Formats: - HTML - YAML - JSON - 2026-07-18T18:30:27.952892
  • gps_subgroup_search • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1259712.ji', 'ambient_counter': 243, 'ambient_order': 1259712, 'ambient_tex': 'D_9^2\\wr C_2.C_6', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 81, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1259712.ji.108._.D', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.D', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11664.kk', 'subgroup_hash': None, 'subgroup_order': 11664, 'subgroup_tex': 'S_3^2:D_9^2', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '1259712.ji', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [523587, 425088, 1028736, 202752, 466560, 910308, 987792, 419904, 576, 944880], 'label': '1259712.ji.108._.D', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '108.D', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108._.D', 'subgroup_fusion': None, 'weyl_group': None}
  • 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': 3, 'aut_exponent': 36, 'aut_gen_orders': [18, 18, 36, 12, 4], 'aut_gens': [[1, 2, 36, 648, 3888], [6509, 6914, 6876, 3564, 1296], [5537, 5366, 2844, 8424, 7776], [357, 418, 6516, 11340, 1296], [558, 497, 6832, 11340, 1296], [10705, 10870, 10980, 11340, 1296]], 'aut_group': None, 'aut_hash': 417177536885461405, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 419904, 'aut_permdeg': 114, 'aut_perms': [228577826887034130864817728092281327070605510272162299831972495600361937875608138090346769190963197314468998571163735411022229020318782271185489848697008282664279439370446385213543388530, 2524744939441987904527019434224440969758592750722357741946163764975075991591242611365321729796153656374178137570662354594499262275619333264701825806788875435731575931245816755864434989960, 262669183787752557467020594436618771624332323189068563831084126319657668431179394893826058586417150494590387841274651994120743517566985421461593329935173150619435228399492978809391458179, 1096297790191535461300132417584253120144306192129901526711540145677975404094465749879923527220680233804700425244550217516221837779074176577527550483762874413972989825281913970733227964704, 2405311888887446501225023693061851148245103517861070278134077144446556347661224172563782498704657679097356076198093522252715557335185759763689613427000340925317291973075439694486078693010], 'aut_phi_ratio': 108.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 54, 2, 1], [2, 81, 1, 1], [2, 486, 1, 1], [2, 729, 1, 1], [3, 2, 2, 1], [3, 4, 1, 3], [3, 8, 2, 3], [3, 16, 1, 1], [4, 162, 2, 1], [6, 12, 1, 1], [6, 12, 2, 2], [6, 18, 2, 1], [6, 24, 2, 2], [6, 36, 1, 1], [6, 108, 2, 2], [6, 216, 2, 1], [6, 324, 1, 2], [6, 972, 1, 1], [9, 2, 6, 1], [9, 4, 6, 1], [9, 4, 9, 1], [9, 8, 6, 2], [9, 8, 12, 1], [9, 8, 18, 1], [9, 16, 6, 1], [9, 16, 9, 1], [12, 324, 2, 1], [18, 12, 6, 1], [18, 12, 12, 1], [18, 12, 18, 1], [18, 18, 6, 1], [18, 24, 6, 1], [18, 24, 12, 1], [18, 24, 18, 1], [18, 36, 6, 1], [18, 36, 9, 1], [18, 108, 6, 1], [18, 216, 6, 1], [36, 324, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_3^3.(C_3\\times D_4^2)', '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': 36, 'autcentquo_group': None, 'autcentquo_hash': 417177536885461405, 'autcentquo_nilpotent': False, 'autcentquo_order': 419904, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_3^3.(C_3\\times D_4^2)', 'cc_stats': [[1, 1, 1], [2, 6, 1], [2, 9, 1], [2, 54, 2], [2, 81, 1], [2, 486, 1], [2, 729, 1], [3, 2, 2], [3, 4, 3], [3, 8, 6], [3, 16, 1], [4, 162, 2], [6, 12, 5], [6, 18, 2], [6, 24, 4], [6, 36, 1], [6, 108, 4], [6, 216, 2], [6, 324, 2], [6, 972, 1], [9, 2, 6], [9, 4, 15], [9, 8, 42], [9, 16, 15], [12, 324, 2], [18, 12, 36], [18, 18, 6], [18, 24, 36], [18, 36, 15], [18, 108, 6], [18, 216, 6], [36, 324, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '11664.kk', 'commutator_count': 1, 'commutator_label': '1458.1401', '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', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 271, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 54, 1, 2], [2, 81, 1, 1], [2, 486, 1, 1], [2, 729, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 8, 1, 6], [3, 16, 1, 1], [4, 162, 1, 2], [6, 12, 1, 5], [6, 18, 1, 2], [6, 24, 1, 4], [6, 36, 1, 1], [6, 108, 1, 4], [6, 216, 1, 2], [6, 324, 1, 2], [6, 972, 1, 1], [9, 2, 3, 2], [9, 4, 3, 5], [9, 8, 3, 14], [9, 16, 3, 5], [12, 324, 1, 2], [18, 12, 3, 12], [18, 18, 3, 2], [18, 24, 3, 12], [18, 36, 3, 5], [18, 108, 3, 2], [18, 216, 3, 2], [36, 324, 3, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 967680, 'exponent': 36, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 36], [16, 1, 9]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '1296.3528', 'hash': 9200534730324170991, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [2, 18, 18, 6, 3], 'inner_gens': [[1, 34, 36, 972, 1296], [5, 2, 612, 972, 1296], [1, 74, 36, 11016, 7776], [5509, 5510, 5220, 648, 7776], [6481, 6482, 7812, 8424, 3888]], 'inner_hash': 9200534730324170991, 'inner_nilpotent': False, 'inner_order': 11664, 'inner_split': True, 'inner_tex': 'S_3^2:D_9^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 34], [4, 80], [8, 96], [16, 16]], 'label': '11664.kk', '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': 'S3^2:D9^2', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 51, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 234, 'number_divisions': 108, 'number_normal_subgroups': 65, 'number_subgroup_autclasses': 917, 'number_subgroup_classes': 1937, 'number_subgroups': 139666, 'old_label': None, 'order': 11664, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1419], [3, 80], [4, 324], [6, 2712], [9, 648], [12, 648], [18, 3888], [36, 1944]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[10710, 10549, 4240, 648, 7776], [1, 22, 180, 972, 1296]], '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': 5, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 14], [6, 8], [8, 12], [12, 22], [16, 1], [24, 28], [48, 5]], 'representations': {'PC': {'code': '40078105458340006382204013870175894612058980975827685111325407646701173899538263335214085744661027035', 'gens': [1, 2, 5, 8, 10], 'pres': [10, 2, 2, 3, 3, 2, 3, 3, 2, 3, 3, 681, 51, 962, 112, 963, 15314, 144, 17295, 235, 15136, 77767, 38897, 24527, 237, 349928, 174978, 6528, 129609, 64819, 21649, 1279]}, 'Perm': {'d': 24, 'gens': [25963950505465261376645, 1131549191849078155611, 54118088409430950030247]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_3^2:D_9^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 216, 'aut_gen_orders': [36, 12], 'aut_gens': [[1, 6, 24, 96, 1728, 15552, 139968], [939025, 878139, 1234953, 1023996, 991296, 544896, 110400], [260989, 526722, 445677, 591132, 366336, 721728, 1110336]], 'aut_group': '7558272.ok', 'aut_hash': 4843973011977204879, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7558272, 'aut_permdeg': 1089, 'aut_perms': 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'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 162, 3, 1], [2, 324, 3, 1], [2, 2916, 1, 1], [2, 6561, 1, 1], [3, 8, 1, 1], [3, 8, 3, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 81, 1, 2], [4, 5832, 3, 1], [4, 26244, 3, 1], [6, 72, 3, 1], [6, 144, 3, 1], [6, 288, 1, 1], [6, 648, 3, 2], [6, 972, 1, 2], [6, 1296, 3, 2], [6, 1458, 3, 2], [6, 2916, 3, 2], [6, 5832, 1, 1], [6, 6561, 1, 2], [6, 8748, 1, 2], [9, 24, 1, 1], [9, 24, 3, 1], [9, 48, 1, 1], [9, 48, 3, 2], [9, 96, 1, 1], [9, 96, 2, 1], [9, 96, 3, 6], [9, 96, 6, 1], [9, 192, 1, 4], [9, 192, 2, 1], [9, 192, 3, 4], [9, 648, 1, 2], [9, 648, 3, 2], [9, 1296, 1, 2], [9, 2592, 1, 2], [12, 11664, 3, 1], [12, 17496, 3, 2], [12, 26244, 3, 2], [18, 216, 3, 1], [18, 432, 3, 1], [18, 432, 6, 2], [18, 864, 1, 1], [18, 864, 2, 1], [18, 864, 3, 4], [18, 864, 6, 1], [18, 1944, 3, 4], [18, 3888, 3, 6], [18, 5832, 3, 4], [18, 7776, 1, 2], [18, 7776, 3, 2], [18, 11664, 3, 4], [18, 17496, 1, 3], [36, 34992, 3, 3]], 'aut_supersolvable': False, 'aut_tex': 'D_9\\wr A_4.C_6', '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': 216, 'autcentquo_group': '7558272.ok', 'autcentquo_hash': 4843973011977204879, 'autcentquo_nilpotent': False, 'autcentquo_order': 7558272, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_9\\wr A_4.C_6', 'cc_stats': [[1, 1, 1], [2, 36, 1], [2, 162, 3], [2, 324, 3], [2, 2916, 1], [2, 6561, 1], [3, 8, 4], [3, 16, 1], [3, 32, 1], [3, 81, 2], [4, 5832, 3], [4, 26244, 3], [6, 72, 3], [6, 144, 3], [6, 288, 1], [6, 648, 6], [6, 972, 2], [6, 1296, 6], [6, 1458, 6], [6, 2916, 6], [6, 5832, 1], [6, 6561, 2], [6, 8748, 2], [9, 24, 4], [9, 48, 7], [9, 96, 27], [9, 192, 18], [9, 648, 8], [9, 1296, 2], [9, 2592, 2], [12, 11664, 3], [12, 17496, 6], [12, 26244, 6], [18, 216, 3], [18, 432, 15], [18, 864, 21], [18, 1944, 12], [18, 3888, 18], [18, 5832, 12], [18, 7776, 8], [18, 11664, 12], [18, 17496, 3], [36, 34992, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '1259712.ji', 'commutator_count': 1, 'commutator_label': '52488.rj', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 15, 'conjugacy_classes_known': True, 'counter': 243, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 36, 1, 1], [2, 162, 1, 3], [2, 324, 1, 3], [2, 2916, 1, 1], [2, 6561, 1, 1], [3, 8, 1, 4], [3, 16, 1, 1], [3, 32, 1, 1], [3, 81, 2, 1], [4, 5832, 1, 3], [4, 26244, 1, 3], [6, 72, 1, 3], [6, 144, 1, 3], [6, 288, 1, 1], [6, 648, 1, 6], [6, 972, 2, 1], [6, 1296, 1, 6], [6, 1458, 2, 3], [6, 2916, 2, 3], [6, 5832, 1, 1], [6, 6561, 2, 1], [6, 8748, 2, 1], [9, 24, 1, 4], [9, 48, 1, 7], [9, 96, 1, 27], [9, 192, 1, 18], [9, 648, 2, 4], [9, 1296, 2, 1], [9, 2592, 2, 1], [12, 11664, 1, 3], [12, 17496, 2, 3], [12, 26244, 2, 3], [18, 216, 1, 3], [18, 432, 1, 15], [18, 864, 1, 21], [18, 1944, 1, 6], [18, 1944, 2, 3], [18, 3888, 1, 12], [18, 3888, 2, 3], [18, 5832, 2, 6], [18, 7776, 1, 6], [18, 7776, 2, 1], [18, 11664, 2, 6], [18, 17496, 1, 1], [18, 17496, 2, 1], [36, 34992, 1, 3], [36, 34992, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [9, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 20], [48, 1, 31], [96, 1, 54], [192, 1, 18]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '15552.br', 'hash': 9066509327683176825, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [18, 36, 4, 18, 9, 9, 9], 'inner_gens': [[1, 1053762, 569448, 1067232, 13440, 110208, 981312], [715837, 6, 1054968, 1087248, 715200, 63936, 979008], [771601, 890790, 24, 687072, 290496, 694848, 419136], [349825, 710646, 730008, 96, 162432, 148608, 649728], [5569, 563526, 988248, 1254624, 1728, 15552, 139968], [47041, 107142, 737688, 1142304, 1728, 15552, 139968], [420097, 577926, 1137816, 905568, 1728, 15552, 139968]], 'inner_hash': 9066509327683176825, 'inner_nilpotent': False, 'inner_order': 1259712, 'inner_split': True, 'inner_tex': 'D_9^2\\wr C_2.C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 24], [2, 18], [4, 6], [8, 60], [16, 21], [24, 20], [32, 6], [48, 31], [96, 54], [192, 18]], 'label': '1259712.ji', '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': 'D9^2wrC2.C6', 'ngens': 15, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 1, 0, 7, 0, 3, 7, 0, 7, 7, 7, 1, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 107, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 258, 'number_divisions': 213, 'number_normal_subgroups': 57, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1259712, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 10971], [3, 242], [4, 96228], [6, 77238], [9, 19440], [12, 297432], [18, 443232], [36, 314928]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [572832, 360048], 'outer_gens': [[43201, 387438, 525144, 1199136, 186624, 1181952, 675648], [1141249, 592302, 559941, 1091724, 236544, 506496, 518208]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 14], [4, 8], [8, 22], [16, 27], [24, 20], [32, 9], [48, 31], [64, 2], [96, 54], [192, 18]], 'representations': {'PC': {'code': '71449835192202259445656356467644949331891126711407909178735435978871173975744511823884642224320139747103759602429956579503732894298672444849066806738632469213471816854490503017747199657787549474214169618210293526948801966919226920643001660498075093964594387003130325948166656245050647126508758625701827330946289172268323536448356795921083208337936367967690190184591488085095235897857076135748383966300068116976548813862702683301487596402143782323375063079667889455164802945465716125631341990861840639', 'gens': [1, 3, 5, 7, 10, 12, 14], 'pres': [15, 2, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 30, 7853776, 47419292, 21487832, 122, 29849043, 27613818, 1821168, 42708604, 27454519, 13187134, 2838499, 214, 16212965, 55600580, 7831475, 314330, 112059366, 18390981, 19026876, 3176091, 3006006, 827691, 306, 46087, 46102, 23120677, 1565827, 3922, 472, 155528, 20995238, 5284508, 3323, 2016009, 518424, 17880039, 14448054, 1815669, 43284, 253899, 594, 950410, 23411560, 12988855, 5777710, 35725, 810910, 19837451, 5598746, 1918121, 12231416, 5211431, 466646, 278741, 716, 9210252, 1684842, 14423817, 4174632, 379167, 874092, 206075533, 58786588, 34265323, 19609018, 3667513, 4898968, 1421383, 838, 94737614, 3931244, 15757259, 8856074, 3936689, 1215104]}, 'Perm': {'d': 36, 'gens': [84490573458278943623698269943043350155354, 20666830637072850503482355965619989893094, 159556487571442990775825396316305356533719]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 108, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'D_9^2\\wr C_2.C_6', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}