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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3484800.e', 'ambient_counter': 5, 'ambient_order': 3484800, 'ambient_tex': '\\PSL(2,11)^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3484800.e.1320._.G', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.G', 'outer_equivalence': False, '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': 1320, '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': '2640.bt', 'subgroup_hash': None, 'subgroup_order': 2640, 'subgroup_tex': 'C_2^2\\times \\PSL(2,11)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3484800.e', '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': 110, 'diagramx': None, 'generators': [248840993280564585934796282, 259697824342176288101781, 264341474334123842533132920, 2], 'label': '3484800.e.1320._.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1320.G', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320._.G', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 2], 'aut_gens': [[100243232767, 194643121816], [47102565007, 581682287543], [555900402976, 887361805447]], 'aut_group': '7920.q', 'aut_hash': 1157788818429169362, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7920, 'aut_permdeg': 58, 'aut_perms': [81767740129895361781314865737532634877916766745654378449289700586534228932508, 40533160917917653740324168618847765472321981204546482113282876094633686212699], 'aut_phi_ratio': 12.375, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 55, 1, 1], [2, 55, 3, 1], [3, 110, 1, 1], [5, 132, 1, 2], [6, 110, 1, 1], [6, 110, 3, 2], [10, 132, 3, 2], [11, 60, 2, 1], [22, 60, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times \\PGL(2,11)', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '1320.133', 'autcentquo_hash': 133, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PGL(2,11)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 55, 4], [3, 110, 1], [5, 132, 2], [6, 110, 7], [10, 132, 6], [11, 60, 2], [22, 60, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '660.13', 'commutator_count': 1, 'commutator_label': '660.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '660.13'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 46, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['660.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 55, 1, 4], [3, 110, 1, 1], [5, 132, 2, 1], [6, 110, 1, 7], [10, 132, 2, 3], [11, 60, 2, 1], [22, 60, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 330, 'exponents_of_order': [4, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2640.bt', 'hash': 6613815745579852445, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [5, 5], 'inner_gens': [[100243232767, 277080744256], [711616077367, 194643121816]], 'inner_hash': 13, 'inner_nilpotent': False, 'inner_order': 660, 'inner_split': True, 'inner_tex': '\\PSL(2,11)', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [5, 8], [10, 8], [11, 4], [12, 8]], 'label': '2640.bt', '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*PSL(2,11)', 'ngens': 2, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 32, 'number_divisions': 24, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 142, 'number_subgroups': 7456, 'old_label': None, 'order': 2640, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 223], [3, 110], [5, 264], [6, 770], [10, 792], [11, 120], [22, 360]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 268720262056], 'outer_gens': [[100243232776, 194643121807], [226351249343, 554725318327]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [10, 12], [11, 4], [24, 4]], 'representations': {'Perm': {'d': 15, 'gens': [100243232767, 194643121816]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], '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 \\PSL(2,11)', 'transitive_degree': 44, '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': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 660, 'aut_gen_orders': [6, 10, 110, 10, 22], 'aut_gens': [[32993117835616624321406176, 16834429088759480192478850], [128135284203913638455947687, 211359881830263776660176690], [158931849732243132400013527, 298187863549519938833030410], [209849474502489727463050927, 313139061035838545920404493], [32670532194836066210460247, 210705724873379511717188413], [312706366059174009722560216, 307234770219772030023102013]], 'aut_group': None, 'aut_hash': 2269088628342978270, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6969600, 'aut_permdeg': 1322, 'aut_perms': 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4, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times \\PSL(2,11)^2.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': '1742400.c', 'autcentquo_hash': 8907486698060875046, 'autcentquo_nilpotent': False, 'autcentquo_order': 1742400, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\POPlus(4,11)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 110, 4], [2, 1320, 1], [2, 3025, 2], [2, 6050, 1], [3, 220, 1], [3, 12100, 1], [4, 1320, 1], [4, 72600, 2], [5, 264, 2], [5, 17424, 2], [5, 34848, 1], [6, 220, 7], [6, 12100, 11], [6, 24200, 6], [6, 145200, 1], [10, 264, 6], [10, 14520, 8], [10, 17424, 2], [10, 34848, 5], [10, 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'hash': 4097294603936226366, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 660, 'inner_gen_orders': [10, 22], 'inner_gens': [[32993117835616624321406176, 320876680315773537040227853], [205171062557194180359089287, 16834429088759480192478850]], 'inner_hash': 3836868429214239020, 'inner_nilpotent': False, 'inner_order': 1742400, 'inner_split': True, 'inner_tex': 'C_2\\times \\PSL(2,11)\\wr C_2', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 4], [2, 1], [10, 8], [20, 8], [22, 4], [24, 8], [25, 8], [50, 6], [100, 24], [110, 8], [120, 16], [121, 4], [144, 8], [200, 6], [220, 8], [240, 16], [242, 1], [264, 8], [288, 6]], 'label': '3484800.e', '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': 'PSL(2,11)^2.D4', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 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, 1, 0, 0, 1, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 101, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 152, 'number_divisions': 96, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 3484800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 13863], [3, 12320], [4, 146520], [5, 70224], [6, 425040], [10, 675312], [11, 14640], [12, 435600], [15, 58080], [20, 348480], [22, 255120], [30, 406560], [33, 26400], [44, 158400], [55, 63360], [66, 184800], [110, 190080]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [3766055919999432475087560, 0], 'outer_gens': [[313829473127791269395703736, 295166449045956666895608370], [32993117835616624321406176, 16834429088759480192478853]], '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': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [20, 12], [22, 4], [48, 4], [50, 6], [100, 10], [121, 4], [200, 14], [220, 12], [242, 1], [288, 6], [480, 12], [528, 4], [576, 2]], 'representations': {'Perm': {'d': 26, 'gens': [32993117835616624321406176, 16834429088759480192478850]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 23232, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': '\\PSL(2,11)^2.D_4', 'transitive_degree': 44, 'wreath_data': None, 'wreath_product': None}
