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': 4, 'aut_exponent': 48, 'aut_gen_orders': [4, 4, 8], 'aut_gens': [[3514922837851602, 2581710453170261, 2135719723867333], [4200050242550957, 2179047813585380, 129921523661554], [4516526639669097, 2954056040260558, 2135719723798883], [6332792013425709, 1073775495640382, 2513698892136133]], 'aut_group': '41472.m', 'aut_hash': 7917341340725978817, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 204, 'aut_perms': [1309345485919600749745934577640419337302230733088758364920560568185301816444415756636074728040140178233024704690984694709862097595294845047978309409911408501512987974428598771665713645519250301391504222859685660769941573225096562774513043862322495811203297779939781931589486409854710028129740049070633453128132184482379391463902054065372251089684139270315952799577249615940864675838487, 2594606410385872344599837413985881538830504448751372070418139790425258970876659336254484712044212191744353759717762566046587065395239653399888212617774726309440990757678281773420115186558808454413667598590162740679766065633083736402834173298455471960961555635753495248571306121897555846729329965983667496301954923938954752109255553652165252643249479520279574283766879335840008859114, 1194328403875403437524957653684777636902823975383181744178389705632957166665117555029927556289489547622267908098473537423880585006004329630912057855203433722666346627750545155898096857477041711591529215985159004915113844333031344192605063754373054866973389228924927652503254496566452286516980830520382233405637361200079713509790150485630812880310866196271095149338244099960157621946915], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 24, 1, 1], [2, 81, 1, 1], [2, 144, 1, 2], [2, 216, 1, 1], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 1], [4, 72, 1, 1], [4, 324, 1, 2], [4, 432, 1, 1], [4, 648, 1, 1], [4, 864, 1, 1], [4, 1296, 1, 3], [4, 1728, 1, 1], [6, 48, 1, 1], [6, 144, 1, 1], [6, 192, 1, 1], [6, 384, 1, 1], [6, 432, 1, 1], [6, 576, 1, 2], [6, 1152, 1, 1], [8, 36, 1, 2], [8, 324, 1, 4], [8, 432, 1, 2], [8, 648, 1, 3], [8, 1296, 1, 2], [8, 2592, 1, 1], [8, 5184, 1, 1], [12, 288, 1, 1], [12, 576, 1, 1], [12, 864, 1, 1], [12, 1728, 1, 1], [12, 3456, 1, 1], [16, 2592, 1, 2], [24, 288, 1, 2], [24, 864, 1, 2]], 'aut_supersolvable': False, 'aut_tex': '\\SOPlus(4,2)^2.D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', '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, 18, 1], [2, 24, 1], [2, 81, 1], [2, 144, 2], [2, 216, 1], [3, 16, 1], [3, 64, 1], [4, 36, 1], [4, 72, 1], [4, 324, 2], [4, 432, 1], [4, 648, 1], [4, 864, 1], [4, 1296, 3], [4, 1728, 1], [6, 48, 1], [6, 144, 1], [6, 192, 1], [6, 384, 1], [6, 432, 1], [6, 576, 2], [6, 1152, 1], [8, 36, 2], [8, 324, 4], [8, 432, 2], [8, 648, 3], [8, 1296, 2], [8, 2592, 1], [8, 5184, 1], [12, 288, 1], [12, 576, 1], [12, 864, 1], [12, 1728, 1], [12, 3456, 1], [16, 2592, 2], [24, 288, 2], [24, 864, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '41472.m', 'commutator_count': 1, 'commutator_label': '5184.pf', 'complements_known': True, 'complete': True, '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': 13, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 24, 1, 1], [2, 81, 1, 1], [2, 144, 1, 2], [2, 216, 1, 1], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 1], [4, 72, 1, 1], [4, 324, 1, 2], [4, 432, 1, 1], [4, 648, 1, 1], [4, 864, 1, 1], [4, 1296, 1, 3], [4, 1728, 1, 1], [6, 48, 1, 1], [6, 144, 1, 1], [6, 192, 1, 1], [6, 384, 1, 1], [6, 432, 1, 1], [6, 576, 1, 2], [6, 1152, 1, 1], [8, 36, 2, 1], [8, 324, 2, 2], [8, 432, 2, 1], [8, 648, 1, 1], [8, 648, 2, 1], [8, 1296, 2, 1], [8, 2592, 1, 1], [8, 5184, 1, 1], [12, 288, 1, 1], [12, 576, 1, 1], [12, 864, 1, 1], [12, 1728, 1, 1], [12, 3456, 1, 1], [16, 2592, 2, 1], [24, 288, 2, 1], [24, 864, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 564264960, 'exponent': 48, 'exponents_of_order': [9, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 8], [32, 0, 4], [32, 1, 2], [64, 1, 4], [128, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '41472.m', 'hash': 7917341340725978817, 'hyperelementary': 1, 'id': 152282, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [4, 4, 8], 'inner_gens': [[3514922837851602, 1199231319751772, 2887451422921836], [4894530313270472, 2581710453170261, 796566727974047], [4849814994939732, 2954056040229783, 2135719723867333]], 'inner_hash': 7917341340725978817, 'inner_nilpotent': False, 'inner_order': 41472, 'inner_split': True, 'inner_tex': '\\SOPlus(4,2)^2.D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 6], [4, 18], [8, 3], [16, 8], [32, 6], [64, 4], [128, 1]], 'label': '41472.m', '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': 'SO+(4,2)^2.D4', 'ngens': 3, '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': 54, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 54, 'number_divisions': 45, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 1431, 'number_subgroup_classes': 1431, 'number_subgroups': 227218, 'old_label': None, 'order': 41472, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 627], [3, 80], [4, 8316], [6, 3504], [8, 14544], [12, 6912], [16, 5184], [24, 2304]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 6], [8, 7], [16, 9], [32, 2], [64, 6], [128, 1]], 'representations': {'PC': {'code': '608206385848814155080286995649919776217912322121576815200009590529477716958513242942021562003967954107832242606694721154374797199536696894112922620338057991926128524858919128409892167136808445715415033012375710812472058515584327639713597979999482160936061333504564387465913675203251471586505989284631618338479947866127', 'gens': [1, 2, 4, 7, 11, 12, 13], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 226720, 627277, 66, 775790, 926435, 276864, 180053, 146, 19764, 1008297, 458410, 186, 2678213, 1558770, 280207, 2614982, 1112039, 27696, 262853, 119814, 33741, 266, 1504263, 674772, 23329, 401070, 233851, 17128, 306, 3384584, 1873893, 295823, 144204, 15985, 346, 1930249, 199702, 457648, 233021, 4234, 1098250, 73239, 164785, 96158, 13803, 10384, 12113, 1830, 958475, 1078296, 479269, 149810, 119871, 45004, 26297, 15078, 5731, 2422796, 1038361, 1189798, 21683, 156896, 146093]}, 'Perm': {'d': 18, 'gens': [2581710453170261, 2135719723867333, 3514922837851602]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SOPlus(4,2)^2.D_4', 'transitive_degree': 18, 'wreath_data': ['288.bd1', '20736.e1', '41472.a1', '2T1'], 'wreath_product': True}