-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '82944.bd', 'ambient_counter': 30, 'ambient_order': 82944, 'ambient_tex': 'A_4^2:\\POPlus(4,3)', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 41472, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '82944.bd.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 4771581563444804662, 'subgroup_order': 41472, 'subgroup_tex': 'C_2^8.C_3^4.C_2', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '82944.bd', 'aut_centralizer_order': None, 'aut_label': '2.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '82944.a1', 'complements': ['41472.F'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.E', '6.F', '6.G', '6.H', '6.I', '6.J', '8.a1'], 'core': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': [6871, 1710, 2037, 2974], 'generators': [79838071, 39309, 6720991568236, 1963546974, 314, 8388882034378, 134, 8230485895, 205535634063, 29821, 43545638, 89138245551, 79833600], 'label': '82944.bd.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': None}
-
label None does not appear in gps_groups
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [6, 6, 6], 'aut_gens': [[2903356086226, 174436421116, 1327353724969], [1589374862710, 6806692572683, 4272814056104], [2629359549430, 31258876285, 9535532421466], [4272814036101, 118916168971, 9529301760841]], 'aut_group': '1327104.a', 'aut_hash': 6438584053786730791, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1327104, 'aut_permdeg': 288, 'aut_perms': [516804020543448295625902196459123353823209445655390511229596009188160749574226059060593914705898210643703308641907979829377361564666465531981009950381451762244179220072475228321831404877779875446133595149124161086437418729486865826619044733148028849476467730320043126581998464940767205946691935928413449284996133584933564875215776949730124540382512620643478935810160277244118246772162254436952336520578234589548326144791588270079525584629765678951663821661750345528074349251492850883896802319986416333321069500920481874125562126132893087213263893440784081150835296296310311490294827625, 713800286101660295325076454909566559017663739182777646223947985617349347076073509403507629276617801985624778875081243813758097354348637619038157554790864992213986156289871282197977436922290084999005908748437975623326169004602940834703435252134960528594850323075400574628515482828422379352570773593954673639499312606888186970070260657279556154282472849739356305966226137179792126547113434194574787126529138065695694586471205889871673631648685879896532795586052251951542858296716790085547734166081351794230094862682938035261011574372607250450220360514732776885366317863002257033749042489, 513412292163577803523212128854556522547030535341800900128167116150741041895546263404691327243695262401924809491357232399860878527189450259035371050278227761544263951762512751783181789148146837140469542045061574521310889915683144248501939487106194801227035007528644973298594052651677483980245542998581688918828840681804803895972140011490205798057477139531323115293981198591990516861378352958536250222451496131376212245102626200700558157674094995464748326009277440000200456187151022749931835819668260469702046969578501348654530939469279891956287807454210232532561247007644914474153516942], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 2, 1], [2, 9, 2, 1], [2, 18, 2, 1], [2, 54, 2, 1], [2, 81, 1, 1], [2, 144, 2, 1], [2, 1296, 1, 1], [3, 16, 2, 1], [3, 32, 4, 1], [3, 64, 4, 1], [3, 256, 8, 1], [3, 512, 4, 1], [3, 1024, 2, 1], [4, 432, 4, 1], [4, 1296, 1, 1], [4, 1296, 2, 2], [4, 2592, 2, 3], [6, 48, 2, 1], [6, 48, 4, 1], [6, 144, 2, 1], [6, 144, 4, 1], [6, 192, 4, 1], [6, 192, 8, 1], [6, 288, 4, 1], [6, 432, 2, 1], [6, 576, 4, 1], [6, 768, 8, 1], [6, 1152, 4, 1], [6, 4608, 4, 1], [12, 3456, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4^2\\wr C_2.C_4.D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '1327104.a', 'autcentquo_hash': 6438584053786730791, 'autcentquo_nilpotent': False, 'autcentquo_order': 1327104, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'A_4^2\\wr C_2.C_4.D_4', 'cc_stats': [[1, 1, 1], [2, 6, 2], [2, 9, 2], [2, 18, 2], [2, 54, 2], [2, 81, 1], [2, 144, 2], [2, 1296, 1], [3, 16, 2], [3, 32, 4], [3, 64, 4], [3, 256, 8], [3, 512, 4], [3, 1024, 2], [4, 432, 4], [4, 1296, 5], [4, 2592, 6], [6, 48, 6], [6, 144, 6], [6, 192, 12], [6, 288, 4], [6, 432, 2], [6, 576, 4], [6, 768, 8], [6, 1152, 4], [6, 4608, 4], [12, 3456, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '82944.bd', 'commutator_count': 1, 'commutator_label': None, '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', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 14, 'conjugacy_classes_known': True, 'counter': 30, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [2, 54, 1, 2], [2, 81, 1, 1], [2, 144, 1, 2], [2, 1296, 1, 1], [3, 16, 1, 2], [3, 32, 1, 4], [3, 64, 1, 4], [3, 256, 1, 8], [3, 512, 1, 4], [3, 1024, 1, 2], [4, 432, 1, 4], [4, 1296, 1, 5], [4, 2592, 1, 6], [6, 48, 1, 6], [6, 144, 1, 6], [6, 192, 1, 12], [6, 288, 1, 4], [6, 432, 1, 2], [6, 576, 1, 4], [6, 768, 1, 8], [6, 1152, 1, 4], [6, 4608, 1, 4], [12, 3456, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 98317800, 'exponent': 12, 'exponents_of_order': [10, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 4], [36, 1, 8], [54, 1, 4], [81, 1, 4], [108, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '82944.bd', 'hash': 2551087645679240259, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 6], 'inner_gens': [[2903356086226, 182587073729, 1321572683588], [1676549527801, 174436421116, 4209473350095], [4291941807742, 5332326033881, 1327353724969]], 'inner_hash': 2551087645679240259, 'inner_nilpotent': False, 'inner_order': 82944, 'inner_split': False, 'inner_tex': 'A_4^2:\\POPlus(4,3)', 'inner_used': [1, 2, 3], 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 4], [2, 16], [4, 16], [6, 4], [9, 8], [12, 26], [18, 12], [36, 10], [54, 4], [81, 4], [108, 2]], 'label': '82944.bd', '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': 'A4^2:PO+(4,3)', 'ngens': 3, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 34, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 106, 'number_divisions': 106, 'number_normal_subgroups': 59, 'number_subgroup_autclasses': 3343, 'number_subgroup_classes': 16051, 'number_subgroups': 5123980, 'old_label': None, 'order': 82944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1839], [3, 6560], [4, 23760], [6, 36960], [12, 13824]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 1963546974, 0], 'outer_gens': [[2901838883992, 523672496122, 1327912207969], [2895604969426, 7947602172796, 1334142846889], [3069928533790, 6831524846457, 1334059747207], [2895604969426, 523636207996, 1334142846889]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 7, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 16], [4, 16], [6, 4], [9, 8], [12, 26], [18, 12], [36, 10], [54, 4], [81, 4], [108, 2]], 'representations': {'PC': {'code': '187842555810301229738338913454422391517796949439600175557075772100086402116210381363418926567023867779895233197049924811717480760037182209494972144347218951207467432495486984829739503644522876664272140454368312573366295870757561212597473164013004290702029115404751968441542327081018395186194513071802592139634603318603349312452385756553244371038019031215152639041677435297790023813090624', 'gens': [1, 2, 4, 5, 7, 9, 10, 11, 12, 13, 14], 'pres': [14, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 328608, 872201, 71, 2749154, 1166595, 1582913, 473455, 5181124, 2361258, 579002, 19786, 200, 1639013, 604819, 409785, 54983, 3149334, 3867296, 277864, 2694, 21818, 7426, 286, 3251143, 995253, 2116835, 9471, 12845, 81656, 40846, 1347228, 435506, 24284, 12580, 3991689, 1995863, 181477, 60531, 20225, 15199, 5133, 1787, 2993770, 2494824, 299414, 99844, 33330, 5624, 1942, 2880, 6858443, 1469689, 2884935, 1070549, 157315, 57537, 50495, 29341, 6840300, 1297322, 1592176, 255582, 85244, 95086, 31764, 7208, 21181, 74115, 63545, 698599, 38905, 699]}, 'Perm': {'d': 16, 'gens': [2903356086226, 174436421116, 1327353724969]}}, 'schur_multiplier': [2, 6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4^2:\\POPlus(4,3)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}
