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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '13200.u', 'ambient_counter': 21, 'ambient_order': 13200, 'ambient_tex': '\\SL(2,11):D_5', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 20, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '13200.u.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.a1', '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': 11, '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': '1200.481', 'subgroup_hash': 481, 'subgroup_order': 1200, 'subgroup_tex': '\\SL(2,5):D_5', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '13200.u', 'aut_centralizer_order': None, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6600.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '55.a1.a1', '55.b1.a1', '66.a1.a1', '110.b1.a1'], 'core': '660.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [5370, -1, 4994, -1, 4988, -1, 4923, -1], 'generators': [45395521420732172, 16201990098291477, 32176413436297456, 27925637260618714, 41772741070013040], 'label': '13200.u.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '600.146'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [4, 30, 4, 10, 2, 2], 'aut_gens': [[122109387504, 73876491433, 149770320628, 135774457122, 69679291610], [122109387504, 97993917916, 149770320628, 43907530549, 45561477502], [122109387504, 73876491433, 119692785530, 1574781090, 149660218931], [122109387504, 25631485987, 4706425968, 9398928656, 95027186848], [122109387504, 73876491433, 149770320628, 20931908132, 65141270182], [122109387504, 73876491433, 149770320628, 54716187408, 119776274790], [122109387504, 49748912470, 149770320628, 114216429080, 65141270182]], 'aut_group': '4800.cf', 'aut_hash': 6606067472031944380, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4800, 'aut_permdeg': 30, 'aut_perms': [212518488884132706665152006552464, 247362072801408138700048165150067, 246377761711248944963503173262685, 106417351784188702631950239984768, 44525005985431816212575533307088, 230202018455647724061594054475848], 'aut_phi_ratio': 15.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 150, 1, 1], [3, 20, 1, 1], [4, 5, 2, 1], [4, 30, 1, 1], [5, 2, 2, 1], [5, 12, 2, 1], [5, 24, 4, 1], [6, 20, 1, 1], [10, 2, 2, 1], [10, 12, 2, 1], [10, 24, 4, 1], [12, 100, 2, 1], [15, 40, 2, 1], [20, 60, 2, 1], [20, 60, 4, 1], [30, 40, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times F_5\\times S_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', '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, 1], [2, 150, 1], [3, 20, 1], [4, 5, 2], [4, 30, 1], [5, 2, 2], [5, 12, 2], [5, 24, 4], [6, 20, 1], [10, 2, 2], [10, 12, 2], [10, 24, 4], [12, 100, 2], [15, 40, 2], [20, 60, 6], [30, 40, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '600.146', 'commutator_count': 1, 'commutator_label': '600.54', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '60.5'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 481, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 150, 1, 1], [3, 20, 1, 1], [4, 5, 2, 1], [4, 30, 1, 1], [5, 2, 2, 1], [5, 12, 2, 1], [5, 24, 2, 2], [6, 20, 1, 1], [10, 2, 2, 1], [10, 12, 2, 1], [10, 24, 2, 2], [12, 100, 2, 1], [15, 40, 2, 1], [20, 60, 2, 1], [20, 60, 4, 1], [30, 40, 2, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 114, 'exponent': 60, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[4, 1, 4], [8, 1, 2], [12, 1, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '600.146', 'hash': 481, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [1, 5, 2, 6, 2], 'inner_gens': [[122109387504, 73876491433, 149770320628, 135774457122, 69679291610], [122109387504, 73876491433, 149770320628, 76469215445, 21444051669], [122109387504, 73876491433, 149770320628, 51333236783, 69679291610], [122109387504, 49748912470, 65040384091, 135774457122, 21444051669], [122109387504, 49748912470, 149770320628, 43907530549, 69679291610]], 'inner_hash': 146, 'inner_nilpotent': False, 'inner_order': 600, 'inner_split': False, 'inner_tex': 'D_5\\times A_5', 'inner_used': [2, 3, 4], 'irrC_degree': 4, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 4, 'irrep_stats': [[1, 2], [2, 6], [3, 4], [4, 8], [5, 2], [6, 6], [8, 4], [10, 2], [12, 2]], 'label': '1200.481', 'linC_count': 12, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,5):D5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 36, 'number_divisions': 20, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 60, 'number_subgroup_classes': 70, 'number_subgroups': 1562, 'old_label': None, 'order': 1200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 151], [3, 20], [4, 40], [5, 124], [6, 20], [10, 124], [12, 200], [15, 80], [20, 360], [30, 80]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [10030720628, 30527346876, 145124556878], 'outer_gens': [[122109387504, 73876491433, 105184217503, 57115357937, 69679291610], [122109387504, 73876491433, 149770320628, 54716187408, 119776274790], [122109387504, 97993917916, 149770320628, 135774457122, 149660218931]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 3], [5, 2], [6, 2], [8, 4], [12, 3], [16, 2], [20, 1], [24, 1]], 'representations': {'GLFp': {'d': 4, 'p': 5, 'gens': [122109387504, 73876491433, 149770320628, 135774457122, 69679291610]}, 'Perm': {'d': 29, 'gens': [359476225705797099128504841682, 983230330386097398936787153225]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,5):D_5', 'transitive_degree': 120, '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': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [10, 60, 12, 4], 'aut_gens': [[30053439468871889, 32176413436297456, 1473410467475422, 2040640196685105, 41772741070013040], [23701060830277243, 21164576091951198, 15653099526443522, 37500550997522313, 41772741070013040], [2522899439069251, 2039694653271902, 1473410467475422, 27456382312880176, 41772741070013040], [29237322755438407, 2039694653271902, 45395521420732172, 22815502468770865, 41772741070013040], [27431423079389070, 25168329919331132, 34389814864764160, 19543836806907355, 41772741070013040]], 'aut_group': None, 'aut_hash': 3284368865768880809, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 52800, 'aut_permdeg': 120, 'aut_perms': [127900209061434257016055359951869887810249281718857254702990494733513979383924911815040444692399895857433038857014947591880994976363862667752170254849179815897724751778180116403352710956437366863107, 5056647004140275702154402441923537144385881631234181751876005736859825365474202900517077869105977334021238690789903348051342985566609192110503291457243044618883405749597051076130349804982631553545254, 6432596888821904936440295118612815642860560975934218677716093312056056254351447585150308768327783119608106213089012919543087513646723966146253391655368474015153983450582808299584262562684946628028616, 220405646958861823537381225107135801333879664791500233268114983253641936187826984713657345096032077390409633632339505739396535561103194121131624865082101501198254699444938421430232080308328317815575], 'aut_phi_ratio': 16.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 550, 1, 1], [3, 110, 1, 1], [4, 5, 2, 1], [4, 110, 1, 1], [5, 2, 2, 1], [5, 132, 1, 2], [5, 264, 2, 2], [6, 110, 1, 1], [6, 550, 2, 1], [10, 2, 2, 1], [10, 132, 1, 2], [10, 264, 2, 2], [11, 60, 2, 1], [12, 110, 1, 2], [12, 550, 2, 1], [15, 220, 2, 1], [20, 220, 2, 1], [20, 660, 2, 2], [22, 60, 2, 1], [30, 220, 2, 1], [44, 300, 4, 1], [55, 120, 4, 1], [60, 220, 2, 2], [110, 120, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times \\PSL(2,11).C_2\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 660, 'autcentquo_group': None, 'autcentquo_hash': 2592424795495991929, 'autcentquo_nilpotent': False, 'autcentquo_order': 26400, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\PSL(2,11).C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 550, 1], [3, 110, 1], [4, 5, 2], [4, 110, 1], [5, 2, 2], [5, 132, 2], [5, 264, 4], [6, 110, 1], [6, 550, 2], [10, 2, 2], [10, 132, 2], [10, 264, 4], [11, 60, 2], [12, 110, 2], [12, 550, 2], [15, 220, 2], [20, 220, 2], [20, 660, 4], [22, 60, 2], [30, 220, 2], [44, 300, 4], [55, 120, 4], [60, 220, 4], [110, 120, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '6600.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '660.13'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 21, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 550, 1, 1], [3, 110, 1, 1], [4, 5, 2, 1], [4, 110, 1, 1], [5, 2, 2, 1], [5, 132, 2, 1], [5, 264, 2, 2], [6, 110, 1, 1], [6, 550, 2, 1], [10, 2, 2, 1], [10, 132, 2, 1], [10, 264, 2, 2], [11, 60, 2, 1], [12, 110, 2, 1], [12, 550, 2, 1], [15, 220, 2, 1], [20, 220, 2, 1], [20, 660, 4, 1], [22, 60, 2, 1], [30, 220, 2, 1], [44, 300, 4, 1], [55, 120, 4, 1], [60, 220, 4, 1], [110, 120, 4, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 1524, 'exponent': 660, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[12, 0, 4], [20, 1, 6], [24, 1, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 3279413284325928414, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 330, 'inner_gen_orders': [2, 2, 5, 15, 1], 'inner_gens': [[30053439468871889, 32176413436297456, 1473410467475422, 15776484315624840, 41772741070013040], [30053439468871889, 32176413436297456, 15653099526443522, 30198132925685354, 41772741070013040], [30053439468871889, 2039694653271902, 1473410467475422, 2040640196685105, 41772741070013040], [41001484573766543, 21164576091951198, 1473410467475422, 2040640196685105, 41772741070013040], [30053439468871889, 32176413436297456, 1473410467475422, 2040640196685105, 41772741070013040]], 'inner_hash': 3712870502229058844, 'inner_nilpotent': False, 'inner_order': 6600, 'inner_split': False, 'inner_tex': 'D_5.\\PSL(2,11)', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 40, 'irrQ_dim': 40, 'irrR_degree': 20, 'irrep_stats': [[1, 2], [2, 2], [5, 4], [6, 4], [10, 14], [11, 2], [12, 12], [20, 10], [22, 2], [24, 8]], 'label': '13200.u', 'linC_count': 8, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 1, 'linQ_dim': 24, 'linQ_dim_count': 1, 'linR_count': 4, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'SL(2,11):D5', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 33, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 60, 'number_divisions': 28, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 94, 'number_subgroup_classes': 118, 'number_subgroups': 16964, 'old_label': None, 'order': 13200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 551], [3, 110], [4, 120], [5, 1324], [6, 1210], [10, 1324], [11, 120], [12, 1320], [15, 440], [20, 3080], [22, 120], [30, 440], [44, 1200], [55, 480], [60, 880], [110, 480]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [2644836745591931, 4177274107001304, 32176413436297456], 'outer_gens': [[9084344666894726, 32176413436297456, 1473410467475422, 27456382312880176, 41772741070013040], [30053439468871889, 18333740744561576, 1473410467475422, 2040640196685105, 41772741070013040], [30053439468871889, 32176413436297456, 45395521420732172, 24617435205279802, 41772741070013040]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 53, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 1], [10, 6], [11, 2], [20, 1], [24, 3], [40, 5], [44, 1], [48, 6], [80, 1]], 'representations': {'GLFp': {'d': 4, 'p': 11, 'gens': [30053439468871889, 32176413436297456, 1473410467475422, 2040640196685105, 41772741070013040]}, 'Perm': {'d': 53, 'gens': [86989235697116365735270350333737769115838205569496263473079883272917, 52, 169166912660207499620864471276230456018190227021402166177330977969207, 251496063225147831256843838375171397652186088923878520888569988760400, 333739321887374656551974234166130687176703550907351514406895407181360]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\SL(2,11):D_5', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
