Query:
/api/gps_groups/?_offset=0
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 64, 'aut_gen_orders': [16, 32, 16, 16], 'aut_gens': [[1, 2], [209, 206], [85, 118], [141, 14], [161, 174]], 'aut_group': None, 'aut_hash': 4100375159357264999, 'aut_nilpotency_class': 6, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 96, 'aut_perms': [499276977300989318134376425606914073348147601778062132505213339374284318383858892534799911749003638681649715077586808547055597177164139027797246186156, 116090741100590695493917183397339221828527565192637139377853734228782445875112383957861849194760159245654924500073352309005479930617994731521213167518, 634055201665240426462811499008375132901780570971399876790203002496095245796288461528618260917726939696477854425928888862422546372839964901788185676915, 383034694351252163740979215098621689687558046207029260156673310847478573584049983781436368078747910900031929005123910680486599295849208382061017601095], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 64, 1, 1], [4, 2, 1, 1], [4, 64, 1, 1], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1], [64, 2, 16, 1], [128, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{32}.C_{16}.C_2^3', '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': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 32, 'autcentquo_group': '1024.dng', 'autcentquo_hash': 7288729358377021530, 'autcentquo_nilpotent': True, 'autcentquo_order': 1024, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{32}:C_{16}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 64, 1], [4, 2, 1], [4, 64, 1], [8, 2, 2], [16, 2, 4], [32, 2, 8], [64, 2, 16], [128, 2, 32]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.161', 'commutator_count': 1, 'commutator_label': '64.1', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 540, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 64, 1, 1], [4, 2, 1, 1], [4, 64, 1, 1], [8, 2, 2, 1], [16, 2, 4, 1], [32, 2, 8, 1], [64, 2, 16, 1], [128, 2, 32, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 128, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[2, 0, 32]], 'familial': True, 'frattini_label': '64.1', 'frattini_quotient': '4.2', 'hash': 540, 'hyperelementary': 2, 'id': 142233, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 64, 'inner_gen_orders': [2, 64], 'inner_gens': [[1, 126], [133, 2]], 'inner_hash': 161, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': True, 'inner_tex': 'D_{64}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 64, 'irrQ_dim': 64, 'irrR_degree': 4, 'irrep_stats': [[1, 4], [2, 63]], 'label': '256.540', 'linC_count': 32, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 64, 'linQ_degree_count': 1, 'linQ_dim': 64, 'linQ_dim_count': 1, 'linR_count': 16, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'SD256', 'ngens': 2, 'nilpotency_class': 7, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 67, 'number_divisions': 10, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 22, 'number_subgroup_classes': 22, 'number_subgroups': 199, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 65], [4, 66], [8, 4], [16, 8], [32, 16], [64, 32], [128, 64]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 32, 'outer_gen_orders': [32], 'outer_gen_pows': [0], 'outer_gens': [[1, 10]], 'outer_group': '32.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 32, 'outer_perms': [9594892858980471636264762118745970], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{32}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 128, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [4, 1], [8, 1], [16, 1], [32, 1], [64, 1]], 'representations': {'PC': {'code': 10759584490553416770205641161127763966, 'gens': [1, 2], 'pres': [8, -2, 2, -2, -2, -2, -2, -2, -2, 2017, 41, 6050, 66, 7939, 91, 9604, 116, 10757, 141, 10758, 166]}, 'GLFp': {'d': 2, 'p': 191, 'gens': [1323895491, 502496242]}, 'Perm': {'d': 128, 'gens': [197353426665795192019649144516451265466792727861091881971055211732566956565285840203884001986637074477964958080976691176062935986921248199491523672324081722723401700302711504579941201640825304922036633600000000000000, 188292207798735554531953930666596726211301433291034272114403350171225247525509526722631912453452346278233618582584999734923499839234699307292251224198615500093027247066174319710946379651244083932748770986135737, 145755433775604547297201131150183888861228664815792145484454176965288660467637941385681636977888060401712770242460844205934357642466456129421788144108175427929820522572233815955328185120005720780788385849134055424000, 72877716887802273536159897284555617609071924478605690744980147364027840012664309688408644856697600006828549983620326187881446784435043842386372995733782902289847035111670603886997808542606740929776378575940115641600, 36438858431554066421216745586032441196784360210498157849483967354900691632997244042006716310813673482700358640569461128310786859693629190912455543282135285812616711420274484020851676014096895691099138440830423638456, 18219237868474170926919728959838976579823559277307722706333181915654886656732773753595716234540277498860865646185797683654540335638029203914887565397539138366037951542326723809258492849529393395788412549619313310038, 9085423556866993725410614122025196148146247926140575858058005571111390721149416409151317638340378307900225067121464510745247921800859275922379072823586719781605488843187477526026631467348259157310472617830699100937, 3012848298322462290047636316206070830590600846754565189610607901552871371081335602108479564103390981918887386637702854611498331176338904053322043727351325298295337656606958232198284389401146867497898583379392681647]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\SD_{256}', 'transitive_degree': 128, 'wreath_data': None, 'wreath_product': False}