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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '28800.ci', 'ambient_counter': 61, 'ambient_order': 28800, 'ambient_tex': 'A_4\\times F_5\\times S_5', 'central': False, 'central_factor': False, 'centralizer_order': 9600, 'characteristic': False, 'core_order': 1, 'counter': 2050, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '28800.ci.14400.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14400.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': 14400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '28800.ci', 'aut_centralizer_order': None, 'aut_label': '14400.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2880.b1', '2880.c1', '2880.d1', '4800.a1', '7200.a1', '7200.b1', '7200.c1', '7200.d1', '7200.e1', '7200.f1', '7200.g1', '7200.h1', '7200.i1', '7200.j1', '7200.k1'], 'contains': ['28800.a1'], 'core': '28800.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1037836800], 'label': '28800.ci.14400.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7200.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '14400.a1', 'projective_image': '28800.ci', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14400.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], '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, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [2, 20, 2, 60, 3, 4, 2, 4, 12], 'aut_gens': [[1037836800, 482630400, 562504440, 81381, 1476921600, 1520589720, 63751259067, 1001686440], [1037836800, 482630400, 1476962040, 81381, 562464000, 1520589720, 62836801467, 1440771240], [1520467200, 482630400, 79929480, 177861, 1440633600, 1037959320, 63794804667, 562625400], [1037836800, 482630400, 958043640, 81381, 43545600, 1520589720, 63355719867, 79971240], [482630400, 1037836800, 79845120, 69020232030, 518918400, 1520589720, 64233889467, 958009080], [482630400, 1520467200, 1476962040, 81381, 958003200, 1037959320, 63355719867, 519056040], [1520467200, 482630400, 518929920, 177845, 1001548800, 1037928360, 70460875597, 1476927480], [1520467200, 482630400, 518958840, 81381, 1001548800, 1037959320, 64233889467, 1477059240], [482630400, 1037836800, 519050160, 177861, 79833600, 1520524080, 63794884467, 43596000], [1520467200, 1037836800, 958099080, 126141, 562464000, 482801760, 64270208427, 1440795000]], 'aut_group': '57600.de', 'aut_hash': 449092229698969459, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 57600, 'aut_permdeg': 23, 'aut_perms': [20285665376295336894966, 19177857014000189120070, 7921657362707574036846, 22948673722916432894816, 13541661002997133787646, 14898266419857125004067, 14665661736099317038134, 12419126807808025283214, 20286280376160571802526], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 10, 1, 1], [2, 15, 1, 2], [2, 30, 1, 1], [2, 45, 1, 1], [2, 50, 1, 1], [2, 75, 1, 1], [2, 150, 1, 1], [2, 225, 1, 1], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 5, 1, 2], [4, 15, 1, 2], [4, 30, 1, 1], [4, 50, 1, 2], [4, 75, 1, 2], [4, 90, 1, 1], [4, 150, 1, 5], [4, 225, 1, 2], [4, 450, 1, 3], [5, 4, 1, 1], [5, 24, 1, 1], [5, 96, 1, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 40, 2, 1], [6, 60, 1, 2], [6, 60, 2, 1], [6, 80, 2, 1], [6, 100, 1, 2], [6, 200, 2, 1], [6, 300, 1, 2], [6, 300, 2, 1], [6, 400, 2, 2], [10, 12, 1, 1], [10, 40, 1, 1], [10, 60, 1, 1], [10, 72, 1, 1], [10, 120, 1, 2], [10, 180, 1, 1], [10, 288, 1, 1], [10, 360, 1, 1], [12, 20, 2, 2], [12, 100, 1, 4], [12, 120, 2, 1], [12, 200, 2, 2], [12, 300, 1, 4], [12, 300, 2, 2], [12, 400, 2, 4], [12, 600, 2, 3], [15, 16, 2, 1], [15, 80, 1, 1], [15, 96, 2, 1], [15, 320, 2, 1], [15, 384, 2, 1], [20, 120, 1, 3], [20, 360, 1, 3], [30, 80, 1, 1], [30, 160, 2, 1], [30, 240, 1, 2], [30, 240, 2, 1], [30, 320, 2, 1], [30, 480, 2, 1], [60, 480, 2, 3]], 'aut_supersolvable': False, 'aut_tex': 'F_5\\times S_4\\times S_5', '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': 60, 'autcentquo_group': '57600.de', 'autcentquo_hash': 449092229698969459, 'autcentquo_nilpotent': False, 'autcentquo_order': 57600, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5\\times S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 5, 1], [2, 10, 1], [2, 15, 2], [2, 30, 1], [2, 45, 1], [2, 50, 1], [2, 75, 1], [2, 150, 1], [2, 225, 1], [3, 4, 2], [3, 20, 1], [3, 80, 2], [4, 5, 2], [4, 15, 2], [4, 30, 1], [4, 50, 2], [4, 75, 2], [4, 90, 1], [4, 150, 5], [4, 225, 2], [4, 450, 3], [5, 4, 1], [5, 24, 1], [5, 96, 1], [6, 20, 3], [6, 40, 2], [6, 60, 4], [6, 80, 2], [6, 100, 2], [6, 200, 2], [6, 300, 4], [6, 400, 4], [10, 12, 1], [10, 40, 1], [10, 60, 1], [10, 72, 1], [10, 120, 2], [10, 180, 1], [10, 288, 1], [10, 360, 1], [12, 20, 4], [12, 100, 4], [12, 120, 2], [12, 200, 4], [12, 300, 8], [12, 400, 8], [12, 600, 6], [15, 16, 2], [15, 80, 1], [15, 96, 2], [15, 320, 2], [15, 384, 2], [20, 120, 3], [20, 360, 3], [30, 80, 1], [30, 160, 2], [30, 240, 4], [30, 320, 2], [30, 480, 2], [60, 480, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '28800.ci', 'commutator_count': 1, 'commutator_label': '1200.945', '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', '60.5'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 61, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['120.34', 1], ['20.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 5, 1, 1], [2, 10, 1, 1], [2, 15, 1, 2], [2, 30, 1, 1], [2, 45, 1, 1], [2, 50, 1, 1], [2, 75, 1, 1], [2, 150, 1, 1], [2, 225, 1, 1], [3, 4, 2, 1], [3, 20, 1, 1], [3, 80, 2, 1], [4, 5, 2, 1], [4, 15, 2, 1], [4, 30, 1, 1], [4, 50, 2, 1], [4, 75, 2, 1], [4, 90, 1, 1], [4, 150, 1, 1], [4, 150, 2, 2], [4, 225, 2, 1], [4, 450, 1, 1], [4, 450, 2, 1], [5, 4, 1, 1], [5, 24, 1, 1], [5, 96, 1, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 40, 2, 1], [6, 60, 1, 2], [6, 60, 2, 1], [6, 80, 2, 1], [6, 100, 1, 2], [6, 200, 2, 1], [6, 300, 1, 2], [6, 300, 2, 1], [6, 400, 2, 2], [10, 12, 1, 1], [10, 40, 1, 1], [10, 60, 1, 1], [10, 72, 1, 1], [10, 120, 1, 2], [10, 180, 1, 1], [10, 288, 1, 1], [10, 360, 1, 1], [12, 20, 4, 1], [12, 100, 2, 2], [12, 120, 2, 1], [12, 200, 4, 1], [12, 300, 2, 2], [12, 300, 4, 1], [12, 400, 4, 2], [12, 600, 2, 1], [12, 600, 4, 1], [15, 16, 2, 1], [15, 80, 1, 1], [15, 96, 2, 1], [15, 320, 2, 1], [15, 384, 2, 1], [20, 120, 1, 1], [20, 120, 2, 1], [20, 360, 1, 1], [20, 360, 2, 1], [30, 80, 1, 1], [30, 160, 2, 1], [30, 240, 1, 2], [30, 240, 2, 1], [30, 320, 2, 1], [30, 480, 2, 1], [60, 480, 2, 1], [60, 480, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1824, 'exponent': 60, 'exponents_of_order': [7, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[48, 1, 2], [60, 1, 2], [72, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '28800.ci', 'hash': 6365635586243558856, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 6, 4, 3, 10, 30, 12], 'inner_gens': [[1037836800, 482630400, 43586040, 81381, 958003200, 1520589720, 64270177467, 519056040], [1037836800, 482630400, 958043640, 81381, 43545600, 1520589720, 63355719867, 79971240], [1520467200, 1037836800, 562504440, 46941, 958003200, 482687280, 62836881267, 519056040], [1037836800, 482630400, 562559880, 81381, 1476921600, 1520558760, 82432286801, 1001710200], [1520467200, 1037836800, 43586040, 81381, 1476921600, 482752920, 63355719867, 1001686440], [1037836800, 482630400, 1477053360, 126141, 562464000, 1520589720, 62836801467, 1440684000], [1520467200, 1037836800, 1477089480, 69020200230, 43545600, 482752920, 63751259067, 79920720], [482630400, 1520467200, 958043640, 15141, 1476921600, 1038008160, 62836832427, 1001686440]], 'inner_hash': 6365635586243558856, 'inner_nilpotent': False, 'inner_order': 28800, 'inner_split': True, 'inner_tex': 'A_4\\times F_5\\times S_5', 'inner_used': [1, 2, 3, 4, 7], 'irrC_degree': 48, 'irrQ_degree': 48, 'irrQ_dim': 48, 'irrR_degree': 48, 'irrep_stats': [[1, 24], [3, 8], [4, 30], [5, 24], [6, 12], [12, 10], [15, 8], [16, 6], [18, 4], [20, 6], [24, 3], [48, 2], [60, 2], [72, 1]], 'label': '28800.ci', '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*S5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 105, 'number_characteristic_subgroups': 42, 'number_conjugacy_classes': 140, 'number_divisions': 84, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 2061, 'number_subgroup_classes': 2207, 'number_subgroups': 186152, 'old_label': None, 'order': 28800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 623], [3, 188], [4, 2960], [5, 124], [6, 3940], [10, 1252], [12, 10720], [15, 1712], [20, 1440], [30, 2960], [60, 2880]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[482630400, 1037836800, 1440674040, 81381, 1001548800, 1520589720, 62873089467, 1477059240]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, '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, 8], [5, 4], [6, 4], [8, 8], [10, 6], [12, 9], [15, 4], [16, 4], [18, 2], [20, 4], [24, 4], [30, 2], [32, 2], [36, 1], [40, 2], [48, 3], [60, 2], [72, 1]], 'representations': {'Perm': {'d': 14, 'gens': [1037836800, 482630400, 562504440, 81381, 1476921600, 1520589720, 63751259067, 1001686440]}}, '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': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4\\times F_5\\times S_5', 'transitive_degree': 100, 'wreath_data': None, 'wreath_product': False}
