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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.3014', 'ambient_counter': 3014, 'ambient_order': 864, 'ambient_tex': '(C_3^2\\times A_4):C_8', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.3014.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '864.3014', 'aut_centralizer_order': 864, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 7776, 'centralizer': '24.a1', 'complements': [], 'conjugacy_class_count': 9, 'contained_in': ['6.a1', '9.b1'], 'contains': ['36.b1', '54.a1', '72.f1'], 'core': '18.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7400, 7484, 6144, 7369], 'generators': [2, 432, 56, 4, 72], 'label': '864.3014.18.b1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.b1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['36.b1', '54.a1'], 'normalizer': '1.a1', 'old_label': '18.b1', 'projective_image': '216.165', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 2, 2], 'aut_gens': [[1, 12, 24], [29, 24, 12], [7, 12, 24], [13, 36, 12], [37, 12, 24], [25, 12, 24]], 'aut_group': '48.48', 'aut_hash': 48, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 6, 'aut_perms': [143, 127, 576, 126, 121], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 4, 2, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 4, 2, 1], [12, 4, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_4', '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': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 4, 2], [4, 1, 2], [4, 3, 2], [6, 4, 2], [12, 4, 4]], 'center_label': '4.1', 'center_order': 4, 'central_product': True, 'central_quotient': '12.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 31, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 4, 2, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 4, 2, 1], [12, 4, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 12, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '24.13', 'hash': 31, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 2, 2], 'inner_gens': [[1, 36, 12], [25, 12, 24], [37, 12, 24]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'A_4', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 12], [3, 4]], 'label': '48.31', 'linC_count': 2, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 2, 'linQ_dim': 5, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4*A4', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 16, 'number_divisions': 9, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 19, 'number_subgroup_classes': 19, 'number_subgroups': 42, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 7], [3, 8], [4, 8], [6, 8], [12, 16]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5, 24, 12], [7, 12, 24]], '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': 3, 'perfect': False, 'permutation_degree': 8, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [3, 2], [4, 1], [6, 1]], 'representations': {'PC': {'code': 930066718915811428, 'gens': [1, 4, 5], 'pres': [5, -2, -2, -3, -2, 2, 10, 26, 723, 248, 193, 304, 459, 89]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [706460729522, 330663444220]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1173753, 1278336, 1682075, 1565004, 1247952]}, 'Perm': {'d': 8, 'gens': [9, 840, 16, 5160, 11520]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4\\times A_4', 'transitive_degree': 12, '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': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [8, 4, 8, 6, 6], 'aut_gens': [[1, 8, 24, 144], [49, 496, 240, 24], [37, 832, 840, 192], [371, 832, 744, 240], [351, 56, 720, 168], [51, 64, 480, 408]], 'aut_group': None, 'aut_hash': 1710745556252048373, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 373248, 'aut_permdeg': 216, 'aut_perms': [808687246572580455290389823106201336431408058083975973249724427989711976549147625134306517944660792238799660809360792811269262709367818131814642840218976957584783014811735337296224456321362459848713385102285451063700733583685721245516515223041629985888625215568504927299591064689694825964371316914005331741173571491117603939483697350500559084680424501155094891456146477684191137173167144330290512880146176411279, 8126259586182574703104982461323668024699092641432053646346019450916737595593734238058569044416240135722505689928544010125928354380511955385530778113757860425278151114734844064683366851819471261777590414002989174085364166680439374189805070961412629890960692748407020889782213835544563945888911208396269500831951901247312049788774178010718760101180784073887450890963959737117973568609997496569641631733942284959206, 8604464219145686372884755552310031411141038348135204166075263843652686674915182497472759238728169308535415283352999071727033119849509141119821534321196623345134105957569834278608063304654557029054045841420830494335108961228593619585833069050096650346679435518569515414869161303833510768364959164836068596999287779459830014171801300483212413931871560140725241318655222300742123187296593830228746308885915997027316, 528335333903126726582424004737050868113324697931433161673902465489393329127985815073946811626527059392605831144460365983336090188959347970826523715161711011134478847499665215932620208373060028332405948277211619920615534762269751308211767750428917256235668240142387980752721959717390426914162710314337605318849672735972891276952281945216271281964684756055109041810006275642658977282026669686261220167085008793949, 1460552471651845563790526537497352663689417704366033649855186355183950954819409860127349065712678390840894845695667751424710090943569214491236164955599555620832272773584698201037530796426816619619957079637588651743530355052004375162050873340721025702371786578768976368683558209319185803204259685757090516190134948251379124352176201998821317946712047787152840914693365709941221027321073686656339776449511984091149], 'aut_phi_ratio': 1296.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 4, 1], [3, 8, 9, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 4, 1], [6, 6, 4, 2], [6, 8, 9, 1], [8, 54, 4, 2], [12, 2, 8, 1], [12, 6, 8, 1], [12, 8, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_3^4.(Q_8\\times A_4).D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '93312.jr', 'autcentquo_hash': 7211166090879777373, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(S_4\\times \\GL(2,3))', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 4], [3, 8, 9], [4, 1, 2], [4, 3, 2], [6, 2, 4], [6, 6, 8], [6, 8, 9], [8, 54, 8], [12, 2, 8], [12, 6, 8], [12, 8, 18]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '216.165', 'commutator_count': 1, 'commutator_label': '108.41', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3014, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 4], [3, 8, 1, 9], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 4], [6, 6, 1, 8], [6, 8, 1, 9], [8, 54, 4, 2], [12, 2, 2, 4], [12, 6, 2, 4], [12, 8, 2, 9]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 786240, 'exponent': 24, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '216.165', 'hash': 3014, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 6, 6], 'inner_gens': [[1, 16, 480, 360], [17, 8, 456, 648], [553, 440, 24, 144], [793, 512, 24, 144]], 'inner_hash': 165, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2:S_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 52], [3, 8], [6, 16]], 'label': '864.3014', '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': True, 'name': '(C3^2*A4):C8', 'ngens': 8, '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': 17, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 84, 'number_divisions': 59, 'number_normal_subgroups': 103, 'number_subgroup_autclasses': 78, 'number_subgroup_classes': 284, 'number_subgroups': 1544, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7], [3, 80], [4, 8], [6, 128], [8, 432], [12, 208]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [4, 3, 6, 3, 2, 6, 2, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 584, 360, 528], [1, 392, 24, 144], [5, 688, 528, 312], [1, 104, 24, 144], [3, 8, 24, 144], [3, 112, 816, 24], [5, 352, 528, 648], [1, 632, 312, 768], [1, 688, 528, 648]], 'outer_group': '1728.47845', 'outer_hash': 47845, 'outer_nilpotent': False, 'outer_order': 1728, 'outer_permdeg': 13, 'outer_perms': [2123377920, 3079123920, 653683703, 4072981800, 7, 1620355687, 4040473096, 178905000, 3524347440], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_6^2:\\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 27], [3, 2], [4, 14], [6, 9], [12, 5]], 'representations': {'PC': {'code': 57102759107764657246169466380700430244926229, 'gens': [1, 4, 5, 7], 'pres': [8, 2, 2, 2, 3, 2, 3, 2, 3, 16, 41, 515, 19204, 2308, 116, 4613, 20166, 4566, 166, 36871]}, 'GLZN': {'d': 2, 'p': 60, 'gens': [346333, 1512007, 217201, 10584049, 2916013, 9397843, 6858916, 1547783]}, 'Perm': {'d': 18, 'gens': [20923272972865, 8443680, 12501360, 22237170278400, 6706022403, 4, 356995102464000, 753220435968000]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_3^2\\times A_4):C_8', 'transitive_degree': 216, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 3], 'aut_gens': [[25, 3, 144], [25, 3, 243], [25, 147, 144], [122, 3, 144]], 'aut_group': '432.734', 'aut_hash': 734, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 432, 'aut_permdeg': 9, 'aut_perms': [42648, 223305, 287216], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^2:\\GL(2,3)', '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': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 9, 1], [3, 2, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '18.4', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [3, 2, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 7, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '18.4', 'hash': 4, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3], 'inner_gens': [[25, 4, 240], [29, 3, 144], [265, 3, 144]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': False, 'inner_tex': 'C_3:S_3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [2, 4]], 'label': '18.4', 'linC_count': 6, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 6, 'linQ_dim': 4, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3:S3', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 6, 'number_divisions': 6, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 12, 'number_subgroups': 28, 'old_label': None, 'order': 18, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 9], [3, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [0, 0, 25, 25], 'outer_gens': [[25, 3, 243], [25, 240, 243], [25, 243, 244], [25, 240, 3]], 'outer_group': '24.12', 'outer_hash': 12, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 4, 'outer_perms': [2, 4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 6, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 4]], 'representations': {'PC': {'code': 5475, 'gens': [1, 2, 3], 'pres': [3, -2, -3, -3, 25, 110]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26483560, 35931151, 16858733]}, 'GLFp': {'d': 3, 'p': 3, 'gens': [11017, 8101, 13933]}, 'Perm': {'d': 6, 'gens': [25, 3, 144]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3:S_3', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
