93750, 8, 2], [15, 843750, 4, 2], [30, 28125, 8, 2], [30, 84375, 8, 20], [30, 703125, 8, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 90, 'exponents_of_order': [8, 4, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '63281250.b', 'hash': 5909935124996746655, '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': 63281250, 'inner_split': None, 'inner_tex': 'C_5^8.\\He_3.C_6', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '63281250.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': False, 'metacyclic': False, 'monomial': None, 'name': 'C5^8.He3.C6', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 14, 'number_conjugacy_classes': 6468, 'number_divisions': 1294, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 63281250, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1125], [3, 413900], [5, 390624], [6, 2925000], [9, 14062500], [10, 3514500], [15, 16773600], [30, 25200000]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 64, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 45, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '20707802927184383948667153057062788108822968563732492400464241471181446192463865088556609962557090171105596609043570599961748761546163204196849366869728369673797692820448583854458179589705101405235506519728983394236624932339722638744456285774391166881813140461061044984086800135974008654456287808044101749599980905568776962694426956082133914189993437488641809800899176040731391672737833491971332410755343258593505851179007', 'gens': [1, 3, 4, 6, 8, 9, 10, 11, 12, 13], 'pres': [13, 2, 3, 3, 3, 5, 3, 5, 5, 5, 5, 5, 5, 5, 26, 182147954, 20640674, 564300024, 402925213, 453930987, 421621684, 338147033, 198, 2531899894, 421983345, 4802676845, 986060808, 579818569, 87389684, 304, 896092476, 970871284, 315419045, 95626485, 1465439047, 644014820, 841964793, 70972246, 4770552, 4715944748, 2078353506, 1171787911, 67950137, 1404073, 3574197909, 1880921272, 272551535, 361383798, 13932824, 73552060, 1831677728, 16624215, 272548039, 17458230, 3788904611, 4345457244, 1261391545, 143537990, 16389436, 7193843292, 1920498280, 364932047, 33903141, 15739892]}, 'Perm': {'d': 45, 'gens': [54402522457579950554991253719627201804017088937007030944, 100644598208479656597602084971198966329461359573448765433]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 625, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_5^8.\\He_3.C_6', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': None}
