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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '2239488000.z', 'ambient_counter': 26, 'ambient_order': 2239488000, 'ambient_tex': 'C_2^3.A_6\\wr S_3', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 4, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '2239488000.z.559872000._.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '559872000.A', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '559872000.o', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 559872000, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times A_6\\wr S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': None, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '2239488000.z', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [403, 94], 'label': '2239488000.z.559872000._.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '559872000.A', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '559872000._.A', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, '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': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[2255448845488648002505, 27083450809584893611593], [1406494825782932879305, 192418369598765457549513], [12705018019492013555785, 184497115628754700455753], [1328513536043053199305, 28258542835209663787593], [1362703027787542067785, 36204657660469718789193], [2255494019722875953305, 183219438052775238957513], [391213352926206686499145, 442518308082401523361353], [2255448845488648002505, 81237192437492657677738], [285732346819303725869069, 27083450809584893611969], [2255448845488648002599, 27083450809584893611660], [2255448845488648002505, 27083450809584893611969], [2255448845488648002505, 27083450809584893611593], [2255448845488648002955, 27083450809584893611593], [2872324836062865393865, 52481279231006026061098], [236106157881449615639065, 82681019126509443857578]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 8957952000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 135, 1, 4], [2, 270, 1, 2], [2, 2160, 2, 1], [2, 6075, 1, 4], [2, 12150, 1, 2], [2, 91125, 1, 2], [2, 97200, 2, 1], [2, 273375, 1, 2], [3, 120, 2, 1], [3, 4800, 2, 1], [3, 9600, 1, 1], [3, 64000, 2, 1], [3, 192000, 2, 1], [3, 1036800, 1, 1], [4, 270, 1, 4], [4, 540, 1, 2], [4, 2160, 2, 1], [4, 24300, 1, 12], [4, 48600, 1, 2], [4, 97200, 2, 3], [4, 194400, 2, 2], [4, 546750, 1, 4], [4, 729000, 1, 2], [4, 1093500, 1, 6], [4, 2187000, 1, 4], [4, 4374000, 2, 2], [4, 8748000, 2, 2], [5, 216, 2, 1], [5, 15552, 2, 1], [5, 31104, 1, 1], [5, 373248, 2, 1], [5, 1119744, 2, 1], [6, 120, 2, 3], [6, 240, 2, 2], [6, 4800, 2, 3], [6, 9600, 1, 3], [6, 9600, 2, 4], [6, 10800, 2, 8], [6, 64000, 2, 1], [6, 86400, 4, 2], [6, 192000, 2, 5], [6, 216000, 2, 4], [6, 243000, 2, 4], [6, 384000, 2, 2], [6, 432000, 1, 4], [6, 432000, 2, 4], [6, 486000, 2, 2], [6, 1036800, 1, 1], [6, 3456000, 4, 2], [6, 3888000, 4, 1], [6, 46656000, 1, 2], [8, 194400, 2, 2], [8, 8748000, 2, 2], [8, 17496000, 2, 2], [9, 41472000, 2, 1], [10, 216, 2, 3], [10, 432, 2, 2], [10, 15552, 2, 3], [10, 19440, 2, 8], [10, 31104, 1, 3], [10, 31104, 2, 4], [10, 155520, 4, 2], [10, 373248, 2, 1], [10, 437400, 2, 4], [10, 699840, 2, 4], [10, 874800, 2, 2], [10, 1119744, 2, 5], [10, 1399680, 1, 4], [10, 1399680, 2, 4], [10, 2239488, 2, 2], [10, 6998400, 4, 1], [10, 11197440, 4, 2], [12, 21600, 2, 8], [12, 86400, 4, 2], [12, 432000, 2, 4], [12, 864000, 1, 4], [12, 864000, 2, 4], [12, 972000, 2, 12], [12, 1944000, 2, 2], [12, 3456000, 4, 2], [12, 3888000, 4, 3], [12, 7776000, 4, 2], [12, 93312000, 1, 2], [15, 17280, 4, 1], [15, 345600, 4, 1], [15, 622080, 4, 1], [15, 691200, 2, 1], [15, 1244160, 2, 1], [15, 74649600, 2, 1], [18, 41472000, 2, 1], [20, 38880, 2, 8], [20, 155520, 4, 2], [20, 1399680, 2, 4], [20, 1749600, 2, 12], [20, 2799360, 1, 4], [20, 2799360, 2, 4], [20, 3499200, 2, 2], [20, 6998400, 4, 3], [20, 11197440, 4, 2], [20, 13996800, 4, 2], [24, 7776000, 4, 2], [30, 17280, 4, 7], [30, 345600, 4, 3], [30, 622080, 4, 3], [30, 691200, 2, 3], [30, 691200, 4, 4], [30, 777600, 4, 8], [30, 1244160, 2, 3], [30, 1244160, 4, 4], [30, 6220800, 8, 2], [30, 74649600, 2, 1], [40, 13996800, 4, 2], [60, 1555200, 4, 8], [60, 6220800, 8, 2]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 135, 4], [2, 270, 2], [2, 2160, 2], [2, 6075, 4], [2, 12150, 2], [2, 91125, 2], [2, 97200, 2], [2, 273375, 2], [3, 120, 2], [3, 4800, 2], [3, 9600, 1], [3, 64000, 2], [3, 192000, 2], [3, 1036800, 1], [4, 270, 4], [4, 540, 2], [4, 2160, 2], [4, 24300, 12], [4, 48600, 2], [4, 97200, 6], [4, 194400, 4], [4, 546750, 4], [4, 729000, 2], [4, 1093500, 6], [4, 2187000, 4], [4, 4374000, 4], [4, 8748000, 4], [5, 216, 2], [5, 15552, 2], [5, 31104, 1], [5, 373248, 2], [5, 1119744, 2], [6, 120, 6], [6, 240, 4], [6, 4800, 6], [6, 9600, 11], [6, 10800, 16], [6, 64000, 2], [6, 86400, 8], [6, 192000, 10], [6, 216000, 8], [6, 243000, 8], [6, 384000, 4], [6, 432000, 12], [6, 486000, 4], [6, 1036800, 1], [6, 3456000, 8], [6, 3888000, 4], [6, 46656000, 2], [8, 194400, 4], [8, 8748000, 4], [8, 17496000, 4], [9, 41472000, 2], [10, 216, 6], [10, 432, 4], [10, 15552, 6], [10, 19440, 16], [10, 31104, 11], [10, 155520, 8], [10, 373248, 2], [10, 437400, 8], [10, 699840, 8], [10, 874800, 4], [10, 1119744, 10], [10, 1399680, 12], [10, 2239488, 4], [10, 6998400, 4], [10, 11197440, 8], [12, 21600, 16], [12, 86400, 8], [12, 432000, 8], [12, 864000, 12], [12, 972000, 24], [12, 1944000, 4], [12, 3456000, 8], [12, 3888000, 12], [12, 7776000, 8], [12, 93312000, 2], [15, 17280, 4], [15, 345600, 4], [15, 622080, 4], [15, 691200, 2], [15, 1244160, 2], [15, 74649600, 2], [18, 41472000, 2], [20, 38880, 16], [20, 155520, 8], [20, 1399680, 8], [20, 1749600, 24], [20, 2799360, 12], [20, 3499200, 4], [20, 6998400, 12], [20, 11197440, 8], [20, 13996800, 8], [24, 7776000, 8], [30, 17280, 28], [30, 345600, 12], [30, 622080, 12], [30, 691200, 22], [30, 777600, 32], [30, 1244160, 22], [30, 6220800, 16], [30, 74649600, 2], [40, 13996800, 8], [60, 1555200, 32], [60, 6220800, 16]], 'center_label': '2.1', 'center_order': None, 'central_product': None, 'central_quotient': '1119744000.bc', 'commutator_count': 1, 'commutator_label': '559872000.l', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '360.118', '360.118', '360.118'], 'composition_length': 8, 'conjugacy_classes_known': False, 'counter': 26, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 135, 1, 4], [2, 270, 1, 2], [2, 2160, 1, 2], [2, 6075, 1, 4], [2, 12150, 1, 2], [2, 91125, 1, 2], [2, 97200, 1, 2], [2, 273375, 1, 2], [3, 120, 1, 2], [3, 4800, 1, 2], [3, 9600, 1, 1], [3, 64000, 1, 2], [3, 192000, 1, 2], [3, 1036800, 1, 1], [4, 270, 1, 4], [4, 540, 1, 2], [4, 2160, 1, 2], [4, 24300, 1, 12], [4, 48600, 1, 2], [4, 97200, 1, 6], [4, 194400, 1, 4], [4, 546750, 1, 4], [4, 729000, 1, 2], [4, 1093500, 1, 6], [4, 2187000, 1, 4], [4, 4374000, 1, 4], [4, 8748000, 1, 4], [5, 216, 2, 1], [5, 15552, 2, 1], [5, 31104, 1, 1], [5, 373248, 2, 1], [5, 1119744, 2, 1], [6, 120, 1, 6], [6, 240, 1, 4], [6, 4800, 1, 6], [6, 9600, 1, 11], [6, 10800, 1, 16], [6, 64000, 1, 2], [6, 86400, 1, 8], [6, 192000, 1, 10], [6, 216000, 1, 8], [6, 243000, 1, 8], [6, 384000, 1, 4], [6, 432000, 1, 12], [6, 486000, 1, 4], [6, 1036800, 1, 1], [6, 3456000, 1, 8], [6, 3888000, 1, 4], [6, 46656000, 1, 2], [8, 194400, 1, 4], [8, 8748000, 1, 4], [8, 17496000, 1, 4], [9, 41472000, 1, 2], [10, 216, 2, 3], [10, 432, 2, 2], [10, 15552, 2, 3], [10, 19440, 2, 8], [10, 31104, 1, 3], [10, 31104, 2, 4], [10, 155520, 2, 4], [10, 373248, 2, 1], [10, 437400, 2, 4], [10, 699840, 2, 4], [10, 874800, 2, 2], [10, 1119744, 2, 5], [10, 1399680, 1, 4], [10, 1399680, 2, 4], [10, 2239488, 2, 2], [10, 6998400, 2, 2], [10, 11197440, 2, 4], [12, 21600, 1, 16], [12, 86400, 1, 8], [12, 432000, 1, 8], [12, 864000, 1, 12], [12, 972000, 1, 24], [12, 1944000, 1, 4], [12, 3456000, 1, 8], [12, 3888000, 1, 12], [12, 7776000, 1, 8], [12, 93312000, 1, 2], [15, 17280, 2, 2], [15, 345600, 2, 2], [15, 622080, 2, 2], [15, 691200, 2, 1], [15, 1244160, 1, 2], [15, 74649600, 2, 1], [18, 41472000, 1, 2], [20, 38880, 2, 8], [20, 155520, 2, 4], [20, 1399680, 2, 4], [20, 1749600, 2, 12], [20, 2799360, 1, 4], [20, 2799360, 2, 4], [20, 3499200, 2, 2], [20, 6998400, 2, 6], [20, 11197440, 2, 4], [20, 13996800, 2, 4], [24, 7776000, 1, 8], [30, 17280, 2, 14], [30, 345600, 2, 6], [30, 622080, 2, 6], [30, 691200, 2, 11], [30, 777600, 2, 16], [30, 1244160, 1, 6], [30, 1244160, 2, 8], [30, 6220800, 2, 8], [30, 74649600, 2, 1], [40, 13996800, 2, 4], [60, 1555200, 2, 16], [60, 6220800, 2, 8]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 360, 'exponents_of_order': [13, 7, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[15, 1, 4], [24, 1, 4], [27, 1, 2], [30, 1, 4], [48, 1, 2], [54, 1, 1], [60, 1, 1], [75, 1, 4], [150, 1, 5], [192, 1, 4], [240, 1, 12], [243, 1, 2], [270, 1, 6], [300, 1, 8], [375, 1, 8], [384, 1, 5], [432, 1, 6], [480, 1, 6], [486, 1, 1], [540, 1, 3], [600, 1, 9], [675, 1, 4], [750, 1, 6], [960, 1, 8], [1200, 1, 10], [1215, 1, 4], [1350, 1, 5], [1500, 1, 9], [1536, 1, 8], [1728, 1, 4], [1920, 1, 14], [1944, 1, 4], [2160, 1, 12], [2187, 1, 2], [2400, 1, 16], [2430, 1, 4], [2700, 1, 8], [3000, 1, 4], [3072, 1, 2], [3456, 1, 5], [3840, 1, 5], [3888, 1, 2], [4320, 1, 6], [4800, 1, 2], [4860, 1, 1], [5400, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2239488000.z', 'hash': 2878879580944830932, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_2^2.A_6\\wr S_3', 'inner_used': None, 'irrC_degree': 15, 'irrQ_degree': 15, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 4], [2, 2], [3, 4], [15, 16], [24, 16], [27, 8], [30, 12], [48, 4], [54, 2], [60, 2], [75, 16], [125, 8], [150, 12], [192, 16], [240, 32], [243, 8], [250, 4], [270, 16], [300, 24], [375, 24], [384, 12], [432, 16], [480, 16], [486, 2], [512, 8], [540, 8], [600, 34], [675, 16], [729, 4], [750, 20], [960, 32], [1000, 4], [1024, 4], [1200, 24], [1215, 16], [1350, 12], [1458, 2], [1500, 28], [1536, 24], [1728, 16], [1920, 40], [1944, 16], [2000, 2], [2160, 32], [2187, 4], [2400, 48], [2430, 12], [2700, 24], [3000, 8], [3072, 4], [3456, 12], [3840, 12], [3888, 4], [4320, 16], [4800, 4], [4860, 2], [5400, 2]], 'label': '2239488000.z', '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': 'C2^3.A6wrS3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[262544767578789888, 135583801881274831], [326593531734835968, 1672909502954276911], [326702424607383294, 2167693564250499175], [326814529247398320, 212891612791878847], [313884593775306174, 206572842885963007], [1975580037457903488, 1602126303138851887], [880417113288826368, 1603847112131112001], [262544767578789888, 1096023738638678041], [1857860060261595366, 135583801881274831], [262544767578789888, 135583801881274831], [262544767578789889, 135583801881274831], [1430337775697804928, 465632861867003191], [1771732797342249048, 1601054189612138167]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 2239488000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 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'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 135, 2], [2, 1080, 2], [2, 6075, 2], [2, 48600, 2], [2, 91125, 2], [3, 120, 2], [3, 4800, 2], [3, 9600, 1], [3, 64000, 2], [3, 192000, 2], [3, 259200, 1], [4, 270, 2], [4, 24300, 4], [4, 48600, 2], [4, 97200, 2], [4, 546750, 2], [4, 729000, 2], [4, 1093500, 2], [4, 2187000, 2], [4, 4374000, 2], [5, 216, 2], [5, 15552, 2], [5, 31104, 1], [5, 373248, 2], [5, 1119744, 2], [6, 120, 2], [6, 4800, 2], [6, 9600, 1], [6, 10800, 4], [6, 43200, 8], [6, 64000, 2], [6, 192000, 2], [6, 216000, 4], [6, 243000, 4], [6, 259200, 1], [6, 432000, 2], [6, 1728000, 8], [6, 1944000, 4], [6, 11664000, 2], [8, 97200, 2], [8, 4374000, 2], [8, 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'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'A_6\\wr S_3', 'inner_used': None, 'irrC_degree': 15, 'irrQ_degree': 15, 'irrQ_dim': 15, 'irrR_degree': 15, 'irrep_stats': [[1, 4], [2, 2], [15, 8], [24, 8], [27, 4], [30, 4], [75, 8], [125, 8], [150, 2], [192, 8], [240, 8], [243, 4], [250, 4], [270, 4], [300, 8], [375, 8], [384, 2], [432, 4], [480, 4], [512, 8], [540, 2], [600, 16], [675, 8], [729, 4], [750, 8], [960, 16], [1000, 4], [1024, 4], [1200, 4], [1215, 8], [1350, 2], [1458, 2], [1500, 10], [1536, 8], [1728, 8], [1920, 12], [1944, 8], [2000, 2], [2160, 8], [2400, 16], [2430, 4], [2700, 8], [3456, 2], [3840, 2], [4320, 4]], 'label': '559872000.o', '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, 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27993600], [60, 12441600]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '8.5', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 8, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [15, 8], [27, 4], [30, 4], [48, 4], [75, 8], [125, 8], [150, 2], [243, 4], [250, 4], [270, 4], [300, 8], [375, 8], [384, 6], [480, 4], [540, 2], [675, 8], [729, 4], [750, 8], [864, 2], [960, 2], [1000, 4], [1024, 4], [1200, 8], [1215, 8], [1350, 2], [1458, 2], [1500, 10], [1920, 12], [2000, 2], [2048, 2], [2400, 2], [2430, 4], [2700, 8], [3072, 4], [3456, 6], [3840, 6], [3888, 4], [4320, 4], [4800, 8], [8640, 2]], 'representations': {'Perm': {'d': 20, 'gens': [262544767578789888, 135583801881274831]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 8748, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_2\\times A_6\\wr S_3', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
