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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '115200.d', 'ambient_counter': 4, 'ambient_order': 115200, 'ambient_tex': 'S_5^2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 2, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '115200.d.300.M', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '300.m1', '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': 300, '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': '384.20051', 'subgroup_hash': 20051, 'subgroup_order': 384, 'subgroup_tex': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '115200.d', 'aut_centralizer_order': None, 'aut_label': '300.M', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['60.J', '150.A'], 'contains': ['600.BC', '600.BD', '600.BM', '600.BN', '600.BU', '600.BW', '600.BY', '600.DC', '600.DD'], 'core': '57600.A', 'coset_action_label': None, 'count': 300, 'diagramx': None, 'generators': [771136, 25430635456, 44331411616, 302008463, 5063, 37885841296, 44316488160, 16], 'label': '115200.d.300.M', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.A', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '150.A', 'old_label': '300.m1', 'projective_image': '57600.l', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '300.M', 'subgroup_fusion': None, 'weyl_group': '96.226'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', '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, 2, 2, 4, 2, 2, 2, 2, 2, 2, 3], 'aut_gens': [[40320, 1, 126, 55, 288, 45360, 367920, 806400], [40320, 1, 126, 55, 288, 725760, 367920, 806400], [1134000, 1, 126, 55, 288, 1128960, 367920, 806400], [40608, 1, 126, 265, 288, 80640, 806400, 367920], [40608, 1, 414, 55, 288, 80640, 806400, 367920], [40608, 1, 264, 126, 288, 80640, 806400, 367920], [40608, 1, 414, 265, 288, 80640, 806400, 367920], [40321, 1, 126, 55, 288, 80640, 806400, 367920], [40321, 1, 415, 264, 288, 80640, 806400, 367920], [40320, 1, 126, 55, 288, 80640, 806400, 367920], [40609, 1, 415, 55, 288, 80640, 806400, 367920], [40608, 289, 126, 265, 288, 80640, 806400, 367920], [85680, 1, 126, 55, 288, 45360, 1174320, 367920]], 'aut_group': '6144.bjg', 'aut_hash': 5354572677491971722, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 32, 'aut_perms': [185993208499366924016910399568381, 89323488731079077101390527512528641, 203720707977868294733775053569741, 203682395341979210357753862882332, 234146522569171895299051202510406628, 26207043054991961221106496433409878, 224844833297409915949275012586573561, 224844944621467800137205864282292682, 203676733723247102857329525505741, 203679169009122147699173221869212, 1530262440596788287460241264010087, 20629694151484690995973795083290707], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 4, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 4, 2], [2, 12, 4, 1], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [4, 6, 4, 1], [4, 12, 2, 2], [4, 12, 4, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 16, 4, 1], [12, 16, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times C_2^5:D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '48.48', 'autcentquo_hash': 48, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [2, 3, 4], [2, 6, 8], [2, 12, 4], [3, 8, 1], [4, 2, 2], [4, 6, 6], [4, 12, 8], [6, 8, 3], [6, 16, 4], [12, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '96.226', 'commutator_count': 1, 'commutator_label': '24.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 20051, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.12', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [2, 3, 1, 4], [2, 6, 1, 8], [2, 12, 1, 4], [3, 8, 1, 1], [4, 2, 1, 2], [4, 6, 1, 6], [4, 12, 1, 8], [6, 8, 1, 3], [6, 16, 1, 4], [12, 16, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1031940, 'exponent': 12, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '192.1537', 'hash': 20051, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 1, 2, 2, 1, 3, 2, 2], 'inner_gens': [[40320, 1, 126, 55, 288, 80640, 806400, 367920], [40320, 1, 126, 55, 288, 45360, 367920, 806400], [40320, 1, 126, 265, 288, 45360, 367920, 806400], [40320, 1, 414, 55, 288, 45360, 367920, 806400], [40320, 1, 126, 55, 288, 45360, 367920, 806400], [5040, 1, 126, 55, 288, 45360, 806400, 1174320], [1134000, 1, 126, 55, 288, 1128960, 367920, 806400], [1134000, 1, 126, 55, 288, 448560, 367920, 806400]], 'inner_hash': 226, 'inner_nilpotent': False, 'inner_order': 96, 'inner_split': False, 'inner_tex': 'C_2^2\\times S_4', 'inner_used': [1, 3, 4, 6, 7], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [3, 16], [4, 2], [6, 4]], 'label': '384.20051', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, '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': 'GL(2,Z/4):C2^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 50, 'number_divisions': 50, 'number_normal_subgroups': 116, 'number_subgroup_autclasses': 321, 'number_subgroup_classes': 1295, 'number_subgroups': 6200, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 119], [3, 8], [4, 136], [6, 88], [12, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 151, 0, 0, 0, 0], 'outer_gens': [[40321, 1, 127, 55, 288, 45360, 367920, 806400], [40320, 289, 127, 54, 288, 45360, 367920, 806400], [40320, 1, 55, 126, 288, 45360, 367920, 806400], [40609, 1, 127, 54, 288, 45360, 367920, 806400], [40608, 1, 126, 55, 288, 45360, 367920, 806400], [40320, 1, 127, 54, 288, 45360, 367920, 806400]], 'outer_group': '64.226', 'outer_hash': 226, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 8, 'outer_perms': [5041, 11527, 16, 120, 5160, 7], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [3, 16], [4, 2], [6, 4]], 'representations': {'PC': {'code': 271496701992874256049292994721639051063990276, 'gens': [1, 2, 3, 4, 7, 8], 'pres': [8, -2, -2, -2, -2, -2, -3, -2, 2, 907, 723, 91, 820, 116, 789, 4054, 2046, 710, 550, 799, 1191, 239]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [705686952884, 518949212844, 706461201904, 706461084796]}, 'GLZN': {'d': 2, 'p': 12, 'gens': [12967, 204, 18688, 8645, 18685, 2665, 1733, 1801]}, 'Perm': {'d': 10, 'gens': [40320, 1, 126, 55, 288, 45360, 367920, 806400]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\GL(2,\\mathbb{Z}/4):C_2^2', 'transitive_degree': 24, '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 120, 'aut_gen_orders': [6, 12, 6, 8, 6], 'aut_gens': [[14386070169, 7672776605, 20773152734], [6314288405, 12545301009, 21088812974], [59118635525, 8797829769, 51931812245], [51991683129, 58613522414, 7678677005], [59575270454, 57975568569, 52909039454], [13905684014, 58456500609, 52865131085]], 'aut_group': '460800.bo', 'aut_hash': 1673116337738338913, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 460800, 'aut_permdeg': 320, 'aut_perms': [9126974453583707549525523729537312145254597616333907906670064285036387897771296850570178512518395872091024247774536714863370674655851850720319141038814994605437945633970799237340994982407870471641534642617200568455413571764310432960090731171588497957550605838659929178313708764107006707659306399317253313634874944599077702303826035556008433748062527347832886649794563010668081373278702015248976638265207820080823090565464984216835709974072722436090952959982614582146629041483484815485452146397237855475995996500663356895473416189806907003200791699962893355960401471048800426916408211132062804998112619470879596892803884480853778889059915693892423930843123383126852, 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20300733636529429203902232606038876829369391396196122912796887295014979709166123619548763778540889732709786474923069968372054118664442327341989969720300749275582618699828561303537626773565565955536550808256726328171114158741841221542267705285896794092998660346636992423965375932925770395040909298159846826965793502542679431179913244668058345645369673341647142022305621696767992790277977614269292296822117336718950331365072216356675611105912322856050285943929444445679339776640640951857442132330493746034373152944656702334426363348535084093606548408342049625134500396819696867314866742423496348213882553668912717860496437570998489546145954310532280454477749206533356], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 20, 4, 1], [2, 30, 1, 2], [2, 30, 2, 1], [2, 100, 2, 1], [2, 200, 1, 1], [2, 225, 1, 2], [2, 240, 1, 1], [2, 300, 4, 1], [2, 450, 1, 1], [3, 40, 1, 1], [3, 400, 1, 1], [4, 60, 4, 1], [4, 240, 1, 1], [4, 600, 2, 2], [4, 900, 2, 1], [4, 900, 4, 1], [4, 1800, 1, 1], [4, 2400, 2, 1], [4, 3600, 1, 2], [5, 48, 1, 1], [5, 576, 1, 1], [6, 40, 1, 1], [6, 40, 2, 1], [6, 40, 4, 1], [6, 400, 1, 1], [6, 400, 2, 3], [6, 400, 4, 1], [6, 600, 1, 2], [6, 600, 2, 1], [6, 600, 4, 1], [6, 800, 1, 2], [6, 800, 4, 1], [6, 4800, 1, 1], [8, 7200, 2, 1], [10, 48, 1, 1], [10, 48, 2, 1], [10, 480, 4, 1], [10, 576, 1, 1], [10, 720, 1, 2], [10, 720, 2, 1], [10, 1152, 1, 1], [10, 5760, 1, 1], [12, 1200, 2, 2], [12, 1200, 4, 1], [12, 4800, 1, 1], [12, 4800, 2, 1], [15, 960, 1, 1], [20, 1440, 4, 1], [20, 5760, 1, 1], [30, 960, 1, 1], [30, 960, 2, 1], [30, 960, 4, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2\\times A_5^2).D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '57600.l', 'autcentquo_hash': 3328040073188890159, 'autcentquo_nilpotent': False, 'autcentquo_order': 57600, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 20, 4], [2, 30, 4], [2, 100, 2], [2, 200, 1], [2, 225, 2], [2, 240, 1], [2, 300, 4], [2, 450, 1], [3, 40, 1], [3, 400, 1], [4, 60, 4], [4, 240, 1], [4, 600, 4], [4, 900, 6], [4, 1800, 1], [4, 2400, 2], [4, 3600, 2], [5, 48, 1], [5, 576, 1], [6, 40, 7], [6, 400, 11], [6, 600, 8], [6, 800, 6], [6, 4800, 1], [8, 7200, 2], [10, 48, 3], [10, 480, 4], [10, 576, 1], [10, 720, 4], [10, 1152, 1], [10, 5760, 1], [12, 1200, 8], [12, 4800, 3], [15, 960, 1], [20, 1440, 4], [20, 5760, 1], [30, 960, 7]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '57600.l', 'commutator_count': 1, 'commutator_label': '14400.ca', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '60.5', '60.5'], 'composition_length': 7, '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, 1, 1, 1], [2, 2, 1, 1], [2, 20, 1, 4], [2, 30, 1, 4], [2, 100, 1, 2], [2, 200, 1, 1], [2, 225, 1, 2], [2, 240, 1, 1], [2, 300, 1, 4], [2, 450, 1, 1], [3, 40, 1, 1], [3, 400, 1, 1], [4, 60, 1, 4], [4, 240, 1, 1], [4, 600, 1, 4], [4, 900, 1, 6], [4, 1800, 1, 1], [4, 2400, 1, 2], [4, 3600, 1, 2], [5, 48, 1, 1], [5, 576, 1, 1], [6, 40, 1, 7], [6, 400, 1, 11], [6, 600, 1, 8], [6, 800, 1, 6], [6, 4800, 1, 1], [8, 7200, 1, 2], [10, 48, 1, 3], [10, 480, 1, 4], [10, 576, 1, 1], [10, 720, 1, 4], [10, 1152, 1, 1], [10, 5760, 1, 1], [12, 1200, 1, 8], [12, 4800, 1, 3], [15, 960, 1, 1], [20, 1440, 1, 4], [20, 5760, 1, 1], [30, 960, 1, 7]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 120, 'exponents_of_order': [9, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 1, 8], [10, 1, 8], [12, 1, 4], [32, 1, 4], [40, 1, 8], [48, 1, 4], [50, 1, 4], [60, 1, 4], [72, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '57600.l', 'hash': 8438217488598235417, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 120, 'inner_gen_orders': [4, 8, 4], 'inner_gens': [[14386070169, 15023731814, 58199112845], [6398100138, 7672776605, 14490337694], [58217248218, 52948355885, 20773152734]], 'inner_hash': 3328040073188890159, 'inner_nilpotent': False, 'inner_order': 57600, 'inner_split': True, 'inner_tex': 'S_5^2:C_2^2', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 6], [8, 16], [10, 16], [12, 8], [16, 8], [25, 8], [32, 6], [36, 4], [40, 16], [48, 8], [50, 6], [60, 8], [72, 1]], 'label': '115200.d', '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': False, 'name': 'S5^2: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, 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': 65, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 119, 'number_divisions': 119, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 4913, 'number_subgroup_classes': 14962, 'number_subgroups': 5371298, 'old_label': None, 'order': 115200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 2943], [3, 440], [4, 22080], [5, 624], [6, 19080], [8, 14400], [10, 12432], [12, 24000], [15, 960], [20, 11520], [30, 6720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[14386070169, 7672776614, 20773152734], [14386070174, 7672776609, 20773152734]], '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': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [8, 16], [10, 16], [12, 8], [16, 8], [25, 8], [32, 6], [36, 4], [40, 16], [48, 8], [50, 6], [60, 8], [72, 1]], 'representations': {'Perm': {'d': 14, 'gens': [14386070169, 7672776605, 20773152734]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 720, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'S_5^2:D_4', 'transitive_degree': 20, 'wreath_data': ['C_2\times S_5', 'C_2', '2T1'], 'wreath_product': True}
