Query:
/api/gps_groups/?_offset=0
Table gps_groups
Finite groups
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '14.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1092, 'aut_gen_orders': [6, 12, 6, 6], 'aut_gens': [[415592052, 801250460, 448893330, 772289600, 490366493], [294836845, 106189820, 458546950, 77228960, 497824801], [111840979, 405452040, 555083150, 381317990, 787352083], [437693192, 497161430, 342703510, 473027380, 642707898], [480480096, 106189820, 419932470, 77228960, 525646957]], 'aut_group': None, 'aut_hash': 3088507494921977175, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 26208, 'aut_permdeg': 164, 'aut_perms': [2004630720954118643507715643077900787989263106935190196340145424238025960803084726339798406807074263968727908911009093837885706471000189439805165407962534579848621812507902117052097987266081475168753509035569348768670717027795063471988813513765253586363734615065800372892324111293875017680287, 2004554339521578856567974883907603835253945464870345456422595388492217296351919875879479019910586693078559658157048251100475020293029445990964684418675092012055558088934383464825785067505430677142556218706682281667252472474335706291916433313144348553554990124643781603999967332901511240897641, 2004781111798000207273494004803026670746264360793540055080024420733044546785411988266377259914707740827331921443598256677115764957368809032996401400202868718884890354324744400104328458793004003656073414403365053076855045008290476853170790406336320337717078312278244695872201438325524267793084, 229144408816341723184968750709194632538046268481749525125381334763529433397622501256788183778954298430502683067123392447223972404112642572256210583531866779677380659503310092452154247644793421904634080183011958091347653937689555673599036174946166461434127340770702346943800741961158718234], 'aut_phi_ratio': 3.25, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 1, 3], [7, 156, 6, 3], [12, 182, 1, 2], [12, 182, 2, 1], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 1, 3], [14, 156, 6, 3], [14, 182, 6, 1], [21, 182, 6, 1], [26, 84, 2, 1], [28, 1, 12, 1], [28, 156, 2, 3], [28, 156, 12, 3], [28, 182, 6, 1], [42, 182, 6, 1], [42, 182, 12, 1], [52, 84, 4, 1], [84, 182, 6, 2], [84, 182, 12, 1], [91, 84, 12, 1], [182, 84, 12, 1], [364, 84, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_6\\times \\PSL(2,13).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1092, 'autcentquo_group': '2184.b', 'autcentquo_hash': 7763277135502868404, 'autcentquo_nilpotent': False, 'autcentquo_order': 2184, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,13)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 182, 1], [3, 182, 1], [4, 1, 2], [4, 182, 1], [6, 182, 3], [7, 1, 6], [7, 156, 21], [12, 182, 4], [13, 84, 2], [14, 1, 6], [14, 156, 21], [14, 182, 6], [21, 182, 6], [26, 84, 2], [28, 1, 12], [28, 156, 42], [28, 182, 6], [42, 182, 18], [52, 84, 4], [84, 182, 24], [91, 84, 12], [182, 84, 12], [364, 84, 24]], 'center_label': '28.2', 'center_order': 28, 'central_product': True, 'central_quotient': '1092.25', 'commutator_count': 1, 'commutator_label': '2184.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '1092.25'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['4368.c', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 182, 1, 1], [3, 182, 1, 1], [4, 1, 2, 1], [4, 182, 1, 1], [6, 182, 1, 1], [6, 182, 2, 1], [7, 1, 6, 1], [7, 156, 3, 1], [7, 156, 6, 3], [12, 182, 2, 2], [13, 84, 2, 1], [14, 1, 6, 1], [14, 156, 3, 1], [14, 156, 6, 3], [14, 182, 6, 1], [21, 182, 6, 1], [26, 84, 2, 1], [28, 1, 12, 1], [28, 156, 6, 1], [28, 156, 12, 3], [28, 182, 6, 1], [42, 182, 6, 1], [42, 182, 12, 1], [52, 84, 4, 1], [84, 182, 12, 2], [91, 84, 12, 1], [182, 84, 12, 1], [364, 84, 24, 1]], 'element_repr_type': 'GLFq', 'elementary': 1, 'eulerian_function': 23760, 'exponent': 1092, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 7, 13], 'factors_of_order': [2, 3, 7, 13], 'faithful_reps': [[6, 0, 24], [12, 0, 36], [14, 0, 36]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 4812302980474511629, 'hyperelementary': 1, 'id': 147736, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 546, 'inner_gen_orders': [2, 1, 1, 1, 13], 'inner_gens': [[415592052, 801250460, 448893330, 772289600, 754050027], [415592052, 801250460, 448893330, 772289600, 490366493], [415592052, 801250460, 448893330, 772289600, 490366493], [415592052, 801250460, 448893330, 772289600, 490366493], [461168301, 801250460, 448893330, 772289600, 490366493]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 1092, 'inner_split': True, 'inner_tex': '\\PSL(2,13)', 'inner_used': [1, 5], 'irrC_degree': 6, 'irrQ_degree': 144, 'irrQ_dim': 144, 'irrR_degree': 12, 'irrep_stats': [[1, 14], [6, 28], [7, 28], [12, 84], [13, 14], [14, 70]], 'label': '30576.b', 'linC_count': 24, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 30, 'linQ_degree_count': 2, 'linQ_dim': 30, 'linQ_dim_count': 2, 'linR_count': 12, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,13):C14', 'ngens': 5, '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, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 46, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 238, 'number_divisions': 38, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 103, 'number_subgroup_classes': 125, 'number_subgroups': 9480, 'old_label': None, 'order': 30576, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 183], [3, 182], [4, 184], [6, 546], [7, 3282], [12, 728], [13, 168], [14, 4374], [21, 1092], [26, 168], [28, 7656], [42, 3276], [52, 336], [84, 4368], [91, 1008], [182, 1008], [364, 2016]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [4826810, 4826810, 384816314], 'outer_gens': [[681743844, 106189820, 419932470, 77228960, 693124739], [415592052, 801250460, 429586090, 772289600, 393341787], [446031988, 613004870, 608178060, 598524440, 529201394]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 63, 'pgroup': 0, 'primary_abelian_invariants': [2, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2], [13, 2], [14, 6], [24, 1], [28, 1], [36, 2], [56, 1], [72, 7], [78, 2], [84, 6], [144, 4], [168, 1], [336, 1]], 'representations': {'GLFq': {'d': 2, 'q': 169, 'gens': [415592052, 801250460, 448893330, 772289600, 490366493]}, 'Perm': {'d': 63, 'gens': [32002948941137034641416832985497490978007525106250773638624883403760055231942559171015, 64970972549750024706108539941705397670731766767467678709527345421353203852470876987148, 96998038569281425749773367228660699792763256836694904840270762937020750251723752764328, 1095, 128984611192195342033586122315690645346142148987522422933279218836973360577646295888087]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [14], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,13):C_{14}', 'transitive_degree': 392, 'wreath_data': None, 'wreath_product': False}