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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '96800.c', 'ambient_counter': 3, 'ambient_order': 96800, 'ambient_tex': 'C_{11}^2:C_8:C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '96800.c.9680.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '9680.f1', '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': 9680, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '96800.c', 'aut_centralizer_order': None, 'aut_label': '9680.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1', 'complements': None, 'conjugacy_class_count': 10, 'contained_in': ['880.q1', '880.r1', '880.s1', '880.t1', '1936.c1', '4840.e1', '4840.l1'], 'contains': ['19360.b1', '48400.c1'], 'core': '96800.a1', 'coset_action_label': None, 'count': 1210, 'diagramx': [950, -1, 1575, -1], 'generators': [55140, 19362], 'label': '96800.c.9680.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1', 'old_label': '9680.f1', 'projective_image': '96800.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9680.f1', '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': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [7]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4], [10, 1, 4]], 'center_label': '10.2', 'center_order': 10, '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', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 10]], 'label': '10.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C10', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 10, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[7]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2]], 'representations': {'PC': {'code': 83, 'gens': [1], 'pres': [2, -2, -5, 4]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504]}, 'Perm': {'d': 7, 'gens': [720, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}', 'transitive_degree': 10, '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': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 20, 2, 4, 2, 20], 'aut_gens': [[1, 10, 40, 440], [93541, 24370, 35520, 20880], [3801, 2590, 8880, 91080], [29741, 37550, 280, 93840], [64521, 33050, 400, 96360], [4841, 24230, 52840, 86680], [4801, 72890, 400, 96360], [48161, 55430, 88360, 54120]], 'aut_group': None, 'aut_hash': 5634752407501600181, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3097600, 'aut_permdeg': 781, 'aut_perms': 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'aut_phi_ratio': 88.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 2, 1], [2, 121, 2, 1], [4, 2, 1, 1], [4, 44, 2, 1], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 5, 4], [8, 242, 4, 1], [10, 1, 4, 1], [10, 44, 8, 1], [10, 121, 5, 4], [10, 121, 8, 1], [10, 121, 10, 4], [10, 484, 10, 4], [11, 20, 1, 2], [11, 40, 1, 2], [20, 2, 4, 1], [20, 44, 8, 1], [20, 242, 4, 1], [20, 242, 5, 8], [20, 484, 10, 4], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 2, 1], [40, 242, 16, 1], [40, 242, 20, 4], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 2, 1], [55, 20, 4, 2], [55, 40, 4, 2], [110, 20, 4, 2], [110, 40, 4, 2], [110, 440, 8, 1], [220, 40, 4, 2], [220, 40, 8, 2], [220, 440, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{11}\\times C_{55}).C_2^3.C_{10}.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.236', 'autcent_hash': 236, 'autcent_nilpotent': False, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': None, 'autcentquo_hash': 5713448921273139074, 'autcentquo_nilpotent': False, 'autcentquo_order': 19360, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2.C_{10}.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 44, 2], [2, 121, 2], [4, 2, 1], [4, 44, 2], [4, 242, 1], [5, 1, 4], [5, 121, 20], [8, 242, 4], [10, 1, 4], [10, 44, 8], [10, 121, 68], [10, 484, 40], [11, 20, 2], [11, 40, 2], [20, 2, 4], [20, 44, 8], [20, 242, 44], [20, 484, 40], [22, 20, 2], [22, 40, 2], [22, 440, 2], [40, 242, 96], [44, 40, 6], [44, 440, 2], [55, 20, 8], [55, 40, 8], [110, 20, 8], [110, 40, 8], [110, 440, 8], [220, 40, 24], [220, 440, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '9680.ba', 'commutator_count': 1, 'commutator_label': '484.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '11.1', '11.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['19360.h', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 44, 1, 2], [2, 121, 1, 2], [4, 2, 1, 1], [4, 44, 1, 2], [4, 242, 1, 1], [5, 1, 4, 1], [5, 121, 4, 5], [8, 242, 2, 2], [10, 1, 4, 1], [10, 44, 4, 2], [10, 121, 4, 17], [10, 484, 4, 10], [11, 20, 1, 2], [11, 40, 1, 2], [20, 2, 4, 1], [20, 44, 4, 2], [20, 242, 4, 11], [20, 484, 4, 10], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 1, 2], [40, 242, 8, 12], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 1, 2], [55, 20, 4, 2], [55, 40, 4, 2], [110, 20, 4, 2], [110, 40, 4, 2], [110, 440, 4, 2], [220, 40, 4, 2], [220, 40, 8, 2], [220, 440, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 91494144, 'exponent': 440, 'exponents_of_order': [5, 2, 2], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[40, 0, 24]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 6433433583729693702, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [10, 4, 11, 22], 'inner_gens': [[1, 270, 35520, 40040], [48661, 10, 44400, 800], [61761, 52890, 40, 440], [57201, 90, 40, 440]], 'inner_hash': 7887305892697447099, 'inner_nilpotent': False, 'inner_order': 9680, 'inner_split': True, 'inner_tex': 'C_2\\times D_{11}^2:C_{10}', 'inner_used': [1, 2, 4], 'irrC_degree': 40, 'irrQ_degree': 160, 'irrQ_dim': 160, 'irrR_degree': 80, 'irrep_stats': [[1, 200], [2, 150], [20, 40], [40, 50]], 'label': '96800.c', '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': None, 'name': 'C11^2:C8:C10^2', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 76, 'number_characteristic_subgroups': 36, 'number_conjugacy_classes': 440, 'number_divisions': 116, 'number_normal_subgroups': 182, 'number_subgroup_autclasses': 364, 'number_subgroup_classes': 1040, 'number_subgroups': 61600, 'old_label': None, 'order': 96800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [4, 332], [5, 2424], [8, 968], [10, 27944], [11, 120], [20, 30368], [22, 1000], [40, 23232], [44, 1120], [55, 480], [110, 4000], [220, 4480]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 4, 10], 'outer_gen_pows': [0, 0, 0, 24200], 'outer_gens': [[61601, 61850, 400, 57640], [80961, 61850, 400, 67320], [85801, 86050, 400, 9240], [43561, 48410, 40, 440]], 'outer_group': '320.1595', 'outer_hash': 1595, 'outer_nilpotent': False, 'outer_order': 320, 'outer_permdeg': 11, 'outer_perms': [120, 408367, 294, 8028847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_{10}.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 35, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 50], [8, 12], [16, 12], [20, 8], [40, 6], [80, 10], [160, 6], [320, 2]], 'representations': {'PC': {'code': '616523555900916148759214399820771422033509000207498056946533638685762878504933970343989389853466986743154747993519041718250963045280961828666240375868102803181030090039', 'gens': [1, 3, 5, 6], 'pres': [9, 2, 5, 2, 2, 11, 2, 2, 5, 11, 18, 7292, 599546, 74, 2694963, 798852, 87150, 1598404, 8113, 199822, 931, 2162165, 1675094, 4343, 24980, 158, 5045046, 859335, 7332, 58245, 186, 4561927, 1964176, 13561, 133090, 430, 2138408, 3207617, 72602, 356435]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [5063783017457019, 3352440040187918, 16265167320216339, 30551766872799773, 16267516240797404, 44332910602637236, 10522401710269773, 12531822321003912, 33418192856010432]}, 'Perm': {'d': 35, 'gens': [46, 44026240096457147966622872325797491983, 348477377634661013568323939255620250223, 1611308206, 636293381657302016344704923522698291263, 947025426155669667810891924109032960077, 627610133555545546619982789537505887437, 1250408348587825395092330134279121971263, 1557046041894326188638190842187955000477]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:C_8:C_{10}^2', 'transitive_degree': 440, 'wreath_data': None, 'wreath_product': False}
