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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '172800.n', 'ambient_counter': 14, 'ambient_order': 172800, 'ambient_tex': 'A_4\\times S_5^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 480, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '172800.n.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.a1', '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': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9600.bz', 'subgroup_hash': 1428115898619280212, 'subgroup_order': 9600, 'subgroup_tex': 'C_2^2\\times F_5\\times S_5', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '172800.n', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '43200.A', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '6.F'], 'contains': ['36.A', '36.B', '36.C', '36.D', '36.E', '36.G', '36.H', '90.L', '90.M', '108.a1', '180.BN'], 'core': '360.A', 'coset_action_label': None, 'count': 12, 'diagramx': [8765, -1, 1797, -1], 'generators': [64313631515, 1520467200, 69502815523, 482630400, 1520640120, 482716080, 81956857120], 'label': '172800.n.18.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.F', 'old_label': '18.a1', 'projective_image': '172800.n', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '7200.cr'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [20, 20, 12, 20], 'aut_gens': [[3751320, 62796884667, 137640, 482630400, 3710181, 479042040, 3628800], [482752920, 69023905465, 3790200, 3628800, 75247383752, 479097480, 482630400], [479124120, 81956948685, 50400, 482630400, 69502941630, 3760560, 479001600], [482721960, 75247262803, 482768040, 479001600, 482756525, 3669240, 482630400], [479093160, 63272222800, 3715920, 482630400, 482677322, 3796680, 479001600]], 'aut_group': None, 'aut_hash': 9196359629749534820, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 230400, 'aut_permdeg': 60, 'aut_perms': [1845841853127156957762700145120502377055779253379703705548741052499841196320666830, 767718457453766647075035477502211940858348910470653257984070341556390722095884618, 1062518277984084901697603070289321660464742157176503152840273527055115306580213002, 1916123433412553127434294155549314971967235706001479255880867765843014724816296135], 'aut_phi_ratio': 90.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 5, 1, 1], [2, 5, 3, 1], [2, 10, 4, 1], [2, 15, 1, 1], [2, 15, 3, 1], [2, 50, 4, 1], [2, 75, 1, 1], [2, 75, 3, 1], [3, 20, 1, 1], [4, 5, 4, 2], [4, 30, 4, 1], [4, 50, 4, 2], [4, 75, 4, 2], [4, 150, 4, 3], [5, 4, 1, 1], [5, 24, 1, 1], [5, 96, 1, 1], [6, 20, 3, 1], [6, 20, 4, 1], [6, 100, 1, 1], [6, 100, 3, 1], [6, 100, 4, 1], [10, 4, 3, 1], [10, 24, 3, 1], [10, 40, 4, 1], [10, 60, 1, 1], [10, 60, 3, 1], [10, 96, 3, 1], [10, 120, 1, 1], [10, 120, 3, 1], [12, 100, 4, 4], [15, 80, 1, 1], [20, 120, 4, 3], [30, 80, 3, 1], [30, 80, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_5.S_5\\times C_2^2:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '96.227', 'autcent_hash': 227, 'autcent_nilpotent': False, 'autcent_order': 96, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^2:S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '2400.db', 'autcentquo_hash': 3070016846447328869, 'autcentquo_nilpotent': False, 'autcentquo_order': 2400, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 5, 4], [2, 10, 4], [2, 15, 4], [2, 50, 4], [2, 75, 4], [3, 20, 1], [4, 5, 8], [4, 30, 4], [4, 50, 8], [4, 75, 8], [4, 150, 12], [5, 4, 1], [5, 24, 1], [5, 96, 1], [6, 20, 7], [6, 100, 8], [10, 4, 3], [10, 24, 3], [10, 40, 4], [10, 60, 4], [10, 96, 3], [10, 120, 4], [12, 100, 16], [15, 80, 1], [20, 120, 12], [30, 80, 7]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '2400.db', 'commutator_count': 1, 'commutator_label': '300.22', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '60.5'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 52, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['120.34', 1], ['2.1', 2], ['20.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 5, 1, 4], [2, 10, 1, 4], [2, 15, 1, 4], [2, 50, 1, 4], [2, 75, 1, 4], [3, 20, 1, 1], [4, 5, 2, 4], [4, 30, 1, 4], [4, 50, 2, 4], [4, 75, 2, 4], [4, 150, 1, 4], [4, 150, 2, 4], [5, 4, 1, 1], [5, 24, 1, 1], [5, 96, 1, 1], [6, 20, 1, 7], [6, 100, 1, 8], [10, 4, 1, 3], [10, 24, 1, 3], [10, 40, 1, 4], [10, 60, 1, 4], [10, 96, 1, 3], [10, 120, 1, 4], [12, 100, 2, 8], [15, 80, 1, 1], [20, 120, 1, 4], [20, 120, 2, 4], [30, 80, 1, 7]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 11098143840, 'exponent': 60, 'exponents_of_order': [7, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '9600.bz', 'hash': 1428115898619280212, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [5, 30, 4, 1, 4, 2, 1], 'inner_gens': [[3751320, 62796884667, 50400, 482630400, 3754941, 479133360, 3628800], [3751320, 62796884667, 87120, 482630400, 69023829030, 479169480, 3628800], [3800160, 62796915627, 137640, 482630400, 3643941, 479042040, 3628800], [3751320, 62796884667, 137640, 482630400, 3710181, 479042040, 3628800], [3720360, 81477912401, 161400, 482630400, 3710181, 479097480, 3628800], [3685680, 62796964467, 137640, 482630400, 3675741, 479042040, 3628800], [3751320, 62796884667, 137640, 482630400, 3710181, 479042040, 3628800]], 'inner_hash': 3070016846447328869, 'inner_nilpotent': False, 'inner_order': 2400, 'inner_split': True, 'inner_tex': 'F_5\\times S_5', 'inner_used': [1, 2, 3, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [4, 40], [5, 32], [6, 16], [16, 8], [20, 8], [24, 4]], 'label': '9600.bz', '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': 'C2^2*F5*S5', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 47, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 140, 'number_divisions': 112, 'number_normal_subgroups': 166, 'number_subgroup_autclasses': 887, 'number_subgroup_classes': 4469, 'number_subgroups': 152892, 'old_label': None, 'order': 9600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 623], [3, 20], [4, 2960], [5, 124], [6, 940], [10, 1252], [12, 1600], [15, 80], [20, 1440], [30, 560]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[479124120, 62796884667, 137640, 482630400, 3710181, 3669240, 479001600], [482752920, 62796884667, 137640, 479001600, 3710181, 3669240, 482630400], [3751320, 63275886267, 479139240, 482630400, 3710181, 479042040, 3628800], [3751320, 62793255867, 3766440, 482630400, 3710181, 479042040, 3628800], [3751320, 62796884667, 3766440, 482630400, 81381, 479042040, 3628800], [3751320, 62796884667, 479139240, 482630400, 482711781, 479042040, 3628800]], 'outer_group': '96.227', 'outer_hash': 227, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 8, 'outer_perms': [23737, 843, 16687, 5176, 16703, 11536], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2:S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 24], [5, 16], [6, 8], [8, 8], [10, 8], [12, 4], [16, 8], [20, 8], [24, 4]], 'representations': {'Perm': {'d': 14, 'gens': [3751320, 62796884667, 137640, 482630400, 3710181, 479042040, 3628800]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times F_5\\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': '12.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [24, 12, 30], 'aut_gens': [[1037836800, 562549685, 482630400, 1476921600, 82914956789], [1520467200, 43547174, 1037836800, 1476921600, 69100075708], [1520467200, 70021735470, 482630400, 518918400, 82951325429], [482630400, 958003926, 1520467200, 1476921600, 75766256801]], 'aut_group': '691200.g', 'aut_hash': 1857085433632322154, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 691200, 'aut_permdeg': 28, 'aut_perms': [5238303322673270494860645413, 281936752526667029531280683115, 2422436678282011682606410041], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 10, 2, 1], [2, 15, 2, 1], [2, 30, 2, 1], [2, 45, 2, 1], [2, 100, 1, 1], [2, 150, 2, 1], [2, 225, 1, 1], [2, 300, 1, 1], [2, 450, 2, 1], [2, 675, 1, 1], [3, 4, 2, 1], [3, 20, 2, 1], [3, 80, 4, 1], [3, 400, 1, 1], [3, 1600, 2, 1], [4, 30, 2, 1], [4, 90, 2, 1], [4, 300, 2, 1], [4, 450, 2, 1], [4, 900, 1, 1], [4, 900, 2, 1], [4, 1350, 2, 1], [4, 2700, 1, 1], [5, 24, 2, 1], [5, 576, 1, 1], [6, 20, 2, 1], [6, 40, 4, 1], [6, 60, 2, 2], [6, 60, 4, 1], [6, 80, 4, 1], [6, 200, 2, 2], [6, 300, 2, 2], [6, 400, 1, 1], [6, 400, 2, 2], [6, 600, 2, 2], [6, 600, 4, 1], [6, 800, 4, 2], [6, 900, 2, 3], [6, 1200, 1, 2], [6, 1200, 2, 1], [6, 1200, 4, 2], [6, 1600, 2, 1], [6, 1600, 4, 1], [10, 72, 2, 1], [10, 240, 2, 1], [10, 360, 2, 1], [10, 720, 2, 1], [10, 1080, 2, 1], [10, 1728, 1, 1], [12, 120, 4, 1], [12, 600, 2, 2], [12, 1200, 4, 1], [12, 1800, 2, 2], [12, 1800, 4, 1], [12, 2400, 4, 2], [12, 3600, 2, 1], [15, 96, 4, 1], [15, 480, 2, 1], [15, 1920, 4, 1], [15, 2304, 2, 1], [20, 720, 2, 1], [20, 2160, 2, 1], [30, 480, 2, 1], [30, 960, 4, 1], [30, 1440, 2, 2], [30, 1440, 4, 1], [30, 1920, 4, 1], [60, 2880, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4\\times S_5\\wr C_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': 120, 'autcentquo_group': '691200.g', 'autcentquo_hash': 1857085433632322154, 'autcentquo_nilpotent': False, 'autcentquo_order': 691200, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_5\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 10, 2], [2, 15, 2], [2, 30, 2], [2, 45, 2], [2, 100, 1], [2, 150, 2], [2, 225, 1], [2, 300, 1], [2, 450, 2], [2, 675, 1], [3, 4, 2], [3, 20, 2], [3, 80, 4], [3, 400, 1], [3, 1600, 2], [4, 30, 2], [4, 90, 2], [4, 300, 2], [4, 450, 2], [4, 900, 3], [4, 1350, 2], [4, 2700, 1], [5, 24, 2], [5, 576, 1], [6, 20, 2], [6, 40, 4], [6, 60, 8], [6, 80, 4], [6, 200, 4], [6, 300, 4], [6, 400, 5], [6, 600, 8], [6, 800, 8], [6, 900, 6], [6, 1200, 12], [6, 1600, 6], [10, 72, 2], [10, 240, 2], [10, 360, 2], [10, 720, 2], [10, 1080, 2], [10, 1728, 1], [12, 120, 4], [12, 600, 4], [12, 1200, 4], [12, 1800, 8], [12, 2400, 8], [12, 3600, 2], [15, 96, 4], [15, 480, 2], [15, 1920, 4], [15, 2304, 2], [20, 720, 2], [20, 2160, 2], [30, 480, 2], [30, 960, 4], [30, 1440, 8], [30, 1920, 4], [60, 2880, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '172800.n', 'commutator_count': 1, 'commutator_label': '14400.cf', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '60.5', '60.5'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 14, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['120.34', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 10, 1, 2], [2, 15, 1, 2], [2, 30, 1, 2], [2, 45, 1, 2], [2, 100, 1, 1], [2, 150, 1, 2], [2, 225, 1, 1], [2, 300, 1, 1], [2, 450, 1, 2], [2, 675, 1, 1], [3, 4, 2, 1], [3, 20, 1, 2], [3, 80, 2, 2], [3, 400, 1, 1], [3, 1600, 2, 1], [4, 30, 1, 2], [4, 90, 1, 2], [4, 300, 1, 2], [4, 450, 1, 2], [4, 900, 1, 3], [4, 1350, 1, 2], [4, 2700, 1, 1], [5, 24, 1, 2], [5, 576, 1, 1], [6, 20, 1, 2], [6, 40, 2, 2], [6, 60, 1, 4], [6, 60, 2, 2], [6, 80, 2, 2], [6, 200, 1, 4], [6, 300, 1, 4], [6, 400, 1, 3], [6, 400, 2, 1], [6, 600, 1, 4], [6, 600, 2, 2], [6, 800, 2, 4], [6, 900, 1, 4], [6, 900, 2, 1], [6, 1200, 1, 4], [6, 1200, 2, 4], [6, 1600, 2, 3], [10, 72, 1, 2], [10, 240, 1, 2], [10, 360, 1, 2], [10, 720, 1, 2], [10, 1080, 1, 2], [10, 1728, 1, 1], [12, 120, 2, 2], [12, 600, 1, 4], [12, 1200, 2, 2], [12, 1800, 1, 4], [12, 1800, 2, 2], [12, 2400, 2, 4], [12, 3600, 2, 1], [15, 96, 2, 2], [15, 480, 1, 2], [15, 1920, 2, 2], [15, 2304, 2, 1], [20, 720, 1, 2], [20, 2160, 1, 2], [30, 480, 1, 2], [30, 960, 2, 2], [30, 1440, 1, 4], [30, 1440, 2, 2], [30, 1920, 2, 2], [60, 2880, 2, 2]], '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': [[48, 1, 4], [60, 1, 8], [72, 1, 4], [75, 1, 4], [90, 1, 4], [108, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '172800.n', 'hash': 5516603464045726411, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 6, 2, 3, 30], 'inner_gens': [[1037836800, 43631285, 482630400, 958003200, 81554156789], [1520467200, 562549685, 1037836800, 958003200, 70460874145], [1037836800, 958088885, 482630400, 43545600, 81993241589], [1520467200, 43631285, 1037836800, 1476921600, 81554156789], [482630400, 562469054, 1520467200, 43545600, 82914956789]], 'inner_hash': 5516603464045726411, 'inner_nilpotent': False, 'inner_order': 172800, 'inner_split': True, 'inner_tex': 'A_4\\times S_5^2', 'inner_used': [1, 2, 5], 'irrC_degree': 48, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 48, 'irrep_stats': [[1, 12], [3, 4], [4, 24], [5, 24], [6, 12], [12, 8], [15, 8], [16, 12], [18, 4], [20, 24], [24, 12], [25, 12], [30, 12], [36, 3], [48, 4], [60, 8], [72, 4], [75, 4], [90, 4], [108, 1]], 'label': '172800.n', '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*S5^2', 'ngens': 5, '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': 84, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 196, 'number_divisions': 147, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 5752, 'number_subgroup_classes': 12228, 'number_subgroups': 5495748, 'old_label': None, 'order': 172800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 2703], [3, 3968], [4, 9840], [5, 624], [6, 45600], [10, 6672], [12, 48480], [15, 13632], [20, 5760], [30, 24000], [60, 11520]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [62793296807, 0], 'outer_gens': [[1037836800, 562504334, 482630400, 1476921600, 82914997108], [1520467200, 519004085, 482630400, 1001548800, 82432326389]], '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': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 8], [5, 8], [6, 4], [8, 8], [10, 8], [12, 12], [15, 8], [16, 4], [18, 4], [20, 8], [24, 4], [25, 4], [30, 4], [32, 4], [36, 1], [40, 8], [48, 8], [50, 4], [60, 12], [72, 5], [75, 4], [90, 4], [108, 1]], 'representations': {'Perm': {'d': 14, 'gens': [1037836800, 562549685, 482630400, 1476921600, 82914956789]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 675, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4\\times S_5^2', 'transitive_degree': 100, 'wreath_data': None, 'wreath_product': False}
