Formats: - HTML - YAML - JSON - 2026-07-21T08:00:10.103189
  • gps_subgroup_search • Show schema
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '944784.qw', 'ambient_counter': 439, 'ambient_order': 944784, 'ambient_tex': 'C_3^6.C_3^4:(C_2\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': True, 'core_order': 243, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '944784.qw.3888.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3888.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '3888.ek', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3272242732043843418, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 3888, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:S_3^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C7'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '243.67', 'subgroup_hash': 67, 'subgroup_order': 243, 'subgroup_tex': 'C_3^5', 'supersolvable': True, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '944784.qw', 'aut_centralizer_order': None, 'aut_label': '3888.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1296.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '3888.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 1490, -1, 9283], 'generators': [20666822212130487868504194224764719248884, 17683523987479404620462088192240, 9146650390058004551472915152643, 526261674673969987453451486197943044, 418802671169936714973312003], 'label': '944784.qw.3888.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3888.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '3888.a1.N', 'projective_image': '944784.qw', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3888.A', 'subgroup_fusion': None, 'weyl_group': '1296.3531'}
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '243.67', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 1132560, 'aut_gen_orders': [2, 121], 'aut_gens': [[1, 3, 9, 27, 81], [1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'aut_group': '475566474240.a', 'aut_hash': 5087610779101011723, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 475566474240, 'aut_permdeg': 123, 'aut_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'aut_phi_ratio': 2935595520.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [3, 1, 242, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(5,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 1132560, 'autcent_group': '475566474240.a', 'autcent_hash': 5087610779101011723, 'autcent_nilpotent': False, 'autcent_order': 475566474240, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(5,3)', '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, 242]], 'center_label': '243.67', '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': 67, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 5]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 121]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 5, 11, 13], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '243.67', 'hash': 67, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81], [1, 3, 9, 27, 81]], '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': '243.67', 'linC_count': None, 'linC_degree': 5, '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': 'C3^5', 'ngens': 5, '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': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 243, 'number_divisions': 122, 'number_normal_subgroups': 2664, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 2664, 'number_subgroups': 2664, 'old_label': None, 'order': 243, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 242]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 1132560, 'outer_gen_orders': [2, 121], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 221, 227, 136, 81], [137, 212, 109, 124, 194]], 'outer_group': '475566474240.a', 'outer_hash': 5087610779101011723, 'outer_nilpotent': False, 'outer_order': 475566474240, 'outer_permdeg': 123, 'outer_perms': [2173325930473163168494933070108538650107628394361232555359512641513093137189261028476067853604288948088894908796791799246170274485051140946019001589009351168874945574909129173023449810173348802079455880921, 2320296887375857246951940293789455241616121950690824187255474785887699828555527086044041761683101204617413121467847466058230205801857035117220644345002693782775359667357555797786146238572627101547573150230], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(5,3)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 15, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3, 3, 3], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 121]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4, 5], 'pres': [5, -3, 3, 3, 3, 3]}, 'GLFq': {'d': 2, 'q': 243, 'gens': [1435351114, 2892333419, 2351581309, 576898846, 368382181]}, 'Perm': {'d': 15, 'gens': [174356582400, 79833600, 80640, 240, 4]}}, 'schur_multiplier': [3, 3, 3, 3, 3, 3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 3, 3], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^5', 'transitive_degree': 243, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 12, 6, 12, 18], 'aut_gens': [[32209141036001128179849929440479374092650, 106364121811018077197745115240642770597815, 127648291673555206853734230898516486531652], [297537409080671317722086595475525132516414, 371697822509302109202345624766922146695605, 127943787612273910247032635751412869335864], [159556495876696110771396395195470179201331, 244052238756086767827774115377591133031639, 275960442923219469597885034411639758110881], [42244866632554003791512715380666373302878, 106366295129045824001486249462918882015879, 265922527681987368145264548729727148431316], [169895339654052463070924538239217057095160, 223681438735803168578657617005617127212283, 3794149128440923025055258289027881602], [31913900215265002609556118251374122000145, 371694834518248725752110160769170161921795, 127946520878483977136516178091493643213387]], 'aut_group': None, 'aut_hash': 6829612704809964405, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 17006112, 'aut_permdeg': 1458, 'aut_perms': 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276251881801760078993248977613613401216684], [297835893257694027751564357342144780010611, 371986544567309121241408247049680187381837, 127648291673555206853734230898516486531652]], 'inner_hash': 1329851358491204014, 'inner_nilpotent': False, 'inner_order': 944784, 'inner_split': True, 'inner_tex': 'C_3^6.C_3^4:(C_2\\times D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 2], [4, 16], [8, 8], [12, 4], [16, 2], [18, 12], [24, 36], [36, 49], [48, 20], [72, 36], [144, 30]], 'label': '944784.qw', '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': None, 'name': 'C3^6.C3^4:(C2*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, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 70, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 223, 'number_divisions': 158, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 944784, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 10935], [3, 18224], [4, 52488], [6, 376164], [9, 40824], [12, 183708], [18, 262440]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [295767411432282689301711575833980354956, 0], 'outer_gens': [[170184605406873228357689477974165206082439, 106363850439655190449652701585137610820402, 20672823037373001111784988590760965824695], [32208869673788666659273821872113937119194, 116402036960681094023812759359167651531975, 138276672429835112117115304387448052163891]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [694, 148], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 16], [8, 8], [12, 2], [16, 2], [18, 8], [24, 19], [36, 27], [48, 11], [72, 24], [108, 8], [144, 9], [216, 6], [432, 8]], 'representations': {'PC': {'code': '29463104985362267186465996713022952556092738240927250827734233141549897202549670707996859754539041457184311405658877010590146363913026344784458226966522993285965202508419803456664691261846047804458156657534661558344728255367093180589390338416695898814605831944569319835944880173749214034216279399506318307532156594599827789866632038614377006726062757274539558470078500569347264291080192005391765513629582335', 'gens': [1, 2, 4, 6, 7, 9, 10, 11, 12, 13, 14], 'pres': [14, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 12737760, 10440809, 71, 14509322, 7411854, 23939779, 18864625, 3107247, 157, 52524644, 9448898, 8361952, 102120, 38433029, 379027, 12430689, 218783, 2442949, 47110566, 1514708, 599794, 7243032, 2855978, 745660, 384, 145159, 145173, 24227, 12145, 54440, 27238, 81684, 40874, 34110729, 14968823, 4263877, 14651331, 2097965, 393199, 16473, 36457354, 18228696, 898166, 30627083, 37869913, 12628263, 8259605, 680467, 226881, 294935, 6185, 11911562, 9552856, 2466882, 125060557, 72345979, 29444729, 10995655, 3963777, 1808183, 435805, 26599, 2519]}, 'Perm': {'d': 36, 'gens': [127648291673555206853734230898516486531652, 106364121811018077197745115240642770597815, 32209141036001128179849929440479374092650]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 108, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.C_3^4:(C_2\\times D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'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': 24, 'aut_gen_orders': [6, 4, 8, 4, 8], 'aut_gens': [[1, 2, 8, 48, 144, 432, 1296], [497, 646, 88, 3504, 1440, 3456, 1296], [481, 722, 3484, 304, 2160, 2736, 2592], [2179, 1346, 3224, 3024, 1456, 912, 2592], [3779, 3334, 1496, 3072, 1616, 3504, 2592], [1255, 3730, 232, 960, 304, 96, 1296]], 'aut_group': None, 'aut_hash': 641057888679208724, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15552, 'aut_permdeg': 90, 'aut_perms': [687745654424180225897910730915222618616214195503785820560680125645002984165656216504447309810632755999276932650242387620641451770274257020, 1339197206830937299567864408558339193403082176271238153088509134573405703799158190796376926876536316457114698540538504817326306260781277261, 1169775886111392012462602504979559283938680000869746091329354507656136739113068484934972244277436747545780506891196963412440012417820658330, 1437578482329493225675724344266581534011653277773776211027843316046017893642540045816779289444252138542199912623531193826083909782600791843, 1443998081487990826866780060549434144895175052876218835063155790155277059408631824177080095573183697189132373337918485096184772797548533417], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 2, 1], [2, 27, 2, 1], [2, 54, 2, 1], [2, 81, 1, 1], [3, 2, 1, 1], [3, 12, 4, 1], [3, 24, 2, 2], [3, 48, 2, 1], [4, 162, 1, 1], [4, 486, 1, 1], [6, 36, 2, 1], [6, 108, 4, 3], [6, 162, 1, 1], [6, 216, 2, 2], [12, 324, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:C_3^2.C_4.C_2^4', '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': 24, 'autcentquo_group': None, 'autcentquo_hash': 641057888679208724, 'autcentquo_nilpotent': False, 'autcentquo_order': 15552, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:C_3^2.D_4.C_2^3', 'cc_stats': [[1, 1, 1], [2, 18, 2], [2, 27, 2], [2, 54, 2], [2, 81, 1], [3, 2, 1], [3, 12, 4], [3, 24, 4], [3, 48, 2], [4, 162, 1], [4, 486, 1], [6, 36, 2], [6, 108, 12], [6, 162, 1], [6, 216, 4], [12, 324, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '3888.ek', 'commutator_count': 1, 'commutator_label': '486.249', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 115, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 2], [2, 27, 1, 2], [2, 54, 1, 2], [2, 81, 1, 1], [3, 2, 1, 1], [3, 12, 1, 4], [3, 24, 1, 4], [3, 48, 1, 2], [4, 162, 1, 1], [4, 486, 1, 1], [6, 36, 1, 2], [6, 108, 1, 12], [6, 162, 1, 1], [6, 216, 1, 4], [12, 324, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1209600, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 4], [36, 1, 1]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '1296.3531', 'hash': 3272242732043843418, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 12, 6, 3, 3, 3, 3], 'inner_gens': [[1, 2998, 3592, 528, 2736, 432, 2592], [2997, 2, 1896, 3120, 2608, 480, 1296], [1793, 2482, 8, 1392, 144, 3456, 2592], [961, 2258, 2696, 48, 2736, 432, 1296], [1297, 1474, 8, 1344, 144, 432, 1296], [1, 98, 2168, 48, 144, 432, 1296], [2593, 2, 2600, 48, 144, 432, 1296]], 'inner_hash': 3272242732043843418, 'inner_nilpotent': False, 'inner_order': 3888, 'inner_split': False, 'inner_tex': 'C_3^3:S_3^2:C_2^2', 'inner_used': [1, 2, 3], 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 8], [2, 2], [4, 16], [8, 8], [16, 2], [18, 4], [36, 1]], 'label': '3888.ek', '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': None, 'name': 'C3^3:S3^2:C2^2', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 41, 'number_divisions': 41, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 281, 'number_subgroup_classes': 702, 'number_subgroups': 25451, 'old_label': None, 'order': 3888, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 279], [3, 242], [4, 648], [6, 2394], [12, 324]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [982, 0], 'outer_gens': [[2307, 1810, 248, 1728, 1456, 2208, 2592], [1, 2, 2460, 1472, 3456, 2880, 1296]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 16], [8, 8], [16, 2], [18, 4], [36, 1]], 'representations': {'PC': {'code': '9974425099924765025408242293674641170267230417236872111368710084358760681946798562664221108795633689304095', 'gens': [1, 2, 4, 6, 7, 8, 9], 'pres': [9, -2, -2, -2, -2, -3, 3, 3, 3, -3, 53965, 46, 13934, 8768, 129315, 34140, 8589, 102, 1444, 6493, 14962, 28517, 84254, 1319, 9428, 4577, 172374, 82167, 45384, 3642, 17296, 62233, 31138, 13651, 209960, 26279]}, 'Perm': {'d': 27, 'gens': [7549724245233350948573836948, 10888626160339536217045552585, 403587579360117356426414155]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3:S_3^2:C_2^2', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}