Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [4, 12, 2, 12, 6, 4, 6, 2], 'aut_gens': [[1, 6, 36, 216, 864], [2201, 1014, 1836, 5094, 504], [1879, 1302, 2772, 4104, 864], [1469, 1830, 3204, 2808, 4320], [1763, 3030, 3996, 2142, 504], [1753, 3126, 1404, 2502, 576], [4501, 438, 4860, 5166, 504], [101, 4758, 36, 2376, 864], [4853, 1902, 180, 216, 4320]], 'aut_group': None, 'aut_hash': 2854184908137106426, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 27648, 'aut_permdeg': 98, 'aut_perms': [1948162423213822250601638823198841343514350508126157698409279441635100953522850357485284078088720020466729205888060751736081588159909226735002295330558936, 3844794302363394692754750739303987394511400118711458508038728679282671065654155723633496081626163962211407539345369327654771965229168406978597362616612167, 7396952566542420878685173254274795624225451456543838912027432653517271546477625097398458115338651567141603419533385735927112044975999749417142753944947351, 7191245809112170250041120847744240733852438164006944411167467707418636897100562205146489953276235740628651552641255530640405458488936550150388813506487405, 6669100240514760869396397796037835997691336299561471625609135477138402967970673449921244737946419678673450546349431979687583849401939165334793140246791350, 4389089258875882127487344588430647191283226414395782146547485901037824244889524384612942435081813634090672185912855952037830578909999209610995567186486920, 1048218123087830458218102025187116320701428347515596585796780212839974291426754092915494269438970732990098969399444210128118319247801920684622731357837778, 8474945748344659812898440345835942691338171795126305166365793355607393262989141824898898937847589622773604122270737630573847548728622130131180463494317149], 'aut_phi_ratio': 16.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 1], [2, 36, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 3], [3, 4, 4, 1], [3, 8, 1, 1], [3, 8, 2, 1], [4, 12, 2, 1], [4, 18, 2, 1], [4, 36, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 4, 1, 4], [6, 4, 2, 9], [6, 4, 4, 4], [6, 8, 1, 4], [6, 8, 2, 8], [6, 8, 4, 5], [6, 8, 8, 1], [6, 24, 2, 3], [6, 24, 4, 3], [6, 24, 8, 1], [6, 36, 2, 1], [6, 36, 4, 1], [6, 72, 1, 1], [6, 72, 2, 2], [6, 72, 4, 1], [8, 216, 2, 1], [12, 12, 4, 2], [12, 12, 8, 1], [12, 18, 4, 1], [12, 24, 2, 1], [12, 24, 4, 2], [12, 24, 8, 1], [12, 36, 2, 1], [12, 36, 4, 2], [12, 72, 2, 1], [12, 72, 4, 1], [24, 216, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3.C_2^6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '1728.46671', 'autcentquo_hash': 46671, 'autcentquo_nilpotent': False, 'autcentquo_order': 1728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 24, 1], [2, 36, 3], [3, 1, 2], [3, 2, 3], [3, 4, 12], [3, 8, 3], [4, 12, 2], [4, 18, 2], [4, 36, 2], [6, 1, 2], [6, 2, 11], [6, 4, 38], [6, 8, 48], [6, 24, 26], [6, 36, 6], [6, 72, 9], [8, 216, 2], [12, 12, 16], [12, 18, 4], [12, 24, 18], [12, 36, 10], [12, 72, 6], [24, 216, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '864.4297', 'commutator_count': 1, 'commutator_label': '216.143', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 66, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['1728.33409', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 3], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 2], [3, 4, 2, 5], [3, 8, 1, 1], [3, 8, 2, 1], [4, 12, 1, 2], [4, 18, 1, 2], [4, 36, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 4, 1, 4], [6, 4, 2, 17], [6, 8, 1, 6], [6, 8, 2, 21], [6, 24, 2, 13], [6, 36, 2, 3], [6, 72, 1, 3], [6, 72, 2, 3], [8, 216, 1, 2], [12, 12, 2, 8], [12, 18, 2, 2], [12, 24, 1, 2], [12, 24, 2, 8], [12, 36, 1, 2], [12, 36, 2, 4], [12, 72, 1, 2], [12, 72, 2, 2], [24, 216, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1397760, 'exponent': 24, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[4, 0, 16], [8, 0, 12]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '1296.3570', 'hash': 5428266237022475929, 'hyperelementary': 1, 'id': 469520, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 6, 4, 6], 'inner_gens': [[1, 102, 4860, 5022, 504], [157, 6, 3204, 4104, 4320], [1441, 3102, 36, 648, 864], [3511, 2166, 468, 216, 4320], [1441, 1734, 36, 1944, 864]], 'inner_hash': 4297, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': '(S_3\\times D_6):D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 24], [2, 42], [4, 120], [8, 48]], 'label': '5184.cn', '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*C6^3.D4', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 90, 'number_characteristic_subgroups': 62, 'number_conjugacy_classes': 234, 'number_divisions': 137, 'number_normal_subgroups': 94, 'number_subgroup_autclasses': 1471, 'number_subgroup_classes': 2309, 'number_subgroups': 23140, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 139], [3, 80], [4, 132], [6, 2048], [8, 432], [12, 1488], [24, 864]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1369, 1734, 180, 216, 4320], [1, 3054, 3060, 216, 864], [3529, 1734, 180, 3240, 4320], [1877, 30, 36, 216, 864], [4069, 4326, 180, 216, 4320]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 32], [8, 58], [16, 21]], 'representations': {'PC': {'code': '97435491889092661121535024863479483405649683051206037309238951071927107466260862836278957826479838545', 'gens': [1, 3, 5, 7, 9], 'pres': [10, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 20, 3062, 53022, 82, 963, 243004, 26724, 144, 207365, 1465, 351546, 128536, 47906, 1306, 206, 207367, 45368, 64828, 1868, 268, 14409, 57629, 1669]}, 'Perm': {'d': 20, 'gens': [269654229986294403, 263250542853542400, 134806842923599467]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_6^3.D_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}