Query:
/api/gps_groups/?_offset=0
Table gps_groups
Finite groups
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.9', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [30, 6, 60, 6, 6, 12, 4, 30], 'aut_gens': [[1, 20, 80, 320, 1280, 5120, 10240], [9671, 7280, 5080, 10740, 15100, 10920, 5920], [10031, 12600, 13140, 12180, 10540, 5280, 13440], [15551, 11640, 2360, 13780, 14580, 7840, 12840], [81, 20260, 13260, 12660, 14340, 12800, 7720], [3351, 20460, 14060, 14460, 14180, 12800, 7720], [1591, 12600, 13140, 12180, 10540, 5280, 13440], [9501, 18620, 720, 3080, 4000, 13640, 8520], [11011, 15740, 14300, 4520, 400, 11080, 7840]], 'aut_group': '6552.b', 'aut_hash': 3293705871083303955, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 983040, 'aut_permdeg': 384, 'aut_perms': 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72039161382025607694682225460384517348713742716220859278561357026203801623651382669714609293819912561126184916120438377829166526549457416396977271811359619494425154347750216956721013161760040954013048591473212627783270420872679927837791690166406086206313311902582554565713572225251447055063733828969218479613198782868544893334767704315395745371812890009516007119066498370219912792640041539973733262779862204872672554202108815152496245113867768702713992128958707052355436820780477209874896293209589139812352096022704052698977120865696983733354008091110340166187920252297803869374887730711999787828962156503649659114410704563763644421038425902180139314846787446206616416294326487683156020148350645580073496628672952114016122876514333410697673342996841698835673102716068418972658912917935241813666191472113400535371907050726645773, 8881434765339833898570950748541570472807343040418805346063440237403979263867257253253636432517335431356764319815212529001652812710734757589399217339211698513023891086891323684212110268827162557307620998469460158665721051486710912134491580307867453899580977156557297489296928687492450005940540872678212684390704069259521797494936758164486522136800126714718827454418947186851618068587419976460917098021604881131995301084939562412182288070158795761870129117114048815896172951673261230672505954094809994086457951646228355038161544739250472714563008851094686556378537657011573599965611728652004977086610584436102429697937784562244521871087380449046989322428452168044228612101313529148779801660175325006561339266853765559141866244488926521128709172921548055920786953885312015173932366564446460581623689149184469135375453306366062463], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 5, 3, 2], [2, 10, 3, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 5, 6, 1], [4, 10, 3, 1], [4, 10, 24, 2], [4, 10, 48, 3], [5, 256, 1, 4], [8, 32, 4, 1], [8, 160, 12, 1], [10, 256, 1, 4], [10, 512, 1, 4], [20, 256, 2, 4], [20, 512, 1, 4], [40, 512, 4, 4]], 'aut_supersolvable': False, 'aut_tex': 'C_3\\times \\SL(2,13)', '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': 60, 'autcentquo_group': None, 'autcentquo_hash': 4725625300111063848, 'autcentquo_nilpotent': False, 'autcentquo_order': 122880, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times C_4^4.C_{30}.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 5, 6], [2, 10, 3], [4, 1, 2], [4, 2, 1], [4, 5, 6], [4, 10, 195], [5, 256, 4], [8, 32, 4], [8, 160, 12], [10, 256, 4], [10, 512, 4], [20, 256, 8], [20, 512, 4], [40, 512, 16]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '5120.dx', 'commutator_count': 1, 'commutator_label': '512.420515', 'complements_known': False, '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', '2.1', '2.1', '5.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 458, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 5, 1, 6], [2, 10, 1, 3], [4, 1, 2, 1], [4, 2, 1, 1], [4, 5, 2, 3], [4, 10, 1, 3], [4, 10, 2, 96], [5, 256, 4, 1], [8, 32, 2, 2], [8, 160, 2, 6], [10, 256, 4, 1], [10, 512, 4, 1], [20, 256, 8, 1], [20, 512, 4, 1], [40, 512, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 40, 'exponents_of_order': [12, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[10, 0, 96]], 'familial': False, 'frattini_label': '64.260', 'frattini_quotient': '320.1637', 'hash': 2771965375868575327, 'hyperelementary': 1, 'id': 390011, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [10, 4, 4, 4, 4, 2, 2], 'inner_gens': [[1, 5360, 3520, 15020, 2000, 10440, 7880], [5221, 20, 80, 320, 1280, 5120, 10240], [2961, 20, 80, 320, 1280, 5120, 10240], [12581, 20, 80, 320, 1280, 5120, 10240], [881, 20, 80, 320, 1280, 5120, 10240], [15561, 20, 80, 320, 1280, 5120, 10240], [18121, 20, 80, 320, 1280, 5120, 10240]], 'inner_hash': 6631808013228481333, 'inner_nilpotent': False, 'inner_order': 5120, 'inner_split': True, 'inner_tex': 'C_2\\times C_4^4:C_{10}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 40], [2, 10], [5, 24], [10, 198]], 'label': '20480.rp', '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': True, 'metacyclic': False, 'monomial': None, 'name': 'C4wrC5.C4', 'ngens': 13, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 41, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 272, 'number_divisions': 131, 'number_normal_subgroups': 33, 'number_subgroup_autclasses': 4640, 'number_subgroup_classes': 59301, 'number_subgroups': 604086, 'old_label': None, 'order': 20480, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 63], [4, 1984], [5, 1024], [8, 2048], [10, 3072], [20, 4096], [40, 8192]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 2, 2, 2, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 16], 'outer_gens': [[1, 700, 2680, 2880, 2080, 5120, 10240], [1, 18780, 80, 320, 1280, 13640, 8520], [11, 20, 80, 320, 1280, 5120, 10240], [12961, 20, 80, 320, 1280, 5120, 10240], [1, 60, 240, 960, 3840, 5120, 10240], [1, 18980, 14460, 13740, 4360, 13600, 5760]], 'outer_group': '192.1543', 'outer_hash': 1543, 'outer_nilpotent': True, 'outer_order': 192, 'outer_permdeg': 15, 'outer_perms': [24, 87178291200, 479001600, 3628800, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 40, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 5], [5, 12], [8, 2], [10, 6], [16, 1], [20, 99]], 'representations': {'PC': {'code': '858311831412001382205477287940028990123526948989240201718205238946129057526274102507744202818453403507228690869400335305213196284550443578128392336993400663973676613880282400076233169760681984', 'gens': [1, 4, 6, 8, 10, 12, 13], 'pres': [13, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 26, 66, 182938, 278723, 346336, 189309, 146, 10404, 20817, 52030, 274565, 584238, 265621, 226, 58246, 125599, 942, 1562087, 116500, 23953, 306, 322928, 187221, 4714, 260009, 122222, 458285, 386, 388970, 240263, 92986, 1628651, 652104, 307357, 1331732, 1152605, 439438]}, 'Perm': {'d': 40, 'gens': [460556583839451603614575709788353653672728704006, 795517390824622861180759808008756065835583232127]}}, 'schur_multiplier': [2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 16, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 128, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\wr C_5.C_4', 'transitive_degree': 40, 'wreath_data': None, 'wreath_product': False}