Formats: - HTML - YAML - JSON - 2026-07-21T20:05:07.340479
  • gps_subgroup_search • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '139968.kc', 'ambient_counter': 263, 'ambient_order': 139968, 'ambient_tex': 'C_3^3.S_3\\wr C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '139968.kc.18.B', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, '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': 18, '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': '7776.cc', 'subgroup_hash': 4809026425870751764, 'subgroup_order': 7776, 'subgroup_tex': 'S_3^4:S_3', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '139968.kc', 'aut_centralizer_order': None, 'aut_label': '18.B', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '139968.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.B'], 'contains': ['36.B', '36.F', '36.G', '36.U', '36.V', '36.Y', '36.Z', '54.B', '162.B', '162.I'], 'core': '5184.A', 'coset_action_label': None, 'count': 18, 'diagramx': [9592, -1, 8876, -1], 'generators': [106067251185458763804016841119247291361092, 255290352877328681993020276970385871395984, 212137523839085581940987645956117914065158, 63824548714034113121513358201882058547155, 255294138593625766057562018004482496123478, 127648554914288047844579246576383312972945, 526261674673969987453451405246672644, 20666295941918940249388752344471771097744, 10628907027099616484555487653870021226240, 138273964838529281563923318848128400701440], 'label': '139968.kc.18.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.B', 'old_label': '18.b1', 'projective_image': '139968.kc', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.B', 'subgroup_fusion': None, 'weyl_group': '7776.cc'}
  • 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, 3, 2, 2, 12], 'aut_gens': [[45400, 100670169616, 193995653230], [81078, 94446778014, 280255858070], [45400, 362647756816, 200226302830], [81078, 455131354044, 286486588209], [81348, 94446778313, 280255858436], [435971370240, 180587232449, 448904338190]], 'aut_group': '62208.l', 'aut_hash': 1820680360968750972, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 120, 'aut_perms': [1479522355132891209411357193329702257298515365201155791327356901550291750817479479150538147647415451798341012204555615049465780164912541128080553077706727915110327503492874124121550823066800881606605, 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4, 1], [3, 8, 2, 2], [3, 8, 4, 1], [3, 16, 1, 1], [3, 16, 2, 1], [3, 16, 4, 1], [3, 32, 1, 1], [4, 324, 2, 1], [4, 972, 1, 1], [6, 6, 4, 1], [6, 12, 2, 1], [6, 12, 4, 2], [6, 12, 8, 1], [6, 18, 2, 1], [6, 18, 4, 1], [6, 24, 2, 1], [6, 24, 4, 2], [6, 24, 8, 1], [6, 36, 2, 2], [6, 36, 4, 2], [6, 36, 8, 1], [6, 48, 2, 1], [6, 48, 4, 1], [6, 54, 4, 1], [6, 72, 2, 2], [6, 72, 4, 1], [6, 108, 2, 1], [6, 108, 4, 1], [6, 162, 1, 1], [6, 216, 2, 1], [6, 432, 1, 1], [12, 648, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3^5.D_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': '62208.l', 'autcentquo_hash': 1820680360968750972, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^5.D_4', 'cc_stats': [[1, 1, 1], [2, 6, 2], [2, 9, 2], [2, 18, 2], [2, 54, 2], [2, 81, 1], [2, 108, 1], [3, 2, 1], [3, 4, 8], [3, 8, 8], [3, 16, 7], [3, 32, 1], [4, 324, 2], [4, 972, 1], [6, 6, 4], [6, 12, 18], [6, 18, 6], [6, 24, 18], [6, 36, 20], [6, 48, 6], [6, 54, 4], [6, 72, 8], [6, 108, 6], [6, 162, 1], [6, 216, 2], [6, 432, 1], [12, 648, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '7776.cc', 'commutator_count': 1, 'commutator_label': '972.888', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 55, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 6, 1, 2], [2, 9, 1, 2], [2, 18, 1, 2], [2, 54, 1, 2], [2, 81, 1, 1], [2, 108, 1, 1], [3, 2, 1, 1], [3, 4, 1, 4], [3, 4, 2, 2], [3, 8, 1, 4], [3, 8, 2, 2], [3, 16, 1, 3], [3, 16, 2, 2], [3, 32, 1, 1], [4, 324, 1, 2], [4, 972, 1, 1], [6, 6, 2, 2], [6, 12, 1, 6], [6, 12, 2, 6], [6, 18, 1, 2], [6, 18, 2, 2], [6, 24, 1, 6], [6, 24, 2, 6], [6, 36, 1, 8], [6, 36, 2, 6], [6, 48, 1, 2], [6, 48, 2, 2], [6, 54, 2, 2], [6, 72, 1, 4], [6, 72, 2, 2], [6, 108, 1, 2], [6, 108, 2, 2], [6, 162, 1, 1], [6, 216, 1, 2], [6, 432, 1, 1], [12, 648, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 2150400, 'exponent': 12, 'exponents_of_order': [5, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 16], [16, 0, 8], [32, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '7776.cc', 'hash': 4809026425870751764, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 6, 12], 'inner_gens': [[45400, 100670169682, 193995733943], [45436, 100670169616, 281177573261], [81041, 449822419847, 193995653230]], 'inner_hash': 4809026425870751764, 'inner_nilpotent': False, 'inner_order': 7776, 'inner_split': True, 'inner_tex': 'S_3^4:S_3', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 22], [4, 56], [8, 34], [16, 14], [32, 1]], 'label': '7776.cc', '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': 'S3^4:S3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 48, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 135, 'number_divisions': 99, 'number_normal_subgroups': 55, 'number_subgroup_autclasses': 1122, 'number_subgroup_classes': 2706, 'number_subgroups': 77912, 'old_label': None, 'order': 7776, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 363], [3, 242], [4, 1620], [6, 4254], [12, 1296]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [647, 193077562247], 'outer_gens': [[46015, 100670170257, 193995653376], [94446822960, 25909632449, 449826053541]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, '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, 30], [8, 30], [16, 16], [32, 5]], 'representations': {'PC': {'code': '5667211035620131757192221860287065683835816772621057732795915491870627895447678681785286314736251250568506539', 'gens': [1, 2, 4, 6, 8, 10], 'pres': [10, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 69420, 6441, 51, 242, 723, 6973, 113, 7204, 1214, 169925, 10815, 1835, 175, 3366, 10096, 1716, 397447, 5337, 237, 233288, 2218, 86409, 7259, 1279]}, 'Perm': {'d': 15, 'gens': [45400, 100670169616, 193995653230]}}, 'schur_multiplier': [2, 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_3^4:S_3', 'transitive_degree': 24, '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': 12, 'aut_gen_orders': [12, 4, 6, 12, 6], 'aut_gens': [[116695631750038057511116884221643963965492, 191770534870542345857136736256578962800764, 201804384095843383256611277043493226921996], [170186243334443323617268813228622734584695, 74160684745051814657944626752873306963034, 329446419817020139187192252255250190216894], [170185971871179184993213347672985053804235, 64122769669266808987721392709083779298828, 276256779173841792851964553947498384686904], [297834526583997580324021827493284581376575, 212431398159488177339659375710443349171244, 148608742536480815843098080941981551814974], [170191675904686917519081396210568638727082, 191770806224213288350335240748053732270840, 74162314450084787643944823603030858580109], [170191675969721101698352146844271615462546, 84789065519621245976838185276723453719708, 148611195311988200378246497186054924816078]], 'aut_group': None, 'aut_hash': 6395131201938535785, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 279936, 'aut_permdeg': 468, 'aut_perms': 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'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [2, 108, 1, 1], [2, 162, 1, 2], [2, 324, 1, 2], [2, 972, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 8, 1, 2], [3, 24, 1, 2], [3, 24, 2, 1], [3, 48, 1, 3], [3, 48, 2, 1], [3, 72, 1, 2], [3, 72, 2, 1], [3, 96, 1, 1], [3, 144, 1, 2], [3, 288, 1, 2], [3, 288, 2, 1], [4, 972, 1, 2], [4, 1944, 1, 2], [4, 2916, 1, 1], [4, 5832, 1, 1], [6, 36, 1, 3], [6, 36, 2, 1], [6, 72, 1, 5], [6, 72, 2, 2], [6, 144, 1, 2], [6, 144, 2, 1], [6, 162, 1, 1], [6, 162, 2, 1], [6, 216, 1, 6], [6, 216, 2, 3], [6, 324, 1, 3], [6, 324, 2, 1], [6, 432, 1, 7], [6, 432, 2, 4], [6, 648, 1, 9], [6, 648, 2, 5], [6, 864, 1, 2], [6, 864, 2, 1], [6, 1296, 1, 4], [6, 1296, 2, 2], [6, 2592, 1, 1], [6, 3888, 1, 4], [12, 972, 1, 2], [12, 1944, 1, 7], [12, 1944, 2, 1], [12, 3888, 1, 5], [12, 3888, 2, 1], [12, 5832, 1, 1], [12, 11664, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2.C_3^5.C_2^3.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': 12, 'autcentquo_group': None, 'autcentquo_hash': 6395131201938535785, 'autcentquo_nilpotent': False, 'autcentquo_order': 279936, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2.C_3^5.C_2^3.C_2^4', 'cc_stats': [[1, 1, 1], [2, 18, 1], [2, 36, 1], [2, 81, 1], [2, 108, 1], [2, 162, 2], [2, 324, 2], [2, 972, 1], [3, 2, 1], [3, 4, 2], [3, 8, 2], [3, 24, 4], [3, 48, 5], [3, 72, 4], [3, 96, 1], [3, 144, 2], [3, 288, 4], [4, 972, 2], [4, 1944, 2], [4, 2916, 1], [4, 5832, 1], [6, 36, 5], [6, 72, 9], [6, 144, 4], [6, 162, 3], [6, 216, 12], [6, 324, 5], [6, 432, 15], [6, 648, 19], [6, 864, 4], [6, 1296, 8], [6, 2592, 1], [6, 3888, 4], [12, 972, 2], [12, 1944, 9], [12, 3888, 7], [12, 5832, 1], [12, 11664, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '139968.kc', 'commutator_count': 1, 'commutator_label': None, 'complements_known': True, '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'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 263, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [2, 81, 1, 1], [2, 108, 1, 1], [2, 162, 1, 2], [2, 324, 1, 2], [2, 972, 1, 1], [3, 2, 1, 1], [3, 4, 1, 2], [3, 8, 1, 2], [3, 24, 1, 2], [3, 24, 2, 1], [3, 48, 1, 3], [3, 48, 2, 1], [3, 72, 1, 2], [3, 72, 2, 1], [3, 96, 1, 1], [3, 144, 1, 2], [3, 288, 1, 2], [3, 288, 2, 1], [4, 972, 1, 2], [4, 1944, 1, 2], [4, 2916, 1, 1], [4, 5832, 1, 1], [6, 36, 1, 3], [6, 36, 2, 1], [6, 72, 1, 5], [6, 72, 2, 2], [6, 144, 1, 2], [6, 144, 2, 1], [6, 162, 1, 1], [6, 162, 2, 1], [6, 216, 1, 6], [6, 216, 2, 3], [6, 324, 1, 3], [6, 324, 2, 1], [6, 432, 1, 7], [6, 432, 2, 4], [6, 648, 1, 9], [6, 648, 2, 5], [6, 864, 1, 2], [6, 864, 2, 1], [6, 1296, 1, 4], [6, 1296, 2, 2], [6, 2592, 1, 1], [6, 3888, 1, 4], [12, 972, 2, 1], [12, 1944, 1, 3], [12, 1944, 2, 3], [12, 3888, 1, 3], [12, 3888, 2, 2], [12, 5832, 1, 1], [12, 11664, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 12, 'exponents_of_order': [7, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 4], [24, 1, 4], [48, 0, 8], [72, 1, 4], [96, 1, 2], [144, 1, 1]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '15552.bt', 'hash': 8323456571666149168, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [12, 4, 12], 'inner_gens': [[116695631750038057511116884221643963965492, 64119247193705549109762035632842078588748, 148611450155252570138118343695027176287434], [371991162354039041499876262664633802773732, 191770534870542345857136736256578962800764, 64118440550615145320883781350770123934989], [307869182205473451573977511817084635401011, 329451309150031697567931547363966595512587, 201804384095843383256611277043493226921996]], 'inner_hash': 8323456571666149168, 'inner_nilpotent': False, 'inner_order': 139968, 'inner_split': True, 'inner_tex': 'C_3^3.S_3\\wr C_2^2', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 14], [4, 8], [8, 44], [12, 8], [16, 17], [24, 10], [32, 8], [36, 8], [48, 16], [72, 6], [96, 2], [144, 1]], 'label': '139968.kc', '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.S3wrC2^2', '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, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 123, 'number_characteristic_subgroups': 43, 'number_conjugacy_classes': 150, 'number_divisions': 119, 'number_normal_subgroups': 43, 'number_subgroup_autclasses': 7459, 'number_subgroup_classes': 7963, 'number_subgroups': 2575292, 'old_label': None, 'order': 139968, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 2187], [3, 2186], [4, 14580], [6, 56862], [12, 64152]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[116695631750038057511116884221643963965492, 212437357056452017209923141991442497399624, 191766723827348052817651547303865696691195]], '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': 9, '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, 10], [4, 6], [8, 22], [12, 4], [16, 23], [24, 8], [32, 7], [36, 8], [48, 8], [64, 2], [72, 4], [96, 7], [144, 2]], 'representations': {'PC': {'code': '238638103437265499469713791232840443710516421857702007892443244806384261443913216132738104175327008313195101108964511437748136641265200137734497447670949636334028420128118769828957204226930824567891344976718149443551881738860528385744843294906965268813035510195904617959656649918699646976462570022103', 'gens': [1, 2, 4, 5, 7, 8, 10, 12, 13], 'pres': [13, 2, 2, 3, 2, 2, 3, 3, 2, 3, 2, 3, 3, 3, 911508, 1095693, 66, 1458602, 5323971, 101104, 4553, 865024, 3760007, 1266360, 517053, 186, 808709, 2426130, 2540, 1415238, 1415251, 1150, 5290279, 4753652, 18753, 827470, 99899, 1320, 306, 134792, 325749, 29518, 471791, 85704, 2881, 16813689, 270682, 2611475, 70261, 41440, 12203, 386, 48058, 3407999, 1297332, 61838, 13829, 6120, 44939, 22488, 11334, 2000, 16086108, 16249, 876160, 8241, 2677]}, 'Perm': {'d': 36, 'gens': [201804384095843383256611277043493226921996, 191770534870542345857136736256578962800764, 116695631750038057511116884221643963965492]}}, 'schur_multiplier': [2, 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': 192, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3.S_3\\wr C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}