Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [12, 6, 6], 'aut_gens': [[3669656, 12940708471, 4354574, 12936715356, 4394880, 12940300934, 3669120, 12933043200, 2929212725, 17248099261, 11652480, 12937034954], [5795646063, 12940704488, 2922318000, 2921632680, 4394880, 15339345845, 3669120, 12933043200, 11249594, 12933043736, 11652480, 18210089673], [7983494, 15332092991, 11289794, 15343377974, 200, 12944695920, 134, 12933043200, 5791977327, 17248099261, 536, 12943970064], [5791977357, 18206823753, 2917966481, 18206867829, 3035, 17248094916, 5791976943, 12933043200, 2929620393, 12936712320, 4833974461, 15332091540]], 'aut_group': '331776.k', 'aut_hash': 3604168331467219802, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 216, 'aut_perms': [5319198943914279654632284825881307994314378909496762671417116992803926114248200491894799637634400940057491204360469449156040115231717603813261409184376526758104875231725202374151518879112406204497122690417665340229226156650490281033055310961741269772375151989617871412017702467776568110051082981526123413028671974516832302675514917481301665579438160563580779579965511289117077910487692090601145001313887828738332, 2730357818748105790551042324478072386841424085046405444673261918093627158706784693566835397425228589461219969846339608880724679939901209000459367224032877718879040795416109401227552217012854127214731829734412387283790779773350854875206144891199598972343660583288069834020039340122155243063551842444971351058574119947046457333005040986760353688564696331843665592006799483524651752207290382979517995633374379496686, 5882621917815556354215432951670894325018252559253811973159304403836708677854819342287845875232629019879498273619541079051759659490129745750450987377792183513999278616824102510288530107595057442282661782510243732344938707940082401472244536882581753416161038251495368939044565530316363350422352727539357937969548991443127080291900548206559503049360147961460810118203076657493619856847431397075788493508209396211476], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 3, 2], [2, 9, 3, 2], [2, 27, 1, 2], [2, 36, 6, 1], [2, 108, 6, 1], [3, 8, 3, 1], [3, 64, 3, 1], [3, 256, 2, 1], [4, 36, 6, 1], [4, 36, 12, 1], [4, 108, 6, 1], [4, 108, 12, 1], [6, 8, 3, 1], [6, 24, 6, 2], [6, 64, 3, 1], [6, 72, 3, 2], [6, 192, 3, 2], [6, 256, 2, 1], [6, 288, 6, 1], [12, 288, 6, 1], [12, 288, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4^3.S_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '82944.d', 'autcentquo_hash': 6931629392945487332, 'autcentquo_nilpotent': False, 'autcentquo_order': 82944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'A_4^3.(C_2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 6], [2, 9, 6], [2, 27, 2], [2, 36, 6], [2, 108, 6], [3, 8, 3], [3, 64, 3], [3, 256, 2], [4, 36, 18], [4, 108, 18], [6, 8, 3], [6, 24, 12], [6, 64, 3], [6, 72, 6], [6, 192, 6], [6, 256, 2], [6, 288, 6], [12, 288, 18]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '6912.jj', 'commutator_count': 1, 'commutator_label': '1728.47863', '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', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 147, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['6912.jj', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 6], [2, 9, 1, 6], [2, 27, 1, 2], [2, 36, 1, 6], [2, 108, 1, 6], [3, 8, 1, 3], [3, 64, 1, 3], [3, 256, 2, 1], [4, 36, 1, 18], [4, 108, 1, 18], [6, 8, 1, 3], [6, 24, 1, 12], [6, 64, 1, 3], [6, 72, 1, 6], [6, 192, 1, 6], [6, 256, 2, 1], [6, 288, 1, 6], [12, 288, 1, 18]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1512000, 'exponent': 12, 'exponents_of_order': [9, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[27, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '13824.fq', 'hash': 519320209499247253, 'hyperelementary': 1, 'id': 350364, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 4, 2, 3, 6, 2, 1, 6, 2, 2, 3], 'inner_gens': [[3669656, 12933773431, 7298040, 12936715470, 7257600, 12937438214, 3669120, 12933043200, 2918366645, 17248099261, 11652480, 12943970064], [11653016, 12940708471, 10886414, 12944700167, 7257600, 12933446534, 11652480, 12933043200, 5803226223, 15332088245, 7983360, 12933769034], [7983674, 12940305271, 4354574, 12941029596, 725760, 12943970054, 7983360, 12933043200, 2921955125, 17248099261, 11652480, 12937438118], [3669434, 12933771995, 7297934, 12936715356, 7257600, 12937438214, 3669120, 12933043200, 4834377661, 15332088245, 11652480, 12943969958], [7983896, 12937039351, 8023694, 12941029596, 4394880, 12933446534, 7983360, 12933043200, 2925221045, 17248099261, 3669120, 12933769034], [7983896, 12933773431, 11612174, 12941029596, 11249280, 12940300934, 7983360, 12933043200, 2918366645, 17248099261, 3669120, 12937035158], [3669656, 12933773431, 7297934, 12936715356, 7257600, 12937438214, 3669120, 12933043200, 2918366645, 17248099261, 11652480, 12943969994], [3669656, 12940708471, 4354574, 12936715356, 4394880, 12940300934, 3669120, 12933043200, 2929212725, 17248099261, 11652480, 12937034954], [7983896, 17255756315, 11612174, 18214082087, 403200, 12937438214, 7983360, 12933043200, 2929212725, 17248099261, 3669120, 12943969994], [3669656, 18213758793, 4354574, 18209767847, 4394880, 12940300934, 3669120, 12933043200, 2929212725, 17248099261, 11652480, 12937034954], [3669656, 12943974391, 4354574, 12936715356, 11249280, 12933446534, 3669120, 12933043200, 2922358325, 17248099261, 11652480, 12933769034], [11652794, 12943974391, 4032024, 12944698734, 403200, 12940301336, 11652480, 12933043200, 2922358325, 17248099261, 7983360, 12937034954]], 'inner_hash': 1721632380221528255, 'inner_nilpotent': False, 'inner_order': 6912, 'inner_split': True, 'inner_tex': 'A_4:S_4^2', 'inner_used': [1, 2, 3, 4, 9, 12], 'irrC_degree': 27, 'irrQ_degree': 27, 'irrQ_dim': 27, 'irrR_degree': 27, 'irrep_stats': [[1, 8], [2, 12], [3, 24], [4, 10], [6, 24], [9, 24], [12, 6], [18, 12], [27, 8]], 'label': '13824.fq', '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': 'A4^3.C2^3', 'ngens': 12, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 29, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 128, 'number_divisions': 126, 'number_normal_subgroups': 86, 'number_subgroup_autclasses': 2259, 'number_subgroup_classes': 19020, 'number_subgroups': 935696, 'old_label': None, 'order': 13824, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 991], [3, 728], [4, 2592], [6, 4328], [12, 5184]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [365910, 0, 0, 0, 0], 'outer_gens': [[2917963978, 17248498715, 2917967922, 15332451136, 2917967913, 17248094916, 2917963445, 12933043200, 5799957271, 12936712320, 5791976943, 15332091318], [3669656, 12940707035, 4354574, 12936715356, 4394880, 12940300934, 3669120, 12933043200, 4845223741, 15332088245, 11652480, 12937034954], [2921632565, 17248095899, 2918330791, 15332451136, 2917967913, 17259747270, 2917963445, 12933043200, 5791974444, 12933043514, 5791976943, 15339348870], [3669434, 12940707035, 12937397774, 12936715356, 4394880, 12940300934, 3669120, 12933043200, 4845223741, 15332088245, 11652480, 12937034918], [3669656, 12940708471, 4354574, 3672156, 4394880, 12940300934, 3669120, 12933043200, 2929212725, 17248099261, 11652480, 12937034954]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [143, 127, 576, 126, 121], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 24], [4, 6], [6, 24], [8, 2], [9, 24], [12, 6], [18, 12], [27, 8]], 'representations': {'PC': {'code': '73145921721557612527902008405740540645648438961068352670302349947946121201508693745018079575082315801935546351989133873663208533163782049742464356333635983802221033645794205351276617640712528544', 'gens': [1, 2, 4, 6, 8, 9, 10, 11, 12], 'pres': [12, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 20977, 61, 31394, 7802, 42051, 120687, 59787, 135, 299524, 27376, 61948, 927941, 457505, 226829, 209, 24198, 12114, 290311, 145171, 3523, 2095, 36980, 22412, 67005, 29217, 3669, 1161, 1083466, 501358, 299410, 47566, 8374, 11950, 5626, 808715, 466583, 257939, 132239, 46715, 14759, 10019]}, 'Perm': {'d': 14, 'gens': [3669656, 12940708471, 4354574, 12936715356, 4394880, 12940300934, 3669120, 12933043200, 2929212725, 17248099261, 11652480, 12937034954]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4^3.C_2^3', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}