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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '172800.bm', 'ambient_counter': 39, 'ambient_order': 172800, 'ambient_tex': 'A_4\\times F_5\\times S_6', 'central': False, 'central_factor': False, 'centralizer_order': 5, 'characteristic': False, 'core_order': 60, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '172800.bm.24.L', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1', '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': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7200.dd', 'subgroup_hash': 2899273163031768283, 'subgroup_order': 7200, 'subgroup_tex': 'C_5\\times A_4\\times S_5', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '172800.bm', 'aut_centralizer_order': None, 'aut_label': '24.L', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '34560.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.B', '12.M'], 'contains': ['48.E', '72.M', '96.C', '120.BW', '120.BY', '144.J', '240.CG'], 'core': '2880.A', 'coset_action_label': None, 'count': 12, 'diagramx': [4522, -1, 1065, -1], 'generators': [87657292800, 93416929541, 11617200, 186810624000, 100111334400, 6706023082], 'label': '172800.bm.24.L', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.B', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.H', 'old_label': '24.l1', 'projective_image': '172800.bm', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.L', 'subgroup_fusion': None, 'weyl_group': '5760.fo'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '30.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [3, 12, 2, 2, 12, 4, 2, 2], 'aut_gens': [[1037836800, 482630400, 1476921600, 1001548801, 50520, 81474308789], [1520467200, 1037836800, 1476921600, 1001548801, 50520, 81474308789], [482630400, 1520467200, 43545600, 69100018710, 172800, 75247342839], [1037836800, 482630400, 1476921600, 1001548801, 82080, 81474277229], [1037836800, 482630400, 958003200, 518918401, 50520, 81474308789], [482630400, 1520467200, 958003200, 518918401, 172800, 75247342840], [1037836800, 482630400, 1476921600, 1001548801, 172800, 81474363629], [1520467200, 482630400, 1001548800, 1476921601, 82080, 81474277229], [1037836800, 482630400, 562464000, 1440633601, 50520, 81474308789]], 'aut_group': '11520.ei', 'aut_hash': 1827323456663704710, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11520, 'aut_permdeg': 22, 'aut_perms': [330122494879758720, 297685978604250367109, 513470917995044083200, 816726161187751712, 280381437785850511232, 258016122043938316800, 513593631440986603832, 1449138159261567512], 'aut_phi_ratio': 6.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 10, 1, 1], [2, 15, 1, 1], [2, 30, 1, 1], [2, 45, 1, 1], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 30, 1, 1], [4, 90, 1, 1], [5, 1, 4, 1], [5, 24, 1, 1], [5, 24, 4, 1], [6, 20, 1, 1], [6, 40, 2, 1], [6, 60, 1, 2], [6, 60, 2, 1], [6, 80, 2, 1], [10, 3, 4, 1], [10, 10, 4, 1], [10, 15, 4, 1], [10, 30, 4, 1], [10, 45, 4, 1], [10, 72, 1, 1], [10, 72, 4, 1], [12, 120, 2, 1], [15, 4, 8, 1], [15, 20, 4, 1], [15, 80, 8, 1], [15, 96, 2, 1], [15, 96, 8, 1], [20, 30, 4, 1], [20, 90, 4, 1], [30, 20, 4, 1], [30, 40, 8, 1], [30, 60, 4, 2], [30, 60, 8, 1], [30, 80, 8, 1], [60, 120, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times S_4\\times S_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '2880.dv', 'autcentquo_hash': 409072078557532110, 'autcentquo_nilpotent': False, 'autcentquo_order': 2880, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 10, 1], [2, 15, 1], [2, 30, 1], [2, 45, 1], [3, 4, 2], [3, 20, 1], [3, 80, 2], [4, 30, 1], [4, 90, 1], [5, 1, 4], [5, 24, 5], [6, 20, 1], [6, 40, 2], [6, 60, 4], [6, 80, 2], [10, 3, 4], [10, 10, 4], [10, 15, 4], [10, 30, 4], [10, 45, 4], [10, 72, 5], [12, 120, 2], [15, 4, 8], [15, 20, 4], [15, 80, 8], [15, 96, 10], [20, 30, 4], [20, 90, 4], [30, 20, 4], [30, 40, 8], [30, 60, 16], [30, 80, 8], [60, 120, 8]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '1440.5846', 'commutator_count': 1, 'commutator_label': '240.190', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '5.1', '60.5'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 82, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['120.34', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 10, 1, 1], [2, 15, 1, 1], [2, 30, 1, 1], [2, 45, 1, 1], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 30, 1, 1], [4, 90, 1, 1], [5, 1, 4, 1], [5, 24, 1, 1], [5, 24, 4, 1], [6, 20, 1, 1], [6, 40, 2, 1], [6, 60, 1, 2], [6, 60, 2, 1], [6, 80, 2, 1], [10, 3, 4, 1], [10, 10, 4, 1], [10, 15, 4, 1], [10, 30, 4, 1], [10, 45, 4, 1], [10, 72, 1, 1], [10, 72, 4, 1], [12, 120, 2, 1], [15, 4, 8, 1], [15, 20, 4, 1], [15, 80, 8, 1], [15, 96, 2, 1], [15, 96, 8, 1], [20, 30, 4, 1], [20, 90, 4, 1], [30, 20, 4, 1], [30, 40, 8, 1], [30, 60, 4, 2], [30, 60, 8, 1], [30, 80, 8, 1], [60, 120, 8, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1368, 'exponent': 60, 'exponents_of_order': [5, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[12, 0, 8], [15, 0, 8], [18, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '7200.dd', 'hash': 2899273163031768283, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 3, 6, 1, 6], 'inner_gens': [[1037836800, 482630400, 958003200, 518918401, 50520, 81474308789], [1037836800, 482630400, 43545600, 79833601, 50520, 81474308789], [1520467200, 1037836800, 1476921600, 1001548801, 50520, 81474308789], [482630400, 1520467200, 1476921600, 1001548801, 50520, 75247287988], [1037836800, 482630400, 1476921600, 1001548801, 50520, 81474308789], [1037836800, 482630400, 1476921600, 1001548806, 50520, 81474308789]], 'inner_hash': 5846, 'inner_nilpotent': False, 'inner_order': 1440, 'inner_split': True, 'inner_tex': 'A_4\\times S_5', 'inner_used': [1, 2, 3, 4, 6], 'irrC_degree': 12, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 24, 'irrep_stats': [[1, 30], [3, 10], [4, 30], [5, 30], [6, 15], [12, 10], [15, 10], [18, 5]], 'label': '7200.dd', 'linC_count': 288, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 11, 'linQ_degree_count': 8, 'linQ_dim': 11, 'linQ_dim_count': 8, 'linR_count': 48, 'linR_degree': 9, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C5*A4*S5', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 140, 'number_divisions': 42, 'number_normal_subgroups': 18, 'number_subgroup_autclasses': 293, 'number_subgroup_classes': 297, 'number_subgroups': 7316, 'old_label': None, 'order': 7200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 103], [3, 188], [4, 120], [5, 124], [6, 500], [10, 772], [12, 240], [15, 1712], [20, 480], [30, 2000], [60, 960]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[1520467200, 482630400, 1001548800, 1476921601, 82080, 81474277229], [1037836800, 482630400, 1476921600, 1001548801, 172800, 81474363629]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [3, 2], [4, 4], [5, 2], [6, 1], [8, 4], [10, 2], [12, 5], [15, 2], [16, 2], [18, 1], [20, 2], [24, 1], [32, 2], [40, 2], [48, 3], [60, 2], [72, 1]], 'representations': {'Perm': {'d': 14, 'gens': [1037836800, 482630400, 1476921600, 1001548801, 50520, 81474308789]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [30], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times A_4\\times S_5', 'transitive_degree': 100, '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': '24.9', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [60, 8, 12, 10, 24], 'aut_gens': [[186810624000, 6721308872, 4440240, 274467916800, 4032000, 7983360, 100111334400, 181066637372], [87657292800, 6714006011, 4440240, 186810624000, 14878080, 11329920, 267761894400, 93420190799], [274467916800, 262025205275, 11617200, 186810624000, 730800, 1174320, 181062604800, 174357313712], [274467916800, 93420598956, 8386560, 186810624000, 12060720, 3633840, 12454041600, 100123395409], [87657292800, 12465371968, 4440240, 274467916800, 12060720, 3633840, 181062604800, 100123395144], [87657292800, 174364566167, 8386560, 186810624000, 730800, 1174320, 100111334400, 12454772480]], 'aut_group': None, 'aut_hash': 3309493389982338751, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 691200, 'aut_permdeg': 43, 'aut_perms': [60197476908028041589252501479315072301966960020950554, 28777274221764409170536344555749746427399593748535287, 40705315137482328322477777740646444867843071102591777, 37938433234031853022693861693502638598152386285112679, 50559876037598016864397153403130219284565857990999349], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 15, 1, 1], [2, 15, 2, 1], [2, 45, 1, 1], [2, 45, 2, 1], [2, 75, 2, 1], [2, 135, 1, 1], [2, 225, 1, 1], [2, 225, 2, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 40, 2, 1], [3, 160, 4, 1], [4, 5, 1, 2], [4, 15, 1, 2], [4, 75, 2, 2], [4, 90, 1, 2], [4, 225, 1, 2], [4, 225, 2, 2], [4, 270, 1, 2], [4, 450, 1, 6], [4, 675, 1, 2], [4, 1350, 1, 6], [5, 4, 1, 1], [5, 144, 1, 1], [5, 576, 1, 1], [6, 20, 2, 1], [6, 60, 4, 1], [6, 120, 2, 2], [6, 180, 2, 1], [6, 200, 2, 1], [6, 300, 4, 1], [6, 360, 2, 1], [6, 480, 4, 1], [6, 600, 2, 2], [6, 800, 4, 1], [6, 900, 2, 1], [6, 1800, 2, 1], [6, 2400, 4, 1], [10, 12, 1, 1], [10, 60, 2, 1], [10, 180, 1, 1], [10, 180, 2, 1], [10, 432, 1, 1], [10, 540, 1, 1], [10, 720, 1, 1], [10, 1728, 1, 1], [10, 2160, 1, 1], [12, 20, 2, 2], [12, 200, 2, 2], [12, 300, 4, 2], [12, 360, 2, 2], [12, 600, 2, 4], [12, 800, 4, 2], [12, 900, 2, 2], [12, 1800, 2, 8], [12, 2400, 4, 2], [15, 16, 2, 1], [15, 160, 2, 1], [15, 576, 2, 1], [15, 640, 4, 1], [15, 2304, 2, 1], [20, 360, 1, 2], [20, 720, 1, 2], [20, 1080, 1, 2], [20, 2160, 1, 2], [30, 240, 4, 1], [30, 480, 2, 2], [30, 720, 2, 1], [30, 1440, 2, 1], [30, 1920, 4, 1], [30, 2880, 2, 1], [60, 1440, 2, 2], [60, 2880, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'F_5.A_6.C_2^2\\times S_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': 120, 'autcentquo_group': None, 'autcentquo_hash': 3309493389982338751, 'autcentquo_nilpotent': False, 'autcentquo_order': 691200, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5.A_6.C_2^2\\times S_4', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 5, 1], [2, 15, 3], [2, 45, 3], [2, 75, 2], [2, 135, 1], [2, 225, 3], [2, 675, 1], [3, 4, 2], [3, 40, 2], [3, 160, 4], [4, 5, 2], [4, 15, 2], [4, 75, 4], [4, 90, 2], [4, 225, 6], [4, 270, 2], [4, 450, 6], [4, 675, 2], [4, 1350, 6], [5, 4, 1], [5, 144, 1], [5, 576, 1], [6, 20, 2], [6, 60, 4], [6, 120, 4], [6, 180, 2], [6, 200, 2], [6, 300, 4], [6, 360, 2], [6, 480, 4], [6, 600, 4], [6, 800, 4], [6, 900, 2], [6, 1800, 2], [6, 2400, 4], [10, 12, 1], [10, 60, 2], [10, 180, 3], [10, 432, 1], [10, 540, 1], [10, 720, 1], [10, 1728, 1], [10, 2160, 1], [12, 20, 4], [12, 200, 4], [12, 300, 8], [12, 360, 4], [12, 600, 8], [12, 800, 8], [12, 900, 4], [12, 1800, 16], [12, 2400, 8], [15, 16, 2], [15, 160, 2], [15, 576, 2], [15, 640, 4], [15, 2304, 2], [20, 360, 2], [20, 720, 2], [20, 1080, 2], [20, 2160, 2], [30, 240, 4], [30, 480, 4], [30, 720, 2], [30, 1440, 2], [30, 1920, 4], [30, 2880, 2], [60, 1440, 4], [60, 2880, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '172800.bm', 'commutator_count': 1, 'commutator_label': '7200.dn', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '360.118'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 39, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['20.3', 1], ['720.763', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 15, 1, 3], [2, 45, 1, 3], [2, 75, 1, 2], [2, 135, 1, 1], [2, 225, 1, 3], [2, 675, 1, 1], [3, 4, 2, 1], [3, 40, 1, 2], [3, 160, 2, 2], [4, 5, 2, 1], [4, 15, 2, 1], [4, 75, 2, 2], [4, 90, 1, 2], [4, 225, 2, 3], [4, 270, 1, 2], [4, 450, 1, 2], [4, 450, 2, 2], [4, 675, 2, 1], [4, 1350, 1, 2], [4, 1350, 2, 2], [5, 4, 1, 1], [5, 144, 1, 1], [5, 576, 1, 1], [6, 20, 2, 1], [6, 60, 2, 2], [6, 120, 1, 4], [6, 180, 2, 1], [6, 200, 1, 2], [6, 300, 2, 2], [6, 360, 1, 2], [6, 480, 2, 2], [6, 600, 1, 4], [6, 800, 2, 2], [6, 900, 2, 1], [6, 1800, 1, 2], [6, 2400, 2, 2], [10, 12, 1, 1], [10, 60, 1, 2], [10, 180, 1, 3], [10, 432, 1, 1], [10, 540, 1, 1], [10, 720, 1, 1], [10, 1728, 1, 1], [10, 2160, 1, 1], [12, 20, 4, 1], [12, 200, 2, 2], [12, 300, 4, 2], [12, 360, 2, 2], [12, 600, 2, 4], [12, 800, 4, 2], [12, 900, 4, 1], [12, 1800, 2, 4], [12, 1800, 4, 2], [12, 2400, 4, 2], [15, 16, 2, 1], [15, 160, 1, 2], [15, 576, 2, 1], [15, 640, 2, 2], [15, 2304, 2, 1], [20, 360, 1, 2], [20, 720, 2, 1], [20, 1080, 1, 2], [20, 2160, 2, 1], [30, 240, 2, 2], [30, 480, 1, 4], [30, 720, 2, 1], [30, 1440, 1, 2], [30, 1920, 2, 2], [30, 2880, 2, 1], [60, 1440, 2, 2], [60, 2880, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 60, 'exponents_of_order': [8, 3, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[60, 1, 4], [108, 1, 2], [120, 1, 2], [192, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '172800.bm', 'hash': 5545698576758383175, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 30, 5, 2, 4, 2, 3, 12], 'inner_gens': [[186810624000, 100126620872, 4440240, 274467916800, 4032000, 7983360, 6706022400, 93409344572], [274467916800, 6721308872, 14595840, 87657292800, 730800, 1174320, 174356582400, 262014606136], [186810624000, 6709656392, 4440240, 274467916800, 730800, 1174320, 100111334400, 181063336172], [186810624000, 174371868872, 4440240, 274467916800, 4032000, 7983360, 267761894400, 262017907772], [186810624000, 6707196872, 11617200, 274467916800, 4032000, 7983360, 100111334400, 181066637372], [186810624000, 6717352472, 14595840, 274467916800, 4032000, 7983360, 100111334400, 181066637372], [274467916800, 267777180872, 4440240, 87657292800, 4032000, 7983360, 100111334400, 93409344572], [87657292800, 100112509211, 11617200, 186810624000, 4032000, 7983360, 174356582400, 181066637372]], 'inner_hash': 5545698576758383175, 'inner_nilpotent': False, 'inner_order': 172800, 'inner_split': True, 'inner_tex': 'A_4\\times F_5\\times S_6', 'inner_used': [1, 2, 3, 5, 8], 'irrC_degree': 60, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': 60, 'irrep_stats': [[1, 24], [3, 8], [4, 6], [5, 48], [9, 24], [10, 24], [12, 2], [15, 16], [16, 12], [20, 12], [27, 8], [30, 8], [36, 6], [40, 6], [48, 4], [60, 4], [64, 3], [108, 2], [120, 2], [192, 1]], 'label': '172800.bm', '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': 'A4*F5*S6', '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, 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': 120, 'number_characteristic_subgroups': 42, 'number_conjugacy_classes': 220, 'number_divisions': 132, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 5443, 'number_subgroup_classes': 10011, 'number_subgroups': 2933820, 'old_label': None, 'order': 172800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1823], [3, 728], [4, 14560], [5, 724], [6, 25960], [10, 6252], [12, 67520], [15, 8672], [20, 8640], [30, 20640], [60, 17280]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [691, 0], 'outer_gens': [[186810624000, 6721309193, 4440240, 274467916800, 4032000, 7983360, 100111334400, 181066636806], [274467916800, 181077891272, 4440240, 186810624000, 4032000, 7983360, 262013875200, 6710054972]], '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': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [3, 4], [4, 4], [5, 8], [6, 2], [8, 2], [9, 4], [10, 16], [12, 2], [15, 8], [16, 2], [18, 6], [20, 14], [27, 4], [30, 8], [32, 3], [36, 4], [40, 8], [48, 2], [54, 2], [60, 6], [64, 2], [72, 2], [80, 2], [96, 1], [108, 2], [120, 2], [128, 1], [192, 1]], 'representations': {'Perm': {'d': 15, 'gens': [186810624000, 6721308872, 4440240, 274467916800, 4032000, 7983360, 100111334400, 181066637372]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 450, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4\\times F_5\\times S_6', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
