Query:
/api/gps_groups/?_offset=0
{'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': 4, 'aut_exponent': 48, 'aut_gen_orders': [12, 8, 8, 4, 12, 4], 'aut_gens': [[149539467511629505, 277798901855431729, 525790413758095927, 377749867068727255], [22140996856117441, 831175841327853288, 530540011646271511, 1079901839518213945], [1102060395491570664, 346316118822537487, 906095913876022369, 2175187699857111871], [175826909012121481, 1323312292687131649, 528322127221592089, 2087601560693334864], [1173965143894953126, 1984830112143065790, 1124141907608095927, 1361455562400445854], [1851661813608176448, 2110779328357929750, 1124141907608095927, 1078205680121534911], [1129781028479494345, 467495351572279105, 701363353812441487, 776481454060342951]], 'aut_group': None, 'aut_hash': 8218745305919483472, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 432, 'aut_perms': [31215278542413218815976150392330284763577044941243547405249433686269802676778630836506166798635085760994312687350125971394809287115290697315212631694676201354438319372968964271743656168930167835109695558607607924355249722473475512292805913993931909508972360149045477614442325777783486157759931726956286491967713994925450865542820398742742442578594635682869159576677000380966502674740296644716745577055219344990015709961295587475387935487292139990613428178180118847057272640300438711956529411184333560774131058631264684357709315871286221055302732396248361683666793042396699575462504398922572193747037384598961240443171510713856988048608463169238915313316107185518255232572869740086248664702277770189719483604605331155285968328480080408983604690227424090660822640473706239087213040167668776182247992741989667811980062775037910340088589863980270946514465429508429922526050285193860334640750103641823433664194241793684905674611117926990917771167035363182655, 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41788481843825926305302159816208177624783607803604769958865375675787977915537033127156458610888225516625684143279416158712293918292360265777041168566168391698489941170970270347696652718299737023861508706605277840334929383248179535889398280114538844997434850741710804956139706057241107408976024950059442860539635698509959410188017610245536866026831146824830675582259928330748386210384173831311944431269694195830573924381542663983542236527310337611007896207031402187845264555853210953573089407376496392674855728535439816780350678602619724783365348724879046041581601977897867161023535536155335287609881269212239922434080683872325151113990662394116034169775414538427511040036835750460109653936865167893166103876485904485170542383084828970504319046446685664363312768315574513492140479514982224286938719582218615732082713783601773038199472232458170544899434115074766008220970451533863086294305978511666750405924604855937448043682585936523979717189323310043541], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 2], [2, 72, 4, 1], [2, 81, 1, 2], [2, 144, 2, 1], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 2], [4, 72, 2, 1], [4, 324, 1, 4], [4, 648, 2, 3], [4, 648, 4, 1], [4, 1296, 2, 1], [6, 16, 1, 1], [6, 64, 1, 1], [6, 144, 1, 2], [6, 576, 2, 2], [6, 576, 4, 1], [8, 324, 2, 2], [8, 432, 2, 2], [8, 648, 2, 1], [8, 1296, 4, 1], [8, 2592, 4, 1], [12, 288, 1, 2], [12, 576, 2, 1], [24, 864, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_4^2.C_2^6.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 48, 'autcentquo_group': '41472.m', 'autcentquo_hash': 7917341340725978817, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)^2.D_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 2], [2, 72, 4], [2, 81, 2], [2, 144, 2], [3, 16, 1], [3, 64, 1], [4, 36, 2], [4, 72, 2], [4, 324, 4], [4, 648, 10], [4, 1296, 2], [6, 16, 1], [6, 64, 1], [6, 144, 2], [6, 576, 8], [8, 324, 4], [8, 432, 4], [8, 648, 2], [8, 1296, 4], [8, 2592, 4], [12, 288, 2], [12, 576, 2], [24, 864, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '20736.w', 'commutator_count': 1, 'commutator_label': '2592.lu', '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', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 249, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['20736.w', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 2], [2, 72, 1, 4], [2, 81, 1, 2], [2, 144, 1, 2], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 2], [4, 72, 1, 2], [4, 324, 1, 4], [4, 648, 1, 10], [4, 1296, 1, 2], [6, 16, 1, 1], [6, 64, 1, 1], [6, 144, 1, 2], [6, 576, 1, 8], [8, 324, 2, 2], [8, 432, 2, 2], [8, 648, 1, 2], [8, 1296, 1, 4], [8, 2592, 1, 4], [12, 288, 1, 2], [12, 576, 1, 2], [24, 864, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 2742740582400, 'exponent': 24, 'exponents_of_order': [9, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 4], [32, 0, 2], [32, 1, 1], [64, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '41472.jo', 'hash': 2915094534016945548, 'hyperelementary': 1, 'id': 455228, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [8, 8, 2, 4], 'inner_gens': [[149539467511629505, 776706548802148441, 1124141907608095927, 1406944610127003055], [174928605379744009, 277798901855431729, 1616167960412761129, 794121313147355071], [93657516308959831, 1528141399327728415, 525790413758095927, 1320486296129542975], [1873460898826737847, 996653958206556655, 88435964694331465, 377749867068727255]], 'inner_hash': 4402493192939309901, 'inner_nilpotent': False, 'inner_order': 20736, 'inner_split': True, 'inner_tex': 'C_3^4:(Q_8^2:C_2^2)', 'inner_used': [1, 2, 4], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 12], [4, 20], [8, 2], [16, 8], [32, 6], [64, 8]], 'label': '41472.jo', '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': 'C3^4:(Q8^2.C2^3)', 'ngens': 4, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 41, 'number_characteristic_subgroups': 28, 'number_conjugacy_classes': 72, 'number_divisions': 66, 'number_normal_subgroups': 116, 'number_subgroup_autclasses': 1579, 'number_subgroup_classes': 3627, 'number_subgroups': 494594, 'old_label': None, 'order': 41472, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 775], [3, 80], [4, 10584], [6, 4976], [8, 19872], [12, 1728], [24, 3456]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1790666911979260710, 279369462202027225, 1908728163059937247, 749094526370501311], [152782500385794295, 277809544226880055, 525790413758095927, 377748913270641984], [149539467511629505, 277798901855431728, 525790413758095927, 377749867068727255], [1790666911979260711, 279369462202027224, 1908728163059937247, 749094526370501310]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [7, 288, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 12], [8, 6], [16, 8], [32, 2], [64, 10]], 'representations': {'PC': {'code': '1394811045689100718296644388088594488764098502067124516755135476791515791672947635023607900897316783578704710448263574766946819803006465596559953146405128625266018670914328494487719553247318591941966949536710969841885915455517526674673263030001593106702169576249856514661102779041607838670906556916267179657183454394553856679963', 'gens': [1, 2, 4, 7, 10, 11, 13], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 180128, 1002717, 66, 738974, 234964, 295779, 788544, 432981, 146, 1800244, 754537, 88170, 186, 1599941, 1109490, 370063, 1381750, 1692619, 633392, 379333, 36822, 55581, 266, 2412807, 540820, 269601, 387758, 213883, 4648, 306, 4492808, 44949, 134818, 142319, 37500, 1945, 599049, 299542, 1248035, 599088, 305821, 6314, 40647, 1660, 1098250, 1867031, 256292, 128177, 25230, 51555, 426, 239627, 2995224, 20005, 10034, 47487, 45004, 1730572, 1254681, 854502, 427283, 362400, 146093, 38622, 42691]}, 'Perm': {'d': 20, 'gens': [149539467511629505, 277798901855431729, 525790413758095927, 377749867068727255]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:(Q_8^2.C_2^3)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}