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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '4116.ba', 'ambient_counter': 27, 'ambient_order': 4116, 'ambient_tex': 'C_{21}.D_7^2', 'central': True, 'central_factor': False, 'centralizer_order': 4116, 'characteristic': True, 'core_order': 3, 'counter': 90, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '4116.ba.1372.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1372.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1372.16', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 16, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1372, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7^2:D_{14}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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gps_subgroup_data • Show schema
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{'ambient': '4116.ba', 'aut_centralizer_order': 24696, 'aut_label': '1372.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 24696, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['196.a1.a1', '196.b1.a1', '196.b1.b1', '196.c1.a1', '196.c1.b1', '196.c1.c1', '686.a1.a1', '686.a1.b1', '686.b1.a1'], 'contains': ['4116.a1.a1'], 'core': '1372.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4055, 7688, 3982, 6518, 5658, 3832, 4572, 5634], 'generators': [28], 'label': '4116.ba.1372.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1372.a1.a1', 'normal_contained_in': ['196.a1.a1'], 'normal_contains': ['4116.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1372.a1.a1', 'projective_image': '1372.16', 'quotient_action_image': '1.1', 'quotient_action_kernel': '1372.16', 'quotient_action_kernel_order': 1372, 'quotient_fusion': None, 'short_label': '1372.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [2]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 3]], 'label': '3.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 84, 'aut_gen_orders': [6, 2, 7, 42, 14, 14, 6, 7, 14], 'aut_gens': [[1, 2, 84, 588], [85, 62, 252, 1176], [1, 58, 84, 588], [2245, 2186, 1848, 588], [169, 1558, 336, 588], [2665, 1511, 12, 3528], [373, 2182, 3612, 3528], [337, 46, 168, 2352], [1, 3530, 84, 588], [169, 814, 84, 588]], 'aut_group': '49392.bb', 'aut_hash': 2546147806097575046, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49392, 'aut_permdeg': 100, 'aut_perms': [39886716433554786861147705782310725141475047354673966892028177187731843174987122473938402855981931768154376797833269726339902141573895020208313972673768067990, 4968829558669574315901366089774607151601309468731257825252349565120650249417866453441784108315939393476283967989447976890625163264000000000000000000000, 79372305083324720254885468194430400227144281942377529629751945413504723940014534052622479723486203270579673375424349747883789459085272605303635184272208354613, 92810245609406383804541843152439771765670218351316333545882750215076314437138865096201387556272502018101432314366866275990966969751552116102059349436862003048, 65116831137900535716334245244604348712325533481243246541899993869225462917513699937880995651690670839536840314634101780766259948259879263903206697917318023374, 17541624061438210713937913701470845456726373877349001575035524504127914759059580579588587590552331921073069563877840211209077501628710774429224414115764378384, 84629917523447951167792536336580414106175815273956419543440049509533462460693551140163770172630860431021699828222202885963907030800324933617570156651444233345, 44310909635164709489252015010530322820270091040017078534072989859918023242554817548046259891161801426904580952431257550985867626331566550566934951621100694880, 74792379734320000475441707095824666889200384957467316058389597393083866337981042412306141326622249240868331416995047726606183103676981956804250099704139912338], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 49, 1, 1], [2, 49, 2, 1], [3, 1, 2, 1], [6, 49, 2, 1], [6, 49, 4, 1], [7, 2, 3, 1], [7, 14, 6, 1], [7, 28, 9, 1], [14, 98, 3, 1], [14, 98, 6, 1], [21, 2, 6, 1], [21, 14, 12, 1], [21, 28, 18, 1], [42, 98, 6, 1], [42, 98, 12, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_7:(C_6^2:C_2^2)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '24696.h', 'autcentquo_hash': 6460325027391172650, 'autcentquo_nilpotent': False, 'autcentquo_order': 24696, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_7:C_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 49, 3], [3, 1, 2], [6, 49, 6], [7, 2, 3], [7, 14, 6], [7, 28, 9], [14, 98, 9], [21, 2, 6], [21, 14, 12], [21, 28, 18], [42, 98, 18]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '1372.16', 'commutator_count': 1, 'commutator_label': '343.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '7.1', '7.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 27, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['1372.16', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 49, 1, 3], [3, 1, 2, 1], [6, 49, 2, 3], [7, 2, 3, 1], [7, 14, 3, 2], [7, 28, 3, 3], [14, 98, 3, 3], [21, 2, 6, 1], [21, 14, 6, 2], [21, 28, 6, 3], [42, 98, 6, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 84, 'exponent': 42, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[14, 0, 12]], 'familial': False, 'frattini_label': '7.1', 'frattini_quotient': '588.49', 'hash': 2041031394734020119, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 14, 7, 7], 'inner_gens': [[1, 1286, 504, 588], [4093, 2, 2856, 3528], [169, 1934, 84, 588], [1, 1178, 84, 588]], 'inner_hash': 16, 'inner_nilpotent': False, 'inner_order': 1372, 'inner_split': True, 'inner_tex': 'C_7^2:D_{14}', 'inner_used': [1, 2], 'irrC_degree': 14, 'irrQ_degree': 84, 'irrQ_dim': 84, 'irrR_degree': 28, 'irrep_stats': [[1, 12], [2, 36], [4, 27], [14, 18]], 'label': '4116.ba', 'linC_count': 12, 'linC_degree': 14, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 44, 'linQ_degree_count': 8, 'linQ_dim': 44, 'linQ_dim_count': 8, 'linR_count': 24, 'linR_degree': 16, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C21.D7^2', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 93, 'number_divisions': 26, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 94, 'number_subgroups': 2218, 'old_label': None, 'order': 4116, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 147], [3, 2], [6, 294], [7, 342], [14, 882], [21, 684], [42, 1764]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 6], 'outer_gen_pows': [253, 0], 'outer_gens': [[2041, 435, 48, 2352], [169, 22, 420, 3528]], 'outer_group': '36.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 36, 'outer_permdeg': 8, 'outer_perms': [750, 10081], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times S_3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 52, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [6, 4], [12, 7], [24, 3], [42, 2], [84, 2]], 'representations': {'PC': {'code': '66374914638807909022467554599475681325088559', 'gens': [1, 2, 5, 6], 'pres': [6, -2, -2, -3, -7, -7, -7, 15433, 31, 32690, 68, 29955, 15124, 42850, 27106, 6112, 63515]}, 'GLFp': {'d': 4, 'p': 7, 'gens': [31392350697539, 611588865287, 9495688004000, 31584908075045, 7394473631462, 28186167033742]}, 'Perm': {'d': 52, 'gens': [122392157881291898313947223698298773040565732814893270413422844720, 1706346053456648766825121617584478599019749040109854405960246182760, 3289727285998847184752714187827877242951891636603417354089227828384, 4871879539460433276768188427234411992507894929765460423018638091667, 3, 6454033016996107993701221292664290746258824536151317386943091056960]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{21}.D_7^2', 'transitive_degree': 147, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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': 4, 'aut_exponent': 84, 'aut_gen_orders': [6, 21, 14, 14, 3, 7, 7, 7], 'aut_gens': [[18902558, 34720862, 21401649, 473244, 4590980], [12798007, 34720862, 39726573, 39650299, 34709006], [20488867, 16014990, 38915967, 3767423, 2943915], [13608270, 16915566, 31161565, 22135981, 31946124], [38887498, 25779729, 21344756, 31061818, 24120759], [10724142, 34720862, 20562789, 24944316, 27414938], [18902558, 2132214, 31122789, 31061818, 9061382], [13608270, 7426523, 577821, 473244, 4590980], [18902558, 5426393, 25872394, 473244, 4590980]], 'aut_group': '24696.h', 'aut_hash': 6460325027391172650, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24696, 'aut_permdeg': 98, 'aut_perms': [8072462525763657423887702027775695715895911117012154301568510614420364347434964987387663919598489908873577320738018286916069031332376005551658206645729583, 7973648044450685043766907102563357622158175401158398038833872247406603965313357925888178547807405946748680004035352917984094022637058134928651307645734741, 1428268859122317160947749691118549436577039933412273933878834232153973079329249071523242759989445452823232247092715339107999061863736166820493591591302153, 1860361354981565449877489976347257140588715883857436270573222205710148967594623653328624922147802799243547750636093363357310266993960960854884468429478447, 7676531147824910761918749237926645851807486595443180145442589715217405723186553033782241772019173118153767963289078074522216544364221428802813419935666361, 4575999928770365575849865302600576453160207894551106387879418952403947478088452135214139955763337048549178957105409835376759985509964387298863877118247217, 13068746034600252549823024523116571394016353712986496744692036808617792947706406641231233336445456949362420625037565073409918239101557244158316633431889, 5649811286836169354106838724954916597346818334812051447262000409334644962152457333418638353733818312182114119765610158294913505064463473153936500717640202], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 49, 1, 1], [2, 49, 2, 1], [7, 2, 3, 1], [7, 14, 6, 1], [7, 28, 9, 1], [14, 98, 3, 1], [14, 98, 6, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_7:C_6\\wr C_2', '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': 84, 'autcentquo_group': '24696.h', 'autcentquo_hash': 6460325027391172650, 'autcentquo_nilpotent': False, 'autcentquo_order': 24696, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_7:C_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 49, 3], [7, 2, 3], [7, 14, 6], [7, 28, 9], [14, 98, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1372.16', 'commutator_count': 1, 'commutator_label': '343.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '7.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 49, 1, 3], [7, 2, 3, 1], [7, 14, 3, 2], [7, 28, 3, 3], [14, 98, 3, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 21, 'exponent': 14, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[14, 1, 6]], 'familial': False, 'frattini_label': '7.1', 'frattini_quotient': '196.9', 'hash': 16, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [7, 2, 14, 7, 7], 'inner_gens': [[18902558, 14367925, 21296951, 21297079, 14355719], [4667088, 34720862, 2224935, 11885048, 13532162], [38887498, 13544368, 21401649, 21297079, 29414704], [3843531, 23309058, 577821, 473244, 4590980], [8314276, 25779729, 31166388, 473244, 4590980]], 'inner_hash': 16, 'inner_nilpotent': False, 'inner_order': 1372, 'inner_split': True, 'inner_tex': 'C_7^2:D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 14, 'irrQ_degree': 42, 'irrQ_dim': 42, 'irrR_degree': 14, 'irrep_stats': [[1, 4], [2, 12], [4, 9], [14, 6]], 'label': '1372.16', 'linC_count': 6, 'linC_degree': 14, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 2, 'linQ_dim': 42, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C7^2:D14', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 31, 'number_divisions': 13, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 47, 'number_subgroups': 1109, 'old_label': None, 'order': 1372, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 147], [7, 342], [14, 882]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [5767203, 9896923], 'outer_gens': [[16018136, 36355943, 16910743, 1344312, 26695785], [33637138, 34720862, 39697976, 4590980, 5414537]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [652, 373], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 49, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [6, 4], [12, 3], [42, 2]], 'representations': {'PC': {'code': 1702653240871935217080098711, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -7, -7, -7, 261, 26, 362, 13448, 2113, 29404, 14709]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [18902558, 34720862, 21401649, 473244, 4590980]}, 'Perm': {'d': 49, 'gens': [1315490939820261104781241293384898516680185382247095762872399, 1315490941020389297941406270674321266170870307462847850030879, 532482879537830020389456268526937482059870595614507008000000000, 200715159680502423232357683145854231081788001750633, 74483493555417151184854488523683573561511365457240384149969120]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7^2:D_{14}', 'transitive_degree': 49, 'wreath_data': None, 'wreath_product': False}
