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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '8599633920000.bt', 'ambient_counter': 46, 'ambient_order': 8599633920000, 'ambient_tex': 'A_6^4.D_4.C_2^3.D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 16796160000, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8599633920000.bt.512._.A', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '512.A', 'outer_equivalence': False, 'perfect': True, 'proper': True, 'quotient': '512.51562', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': True, 'quotient_order': 512, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^6:D_4', 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 16796160000, 'subgroup_tex': 'A_6.A_6.A_6.A_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '8599633920000.bt', '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': [39485333920173304, 44486321472091196837716002302689384467104003112, 67008453291324433744023520486, 135874099242911987, 3661954287267332121088842145560054822153974140, 1285306718573334224892247526609, 18464, 1129372921065336331696151649049910029693887843, 84111833137926138962213828118076716651965371, 106015, 360560613203769124161546972679, 36357937630693647364947924489021, 71073684190974225491877396336571, 67008453290336394403335057434, 1155031886461485], 'label': '8599633920000.bt.512._.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '512.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '512._.A', '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': '8.5', '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': [[334959669399831999514276025906063100046886647790, 731142787998178440543186804267517740167342826971, 272127402598863062138364630141817154672313356912], [334959669399831999514276025906068452364261405785, 731155818401680170130359141257991160967344155620, 272127402598863062138364630141465046261785087279], [334959669399831999514276025905430287663830861045, 629634736089243632879413546439607704465582200853, 272127402598863062138364630142471241715562398740], [334959669399831999514276025905552000582242186585, 731142787998178440543186804266828062350086471938, 272127402598863062138364630142177841600573910294], [334959669399831999514276025906402089530899089975, 731142787998178440543186804267876252091604220832, 272127402598863062138364630142342528802365300807], [209873543775055378348727432276862438678382327790, 731142787998178476247790973085408263987234839771, 272720700365175294295145253995050498405581836912], [376815583544397265940564883619270200331814647790, 731142787998178467992025662872798576677589406171, 290969970542573646483992127180215968797246476912], [334973804859700471837234237994925413560174327790, 731155818401680161286550235412937043965717226971, 272115096131971460963427548423713431281583116912], [315029382053657513628681933211759268536174327790, 794470228706355707848090151916877036508785386971, 332330027628863372366888566484823210874225676912], [334959669399831999514276025906063100046886647790, 373126205403981439444240502837845694007511920540, 333845166199973007958978286398776531508929629774], [752587118333656200323314421626813217118560894383, 731142787998178440543186804267517740167342826971, 713883072056809087040107119958690857120832580977], [271592073505558392200069288387495637377619745352, 230354050314961249420799241833962886185787708317, 272127402598863062138364630141817154672313356912], [752558856565601364285469568275679358652988723115, 376210402067458276827538043933742992358970968848, 734252692952523392299129817478286657019799178733]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 17199267840000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 180, 1, 1], [2, 1800, 1, 1], [2, 2592, 1, 1], [2, 2880, 1, 1], [2, 4050, 1, 1], [2, 5184, 1, 1], [2, 8100, 1, 1], [2, 162000, 1, 1], [2, 233280, 1, 1], [2, 259200, 1, 2], [2, 364500, 1, 1], [2, 466560, 1, 1], [2, 518400, 2, 1], [2, 810000, 1, 1], [2, 1036800, 1, 1], [2, 1296000, 2, 1], [2, 1679616, 1, 1], [2, 2073600, 1, 1], [2, 2332800, 1, 1], [2, 3645000, 1, 1], [2, 3732480, 1, 1], [2, 4100625, 1, 1], [2, 5248800, 1, 1], [2, 5832000, 1, 1], [2, 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-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 4, 4, 4, 2, 4, 4, 2, 2, 2, 2], 'aut_gens': [[11212821043200, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [14002653744023, 4103734118399, 1314028771207, 6920176418496, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [20922749603159, 4103606718720, 8396027136000, 4103693809943, 8396027176319, 4103734078080, 1313941668480, 4103734089616, 1313941673647], [19608888499192, 1313941692096, 4103646986903, 5606234755183, 40284840, 16703, 2789792426303, 5167, 1313941673647], [14002613464336, 8396027136000, 4103647003560, 8396027171152, 40279687, 2789792409600, 2789792426303, 1313941668480, 1313941673647], [12526762716847, 9709968821183, 1313988496687, 5606234750016, 2789832700823, 4103734078080, 4103734089616, 1313941668480, 1313941673647], [12526722437160, 5606234731567, 127382400, 6920176418496, 2789832700823, 4103734078080, 4103734089616, 1313941668480, 1313941673647], [18132997466863, 40319, 87091223, 9709968844799, 4103693809943, 16703, 2789792426303, 5167, 1313941673647], [15316555137983, 23616, 4103646998407, 5606234750016, 1313901393960, 16703, 2789792426303, 5167, 1313941673647], [14002613464336, 2789792449919, 1314028771207, 6920176423663, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [14002613464336, 23616, 4103646998407, 5606234750016, 1313901393960, 16703, 2789792426303, 5167, 1313941673647], [15316555137983, 4103734118399, 4103646992056, 5606234750016, 2789832700823, 16703, 2789792426303, 5167, 1313941673647]], 'aut_group': '32768.en', 'aut_hash': 3344981565538355154, 'aut_nilpotency_class': 5, 'aut_nilpotent': True, 'aut_order': 32768, 'aut_permdeg': 80, 'aut_perms': 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714740431970520341994712092608406856726632881214329638767949089969607233192666291474313181780254555643250958675586552, 34016026560300027842593341745804782432911389142724709288533113150781775689376791368204357797120916061572464491002628400, 71513243003067177467767841462489154457239284404076061277949542865546148429997225548110535830595127925528159867950141193], 'aut_phi_ratio': 128.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 3], [2, 4, 4, 1], [2, 8, 2, 1], [2, 8, 8, 1], [2, 16, 1, 1], [4, 8, 1, 2], [4, 16, 1, 1], [4, 16, 2, 1], [4, 16, 4, 2], [4, 32, 4, 1], [8, 32, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^9.D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 8, 'autcentquo_group': '512.418986', 'autcentquo_hash': 124029878967622033, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4^2:D_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 6], [2, 4, 4], [2, 8, 10], [2, 16, 1], [4, 8, 2], [4, 16, 11], [4, 32, 4], [8, 32, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '128.753', 'commutator_count': 1, 'commutator_label': '64.261', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 51562, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 6], [2, 4, 1, 4], [2, 8, 1, 10], [2, 16, 1, 1], [4, 8, 1, 2], [4, 16, 1, 11], [4, 32, 1, 4], [8, 32, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 8, 'exponents_of_order': [9], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '64.261', 'frattini_quotient': '8.5', 'hash': 51562, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 1], 'inner_gens': [[11212821043200, 9709968821183, 2789745603263, 5606234750016, 4103693815096, 4103734078080, 4103734089616, 1313941668480, 1313941673647], [16819055793216, 4103734118399, 1314028764856, 5606234750016, 4103693809943, 16703, 2789792426303, 5167, 1313941673647], [15316514858296, 4103734101696, 1314028771207, 8396027176319, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 4103734118399, 4103646992056, 5606234750016, 2789832700823, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 4103734113232, 1314028771207, 6920176423663, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [15316555137983, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [12526762716847, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [12526762716847, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647]], 'inner_hash': 753, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_2^4:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 14], [4, 20], [8, 2]], 'label': '512.51562', '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': True, 'name': 'C2^6:D4', 'ngens': 9, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 44, 'number_divisions': 43, 'number_normal_subgroups': 60, 'number_subgroup_autclasses': 424, 'number_subgroup_classes': 2083, 'number_subgroups': 11414, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 127], [4, 320], [8, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 4103693815096, 0, 8396067450839, 0, 0, 0, 0], 'outer_gens': [[11212821043200, 4103734106863, 1314028776360, 8396027171152, 2789832700823, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 2789792433216, 1313988496687, 8396027171152, 2789832700823, 11536, 4103734089616, 5167, 1313941673647], [11212821043200, 2789745614767, 6920176411583, 1313901393960, 8396027171152, 4103734078080, 1313941668480, 4103734089616, 1313941673647], [11212821043200, 4103734106863, 1313988485183, 8396027171152, 40279687, 11536, 4103734089616, 5167, 1313941673647], [11212821043200, 4103734118399, 87107880, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 1313941703632, 4103647003560, 9709968844799, 40279687, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 2789792433216, 2789705335080, 8396027171152, 1313901393960, 16703, 2789792426303, 5167, 1313941673647], [11212821043200, 2789792444752, 87107880, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647]], 'outer_group': '256.16888', 'outer_hash': 16888, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 12, 'outer_perms': [123747120, 299185336, 255191766, 255634560, 127376040, 143354280, 179788327, 179788320], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 16, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 21], [8, 2]], 'representations': {'PC': {'code': '26312872376131829094555807675999201983025449938314', 'gens': [1, 2, 4, 6, 7, 8], 'pres': [9, 2, 2, 2, 2, 2, 2, 2, 2, 2, 109, 46, 17571, 3324, 957, 102, 2164, 1093, 20166, 10095, 16144, 6937, 3778, 214]}, 'Perm': {'d': 16, 'gens': [11212821043200, 4103734118399, 1314028771207, 5606234750016, 4103693815096, 16703, 2789792426303, 5167, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 5, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^6:D_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
