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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '6400000000.nt', 'ambient_counter': 358, 'ambient_order': 6400000000, 'ambient_tex': 'C_5^8.C_2^4.C_2^6.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 25000000, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6400000000.nt.256._.F', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '256.F', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '256.23542', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_4^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': None, 'subgroup_order': 25000000, 'subgroup_tex': 'C_5^7.D_{10}.C_2^4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '6400000000.nt', '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': [20425781580706685949950461553676763891342214486, 26584438305803288666811636527140048560, 280217145690, 62762714400179612903149203852833432274120374880, 9157944438164702769965068492864, 936846064197124830880395395783, 647475638566158066480480, 82637945570424624245756541005668330029455651773, 1180931231525464538349410681113093931610, 26584438305803368521974190147214214490, 128424364548480096, 280215936090, 82637945570424624245756592760805575821903268669, 280215936000], 'label': '6400000000.nt.256._.F', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.F', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256._.F', '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': '32.45', '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': [[82637946161408287989950385836183108849728588864, 272113231299691774206819521960646782012839756755, 585120844204261180557189174978412876983005986069, 734323748821978207001483956740723181545022594010], [82637946161408287989949738360672966589703763233, 292539012897230628249619505583822416830463181509, 564695434616881301887091955902161286155241201243, 733773198698329153199631342336579724554017743855], [20935041626013292852309214724363417838733259690, 209350517203699648722717449393476915266888276435, 605518353987944363071234692160323491671254369743, 793934562296523160800246585692826417213636710376], [62253455527384051648154046235254607625881119360, 230285557961372929708422585631925179826701641055, 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585120844204261180557189174978412876983007437530, 815915277146767980436045083700334770972222593973], [82637946161408287989950385836183108849728588890, 272113231308111960988697714926017697820722888970, 585120844204261180557189174978412876983006635413, 774596118373579702705787044996980751381782396675], [1190140793766174900025627923063867633450, 585120844204261189104951073159853904603653678616, 290942045841080625048089770035656751655802964456, 420297989017639377259390809457307542737951049763], [550550732007575938503672578070014624477568033, 271095085581099982383945882092071766311075507109, 564185803759179119524746025555132975504580403753, 420297989312863917483114031732333582594028409669], [1596967656096516260596502220774666032942332163, 209901067353127284620375935649688231780198316735, 523926826271513084333371669367889513349940988189, 500843100392561574887119762451017987624467120513]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 102400000000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 100, 1, 1], [2, 100, 2, 1], [2, 1250, 1, 3], [2, 1250, 4, 1], [2, 5000, 1, 1], [2, 5000, 2, 1], [2, 62500, 1, 1], [2, 62500, 2, 1], [2, 80000, 1, 1], [2, 390625, 1, 1], [4, 1000, 1, 4], [4, 1250, 1, 2], [4, 1250, 4, 2], [4, 2500, 1, 1], [4, 2500, 2, 3], [4, 2500, 4, 1], [4, 5000, 2, 2], [4, 5000, 4, 2], [4, 25000, 1, 8], [4, 25000, 2, 4], [4, 25000, 4, 8], [4, 62500, 1, 4], [4, 62500, 2, 6], [4, 62500, 4, 9], [4, 125000, 1, 8], [4, 125000, 2, 11], [4, 125000, 4, 8], [4, 390625, 1, 2], [4, 625000, 1, 4], [4, 625000, 2, 4], [4, 625000, 4, 12], [4, 781250, 1, 5], [4, 781250, 4, 3], [4, 1562500, 1, 3], [4, 1562500, 2, 5], [4, 1562500, 4, 1], [4, 2000000, 2, 3], [4, 3125000, 1, 9], [4, 3125000, 2, 3], [4, 50000000, 1, 1], [5, 32, 1, 1], [5, 64, 1, 1], [5, 64, 2, 3], [5, 512, 1, 6], [5, 512, 4, 2], [5, 2048, 1, 1], [5, 2048, 2, 3], [5, 4096, 2, 3], [5, 4096, 4, 1], [5, 8192, 4, 3], [5, 16384, 2, 3], [5, 16384, 8, 1], [8, 1000000, 8, 2], [8, 2000000, 4, 4], [8, 5000000, 8, 4], [8, 10000000, 8, 4], [8, 25000000, 8, 2], [8, 50000000, 1, 2], [8, 50000000, 2, 3], [8, 50000000, 4, 4], [10, 800, 1, 3], [10, 800, 2, 1], [10, 800, 4, 1], [10, 1600, 1, 3], [10, 1600, 2, 1], [10, 1600, 4, 1], [10, 3200, 2, 5], [10, 3200, 4, 2], [10, 12800, 1, 6], [10, 12800, 2, 5], [10, 12800, 4, 5], [10, 20000, 1, 3], [10, 20000, 2, 2], [10, 20000, 4, 3], [10, 25600, 2, 1], [10, 25600, 4, 1], [10, 40000, 1, 3], [10, 40000, 2, 3], [10, 40000, 4, 3], [10, 51200, 2, 5], [10, 51200, 4, 2], [10, 80000, 2, 5], [10, 80000, 4, 2], [10, 102400, 2, 3], [10, 102400, 4, 2], [10, 204800, 4, 2], [10, 320000, 1, 6], [10, 320000, 2, 2], [10, 320000, 4, 5], [10, 500000, 1, 1], [10, 500000, 2, 1], [10, 640000, 4, 1], [10, 1000000, 1, 1], [10, 1000000, 2, 1], [10, 1280000, 1, 1], [10, 1280000, 2, 3], [10, 2560000, 8, 1], [10, 5120000, 4, 1], [20, 4000, 1, 4], [20, 4000, 2, 8], [20, 16000, 1, 8], [20, 16000, 2, 8], [20, 16000, 4, 4], [20, 20000, 1, 4], [20, 20000, 4, 19], [20, 40000, 1, 4], [20, 40000, 2, 2], [20, 40000, 4, 11], [20, 64000, 1, 8], [20, 64000, 2, 8], [20, 64000, 4, 4], [20, 80000, 2, 11], [20, 80000, 4, 18], [20, 100000, 1, 8], [20, 100000, 2, 12], [20, 100000, 4, 28], [20, 128000, 2, 4], [20, 256000, 2, 8], [20, 320000, 1, 6], [20, 320000, 2, 1], [20, 320000, 4, 21], [20, 400000, 1, 8], [20, 400000, 2, 12], [20, 400000, 4, 28], [20, 500000, 1, 4], [20, 500000, 2, 20], [20, 500000, 4, 33], [20, 512000, 2, 4], [20, 640000, 2, 3], [20, 640000, 4, 1], [20, 1000000, 1, 4], [20, 1000000, 2, 6], [20, 1000000, 4, 9], [20, 1280000, 2, 2], [20, 1280000, 4, 2], [20, 1600000, 1, 8], [20, 1600000, 2, 4], [20, 1600000, 4, 8], [20, 2000000, 1, 8], [20, 2000000, 2, 11], [20, 2000000, 4, 8], [20, 2500000, 1, 4], [20, 2500000, 2, 4], [20, 2500000, 4, 12], [20, 8000000, 4, 3], [20, 16000000, 4, 1], [20, 32000000, 2, 2], [40, 4000000, 8, 4], [40, 8000000, 8, 4], [40, 16000000, 8, 2], [40, 20000000, 8, 4], [40, 32000000, 4, 4], [40, 40000000, 8, 4]], '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, 100, 3], [2, 1250, 7], [2, 5000, 3], [2, 62500, 3], [2, 80000, 1], [2, 390625, 1], [4, 1000, 4], [4, 1250, 10], [4, 2500, 11], [4, 5000, 12], [4, 25000, 48], [4, 62500, 52], [4, 125000, 62], [4, 390625, 2], [4, 625000, 60], [4, 781250, 17], [4, 1562500, 17], [4, 2000000, 6], [4, 3125000, 15], [4, 50000000, 1], [5, 32, 1], [5, 64, 7], [5, 512, 14], [5, 2048, 7], [5, 4096, 10], [5, 8192, 12], [5, 16384, 14], [8, 1000000, 16], [8, 2000000, 16], [8, 5000000, 32], [8, 10000000, 32], [8, 25000000, 16], [8, 50000000, 24], [10, 800, 9], [10, 1600, 9], [10, 3200, 18], [10, 12800, 36], [10, 20000, 19], [10, 25600, 6], [10, 40000, 21], [10, 51200, 18], [10, 80000, 18], [10, 102400, 14], [10, 204800, 8], [10, 320000, 30], [10, 500000, 3], [10, 640000, 4], [10, 1000000, 3], [10, 1280000, 7], [10, 2560000, 8], [10, 5120000, 4], [20, 4000, 20], [20, 16000, 40], [20, 20000, 80], [20, 40000, 52], [20, 64000, 40], [20, 80000, 94], [20, 100000, 144], [20, 128000, 8], [20, 256000, 16], [20, 320000, 92], [20, 400000, 144], [20, 500000, 176], [20, 512000, 8], [20, 640000, 10], [20, 1000000, 52], [20, 1280000, 12], [20, 1600000, 48], [20, 2000000, 62], [20, 2500000, 60], [20, 8000000, 12], [20, 16000000, 4], [20, 32000000, 4], [40, 4000000, 32], [40, 8000000, 32], [40, 16000000, 16], [40, 20000000, 32], [40, 32000000, 16], [40, 40000000, 32]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '6400000000.nt', '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', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1', '5.1'], 'composition_length': 22, 'conjugacy_classes_known': False, 'counter': 358, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 100, 1, 3], [2, 1250, 1, 7], [2, 5000, 1, 3], [2, 62500, 1, 3], [2, 80000, 1, 1], [2, 390625, 1, 1], [4, 1000, 2, 2], [4, 1250, 2, 5], [4, 2500, 1, 11], [4, 5000, 2, 6], [4, 25000, 2, 24], [4, 62500, 2, 26], [4, 125000, 1, 22], [4, 125000, 2, 20], [4, 390625, 2, 1], [4, 625000, 2, 30], [4, 781250, 1, 7], [4, 781250, 2, 5], [4, 1562500, 1, 11], [4, 1562500, 2, 3], [4, 2000000, 1, 6], [4, 3125000, 1, 3], [4, 3125000, 2, 6], [4, 50000000, 1, 1], [5, 32, 1, 1], [5, 64, 1, 7], [5, 512, 1, 14], [5, 2048, 1, 7], [5, 4096, 1, 10], [5, 8192, 1, 12], [5, 16384, 1, 14], [8, 1000000, 2, 8], [8, 2000000, 2, 8], [8, 5000000, 4, 8], [8, 10000000, 2, 16], [8, 25000000, 2, 8], [8, 50000000, 2, 12], [10, 800, 1, 9], [10, 1600, 1, 9], [10, 3200, 1, 18], [10, 12800, 1, 36], [10, 20000, 1, 19], [10, 25600, 1, 6], [10, 40000, 1, 21], [10, 51200, 1, 18], [10, 80000, 1, 18], [10, 102400, 1, 14], [10, 204800, 1, 8], [10, 320000, 1, 30], [10, 500000, 1, 3], [10, 640000, 1, 4], [10, 1000000, 1, 3], [10, 1280000, 1, 7], [10, 2560000, 1, 8], [10, 5120000, 1, 4], [20, 4000, 2, 10], [20, 16000, 2, 20], [20, 20000, 2, 40], [20, 40000, 2, 26], [20, 64000, 2, 20], [20, 80000, 1, 22], [20, 80000, 2, 36], [20, 100000, 2, 72], [20, 128000, 2, 4], [20, 256000, 2, 8], [20, 320000, 2, 46], [20, 400000, 2, 72], [20, 500000, 2, 88], [20, 512000, 2, 4], [20, 640000, 1, 10], [20, 1000000, 2, 26], [20, 1280000, 2, 6], [20, 1600000, 2, 24], [20, 2000000, 1, 22], [20, 2000000, 2, 20], [20, 2500000, 2, 30], [20, 8000000, 1, 12], [20, 16000000, 1, 4], [20, 32000000, 1, 4], [40, 4000000, 4, 8], [40, 8000000, 2, 16], [40, 16000000, 2, 8], [40, 20000000, 4, 8], [40, 32000000, 2, 8], [40, 40000000, 2, 16]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [14, 8], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '6400000000.nt', 'hash': 1295817177765796774, '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': 'C_5^8.C_2^4.C_2^6.C_2^4', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '6400000000.nt', '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.C2^4.C2^6.C2^4', 'ngens': 4, '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, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 91, 0, 0, 0, 0, 115, 0, 0, 0, 163, 0, 0, 0, 179, 0, 0, 0, 167, 0, 0, 63, 0, 0, 75, 0, 67, 0, 43, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 741, 'number_characteristic_subgroups': 150, 'number_conjugacy_classes': 2110, 'number_divisions': 1258, 'number_normal_subgroups': 1032, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 6400000000, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 682175], [4, 199304000], [5, 390624], [8, 2128000000], [10, 73927200], [20, 925696000], [40, 3072000000]], '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': 16, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '3828026323263320625644747126305705982903615726929286685659327093604070365155997090881698912828680268846899460377416908100381262573501737028397981544633211217379705431735882773500874076046969301424206846407263833038754967236996592812070473096658316081627140324424381775676581246192144517534455023041856682470120853618649775450891813779694735418902860148979744227161143564742154169930903111285452296784949849299638399309275559834588064437171833421082366081506993295429211940284982178542224997315668222162302849131370770987281312158266900580111075149609888910116842063613294426558036270370574332036155801473930165727079105832500988311880525882926449438999101272779190158712976445161840746373768662258139760767362452558929438898648502746491766125682964933464339880849138747498880309621641603214025436303635921497672793997223832469789276888053187097595499199785155704573361542960795947969022946025285323810878223203935336654148460072264352484052620488173225395260371330242274128851308809462452580205453546576000846438903548685906748461879172462751982582409823755139375970031961207814597536104703576644005291013556771667683325336084028000221153031677513550889701036760355306490288901047710480749785893959799217953578513621993800243864530015505620779542561237427977046026230920341860145087914397487519182828179840829282199016964273753890278022553019948126348327348566217763217893111646343832163386217157925083026039159379021179949688470200646858334807243243011329086620967525604122337509753463440375536874135148166291986400157134235012569211502188310587756438133072221465730462354493663705352082902670268149073208486404073998908987639299273150321390549512006515005486326699854918078966302941966403007360658528344480502045440183812515665287431179670886161541593290062901892256467676077073030314434109461032783490064925250376483033828534653027401216217112487500731082733772098422065802822196598698721687466920068768958259615700663836830366432447638409985087816070871214769126329862119199139391765598650474304835583', 'gens': [1, 3, 6, 7, 9, 12, 15, 18, 19, 20, 21, 22], 'pres': [22, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 5, 2, 2, 5, 5, 5, 5, 5, 5, 44, 67279016311, 400671136538, 113345620764, 178, 400480404547, 134539964793, 245, 114582253284, 100817475466, 36596876892, 150483015941, 6001461339, 7432979185, 98017447511, 39408230757, 12437536435, 285050525766, 124647654236, 170033721138, 10512095512, 30195670214, 6580176488, 446, 105222250503, 63799307293, 276366024755, 76920529737, 67756126687, 33787506485, 4605934241, 1143588682376, 134216131134, 126490142644, 43636664882, 43843737264, 32667417406, 6197497556, 686826126, 580, 445205798409, 62905441311, 20435177013, 1386077515, 44978313697, 32640696119, 71883821, 5388529683, 647, 100520837130, 435949285408, 61729034806, 67094728524, 33547317858, 39343237240, 1266930158, 2390580708, 576260653067, 238448246817, 117283083511, 116920624205, 64955810403, 36208347769, 1085082383, 7714808805, 4500772507, 2239145249, 298110351, 781, 733241253900, 405451318306, 230235152632, 205942440782, 32546214372, 16320322426, 3997914064, 14093370886, 2668826348, 1321783530, 353155892, 848, 1942588899341, 960879890467, 62069145657, 168782856783, 62638447973, 26524506747, 2272990865, 10972882087, 4076540349, 2038233331, 1309756631054, 108638238756, 280639732618, 257096336720, 7927202022, 33835760764, 21604176146, 9914150568, 7800632590, 1926236612, 116853234, 6263656, 22021178, 982, 617906634767, 78192705573, 246207926331, 191624159313, 18308100199, 64207987837, 10427084947, 6771410089, 6580203711, 4154360533, 66725377, 21493399, 1049, 1246373562384, 108310017062, 396118012988, 103692858450, 19226927208, 58648717374, 17585779348, 9901246250, 3026228672, 3644301094, 50235938, 32957160, 468762624017, 1622016039, 526792273981, 101376127, 50688149, 1159488193, 6336215, 317059, 317081, 16165, 16187, 51192627218, 82610176040, 384807295550, 38843904084, 19849984106, 4815360128, 5002624150, 115033794, 625328216, 98982660, 1672282, 3043366, 1563668, 1110370877459, 53000273961, 557031946303, 246998231125, 18328837227, 84971152769, 13426688151, 8639558573, 8148166595, 4645414617, 63289861, 45795483, 317127, 2666749, 2286558253076, 246876715050, 437938034752, 310160100182, 16275439596, 55357860226, 31841779352, 17383249134, 10684433956, 3337894778, 77209702, 19422764, 4916008, 2273390, 2385530155029, 54523211819, 398386548801, 379369329239, 150136366445, 136976003, 13298151833, 22083022895, 2708115717, 2069235739, 240722503, 71593565, 9941689, 3039871]}, 'Perm': {'d': 40, 'gens': [82637946161408287989950385836183108849728588864, 734323748821978207001483956740723181545022594010, 272113231299691774206819521960646782012839756755, 585120844204261180557189174978412876983005986069]}}, 'schur_multiplier': None, 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 10, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^8.C_2^4.C_2^6.C_2^4', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 2, 4, 4], 'aut_gens': [[1, 2, 4, 16, 32], [1, 2, 148, 16, 176], [145, 2, 4, 16, 32], [1, 2, 4, 16, 176], [145, 146, 4, 16, 32], [1, 2, 4, 16, 160], [1, 2, 132, 16, 32], [1, 2, 220, 16, 176], [1, 2, 196, 16, 112], [89, 66, 4, 16, 48], [145, 210, 20, 16, 32]], 'aut_group': None, 'aut_hash': 2978329760197401528, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 32, 'aut_perms': [41388603669935458998276229252969104, 769244604904227714133078366409437, 41388603673064732981155277096825427, 42149267520651749138927825939383404, 123616996303066079701111100914668627, 10574688372835307530523769, 41521687695537359365761761224452525, 74279960160402191539719449660398809, 237852955475532422055913589494054192, 75040384729847352580565606355797232], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 8, 1, 2], [2, 8, 2, 1], [2, 16, 1, 1], [4, 2, 1, 4], [4, 8, 1, 6], [4, 8, 2, 1], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 16, 1, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 8, 4], [2, 16, 1], [4, 2, 4], [4, 8, 8], [4, 16, 2], [8, 4, 4], [8, 8, 6], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.226', 'commutator_count': 1, 'commutator_label': '16.10', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 23542, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 8, 1, 4], [2, 16, 1, 1], [4, 2, 1, 4], [4, 8, 1, 6], [4, 8, 2, 1], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 322560, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '16.14', 'hash': 23542, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 2, 4, 1, 4], 'inner_gens': [[1, 2, 220, 16, 176], [1, 2, 196, 16, 112], [89, 66, 4, 16, 48], [1, 2, 4, 16, 32], [145, 210, 20, 16, 32]], 'inner_hash': 226, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4^2', 'inner_used': [1, 2, 3, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 8], [8, 1]], 'label': '256.23542', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 5, 'linQ_dim': 12, 'linQ_dim_count': 5, 'linR_count': 15, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2.D4^2', 'ngens': 4, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 105, 'number_conjugacy_classes': 37, 'number_divisions': 32, 'number_normal_subgroups': 107, 'number_subgroup_autclasses': 396, 'number_subgroup_classes': 448, 'number_subgroups': 1391, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 55], [4, 104], [8, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 148, 16, 176], [145, 2, 4, 16, 32], [1, 2, 4, 16, 176], [145, 146, 4, 16, 32], [1, 2, 4, 16, 160], [1, 2, 132, 16, 32], [1, 2, 4, 16, 32], [1, 2, 4, 16, 32], [1, 2, 4, 16, 32], [1, 2, 4, 16, 32]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320, 0, 0, 0, 0], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 24, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 6], [8, 1], [16, 1]], 'representations': {'PC': {'code': 332475598981293794505291934672014180, 'gens': [1, 2, 3, 5, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 5282, 2362, 66, 4355, 2187, 8453, 2701, 597, 141, 5390, 166]}, 'Perm': {'d': 24, 'gens': [26275861139808674426239, 28575190298455425245873, 5673777345740274583680, 58471211245773326921941, 85935344000346377891899, 112972169853854687980800, 138823834378502354054400, 85935344000346377873280]}}, 'schur_multiplier': [2, 2, 4, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2.D_4^2', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
