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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '729.422', 'ambient_counter': 422, 'ambient_order': 729, 'ambient_tex': 'C_3^2.C_3^4', 'central': True, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 3, 'counter': 28, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '729.422.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '243.61', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 61, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 243, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3\\times C_9', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '729.422', 'aut_centralizer_order': 8503056, 'aut_label': '243.a1', 'aut_quo_index': 234, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 8503056, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1'], 'contains': ['729.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4262, 4830, 4406, 4598], 'generators': [9], 'label': '729.422.243.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '243.a1', 'normal_contained_in': ['81.a1', '81.b1', '81.c1'], 'normal_contains': ['729.a1'], 'normalizer': '1.a1', 'old_label': '243.a1', 'projective_image': '243.61', 'quotient_action_image': '1.1', 'quotient_action_kernel': '243.61', 'quotient_action_kernel_order': 243, 'quotient_fusion': None, 'short_label': '243.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': '243.61', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 72, 'aut_gen_orders': [18, 8, 24], 'aut_gens': [[1, 3, 9, 27, 243], [164, 414, 9, 631, 259], [91, 673, 18, 314, 489], [92, 431, 18, 613, 85]], 'aut_group': None, 'aut_hash': 5481057200711108027, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17006112, 'aut_permdeg': 486, 'aut_perms': [16929790469883398238076023417176546418375484632756412961226568605226402514212890401713599077939459533953273872271516356057358844701140877803978175760268513893776138841845200124168476980938638769977892446315868604559124867396792602889322213982938795619136111558422853556059575424654411774944872307641055153006430252361100837937393234990749159492376264000533822478552630358784110045150941939401536734123231778165268763321236609994507283261524418405080862420029297791076804781171242470150403852954302210980737147578667597414937896398668702234560389478129104609024123920611795760220578806019394026367468160805950454985392057869078280268904325141401180682382816711663166872281150182033012263969792691697353859318261225219817250797890070487444964122151816831858377788685122546887060441252541435506422468634027317316988938368839006340329535578815072822546872115623507000773110469628040934505535132364146901414626429928748551905560209673545373914656435306176515631128805770793416380928119216588694531885371379763761181106804445351710653418853739611923181232705994244539453575905978283612084382616369831843, 12157868966895148735125382464602312256433522038214508713371031796254450373407622235042774951772942473314578449468495692099737016256769245486690138644995258895517550618005283863361577164956042075988567118238438272052276289275556391447902763870852701025162797537936644198747591792912990743701349401767846744011309957551469669296049888139439769491168612336334445308262402489381682749420784434253879293213187694659259503352772877029104697156573933833984179995258793871658887392119416131114433087769280427849538376344456709226284586225569081798401630767864389966149728224146846474394649711317585580508383214532119466876218643554765391602010591744359414789714337236845962355453544327078623423315643222479159901905397560528958466877839520819221059820513871664423084332196540576316093704965667963738681971193850102073527556632974284816336737869967000703450290714136974527571458355611173361235628629171319413012839732625078681959110002996188752335210745340606076709738720968056114223374555514515710093298432147308520794895576581345032601873699945510460102643857307321688572654003204750960375568064550255916, 7307985309030603896858784531685678979971077320024509137800949902569682715104614237649724656867830762431053559415827729782917219709353389020200007693431440962683752193168614800267899677522871114238205971940763987344414565423056670359558919541148000484794476547548816010112538475441884777059581376117910467262746108058262716824899708713349777004567463824715893579373214419415915568855524032920018280259602930248699307223503276840020401554418092206225048286535341010377079336393250653556537910568225069649996045791765686327978621128026169376299036874292759249396568247932349289216250453654358220046758988208144285716408396042661063299299315714553362364951139678497533862280216447893356899213185859438096115062919509929912589077270882526447143226439923856556795208432705405080920154553204378072308230519878975512700675974532862766232032080704628890831577983920768006212991173744573856266703332302271432286919568436245043593602698317893738004576038100599216477188378773869405062124140934509388976238372400557300475416578529812936299560505570147505262304760503342375416810768281001431179558879640076994], 'aut_phi_ratio': 34992.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 2], [3, 1, 4, 1], [3, 3, 6, 1], [3, 3, 72, 1], [9, 3, 162, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^7.C_3:S_3.C_6^2.D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '6561.1396077', 'autcent_hash': 7374565384238773860, 'autcent_nilpotent': True, 'autcent_order': 6561, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '2592.ca', 'autcentquo_hash': 3538079198398614329, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SU(3,2):D_6', 'cc_stats': [[1, 1, 1], [3, 1, 8], [3, 3, 78], [9, 3, 162]], 'center_label': '9.2', 'center_order': 9, 'central_product': True, 'central_quotient': '81.15', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 422, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4], [3, 3, 2, 39], [9, 3, 6, 27]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 9360, 'exponent': 9, 'exponents_of_order': [6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '81.15', 'hash': 422, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [3, 3, 1, 3, 3], 'inner_gens': [[1, 3, 9, 45, 243], [1, 3, 9, 27, 261], [1, 3, 9, 27, 243], [10, 3, 9, 27, 243], [1, 12, 9, 27, 243]], 'inner_hash': 15, 'inner_nilpotent': True, 'inner_order': 81, 'inner_split': True, 'inner_tex': 'C_3^4', 'inner_used': [1, 2, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 243], [9, 6]], 'label': '729.422', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2.C3^4', 'ngens': 4, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 249, 'number_divisions': 71, 'number_normal_subgroups': 400, 'number_subgroup_autclasses': 33, 'number_subgroup_classes': 589, 'number_subgroups': 1471, 'old_label': None, 'order': 729, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 242], [9, 486]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 72, 'outer_gen_orders': [12, 6, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[164, 349, 9, 542, 248], [2, 512, 9, 242, 84], [2, 5, 18, 375, 669]], 'outer_group': None, 'outer_hash': 4381912502052973173, 'outer_nilpotent': False, 'outer_order': 209952, 'outer_permdeg': 83, 'outer_perms': [16167996779730258555473952285465453107341083530798466933682537250831538373857759633586426310979788866417116096965234478896689, 2709874070470138484694338712535165212115822739919895970324000209936945475300399589989289522239650231252367585711770482244711, 30311505535244929090652701516365288080396443975791698812213011146301428861595820438119178793219475212602374810543728359054447], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^4.C_3:S_3.A_4.D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 36, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 9], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 40], [6, 27], [18, 3]], 'representations': {'PC': {'code': 30133120409736, 'gens': [1, 2, 3, 4, 6], 'pres': [6, 3, 3, 3, 3, 3, 3, 1083, 93, 3143]}, 'Perm': {'d': 36, 'gens': [11584910813152087158942842652412741184823, 22197005032721123397287238566827864706356, 32850391621342916487785293966423530395956, 33154308002685149286115670155364150402356, 43792958104144393837218401267281941004800, 98356]}}, 'schur_multiplier': [3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 9], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2.C_3^4', 'transitive_degree': 81, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '243.61', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 936, 'aut_gen_orders': [3, 3, 13, 3, 6, 3, 3, 3, 3, 2], 'aut_gens': [[1, 3, 9, 27], [1, 3, 9, 203], [82, 165, 90, 189], [16, 88, 82, 45], [1, 3, 9, 200], [163, 3, 9, 71], [163, 3, 171, 27], [1, 3, 9, 112], [1, 3, 9, 189], [163, 84, 90, 189], [86, 3, 94, 27]], 'aut_group': '49128768.a', 'aut_hash': 6829789377147908262, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49128768, 'aut_permdeg': 83, 'aut_perms': [1908345068815238937354193556108802943040289821207358369935475573264099584066390679277349104248117090040053137229561290129040, 10241132782696443443314086248258889552096493367769102167529388866584357555382939086758781906325662260631567071779659212225560, 37035478869123520278377129942438887003188538286868829049428777569364336622967055678522614782155528800714990680513870212518360, 1908273499386474982262768441594129856578615409553425176453440429965773946845216973078966775339189437147906883606088029592526, 13204444168824595010106793923441791852908411783546426115544095271979631773747166353248380937167628242599290599697832280947729, 13817847732840502609743152163801392573762640848045621179000516637462697127650716857308509022251237468762506907771731735866264, 64858960289985940498755964324416063228982061190913650903130660063114833994513293279877632171543220707079198020035819792334, 1966316342552749727902267370651089539934028368898663442298455346878080420882197656983932990174027785751270680500101743172200, 7409010302580350760616116636121941329104605923302002027837948965100526332858784624136965851626547461345101456949318786112648, 268866802959050458010886843533925454282204483500860054481959047180565072333878513949201756680960901618043809561139011657808], 'aut_phi_ratio': 303264.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1], [3, 1, 78, 1], [9, 1, 162, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.(C_2\\times C_3^3:\\GL(3,3))', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 936, 'autcent_group': '49128768.a', 'autcent_hash': 6829789377147908262, 'autcent_nilpotent': False, 'autcent_order': 49128768, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_3^4.(C_2\\times C_3^3:\\GL(3,3))', '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, 80], [9, 1, 162]], 'center_label': '243.61', 'center_order': 243, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 61, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 3], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 40], [9, 1, 6, 27]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 40, 'exponent': 9, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '81.15', 'hash': 61, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 3, 9, 27], [1, 3, 9, 27], [1, 3, 9, 27], [1, 3, 9, 27]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 243]], 'label': '243.61', 'linC_count': None, 'linC_degree': 4, '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': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^3*C9', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 243, 'number_divisions': 68, 'number_normal_subgroups': 396, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 396, 'number_subgroups': 396, 'old_label': None, 'order': 243, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 80], [9, 162]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 936, 'outer_gen_orders': [3, 3, 13, 3, 6, 3, 3, 3, 3, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 3, 9, 203], [82, 165, 90, 189], [16, 88, 82, 45], [1, 3, 9, 200], [163, 3, 9, 71], [163, 3, 171, 27], [1, 3, 9, 112], [1, 3, 9, 189], [163, 84, 90, 189], [86, 3, 94, 27]], 'outer_group': '49128768.a', 'outer_hash': 6829789377147908262, 'outer_nilpotent': False, 'outer_order': 49128768, 'outer_permdeg': 83, 'outer_perms': [1908345068815238937354193556108802943040289821207358369935475573264099584066390679277349104248117090040053137229561290129040, 10241132782696443443314086248258889552096493367769102167529388866584357555382939086758781906325662260631567071779659212225560, 37035478869123520278377129942438887003188538286868829049428777569364336622967055678522614782155528800714990680513870212518360, 1908273499386474982262768441594129856578615409553425176453440429965773946845216973078966775339189437147906883606088029592526, 13204444168824595010106793923441791852908411783546426115544095271979631773747166353248380937167628242599290599697832280947729, 13817847732840502609743152163801392573762640848045621179000516637462697127650716857308509022251237468762506907771731735866264, 64858960289985940498755964324416063228982061190913650903130660063114833994513293279877632171543220707079198020035819792334, 1966316342552749727902267370651089539934028368898663442298455346878080420882197656983932990174027785751270680500101743172200, 7409010302580350760616116636121941329104605923302002027837948965100526332858784624136965851626547461345101456949318786112648, 268866802959050458010886843533925454282204483500860054481959047180565072333878513949201756680960901618043809561139011657808], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_3^4.(C_2\\times C_3^3:\\GL(3,3))', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 9], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 40], [6, 27]], 'representations': {'PC': {'code': 16392, 'gens': [1, 2, 3, 4], 'pres': [5, -3, 3, 3, 3, -3, 78]}, 'GLZN': {'d': 2, 'p': 54, 'gens': [157483, 158437, 211285, 7272037, 2991835]}, 'GLZq': {'d': 2, 'q': 27, 'gens': [196840, 19687, 203896, 19693, 19927]}, 'Perm': {'d': 18, 'gens': [357120, 711374856192000, 174356582400, 79833600, 80884]}}, 'schur_multiplier': [3, 3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 9], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3\\times C_9', 'transitive_degree': 243, 'wreath_data': None, 'wreath_product': False}
