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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3993.6', 'ambient_counter': 6, 'ambient_order': 3993, 'ambient_tex': 'C_{11}\\wr C_3', 'central': False, 'central_factor': False, 'centralizer_order': 1331, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '3993.6.363.c1.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '363.c1.i1', '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': 363, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3993.6', 'aut_centralizer_order': 242, 'aut_label': '363.c1', 'aut_quo_index': None, 'aut_stab_index': 120, 'aut_weyl_group': '10.2', 'aut_weyl_index': 29040, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['33.b1.a1', '33.c1.d1', '33.c1.j1', '33.c1.r1', '33.c1.t1', '33.c1.w1', '33.c1.ba1', '33.c1.bd1', '33.c1.bf1', '33.c1.bh1', '33.c1.bj1'], 'contains': ['3993.a1.a1'], 'core': '3993.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8251, -1, 6898, -1, 7421, -1, 6464, -1], 'generators': [1125], 'label': '3993.6.363.c1.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '363.c1.i1', 'projective_image': '3993.6', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '363.c1.i1', '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': '11.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 10, 'aut_gen_orders': [10], 'aut_gens': [[1], [2]], 'aut_group': '10.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 10, 'aut_permdeg': 7, 'aut_perms': [753], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [11, 1, 10, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{10}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', '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], [11, 1, 10]], 'center_label': '11.1', 'center_order': 11, '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': ['11.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [11, 1, 10, 1]], 'element_repr_type': 'PC', 'elementary': 11, 'eulerian_function': 1, 'exponent': 11, 'exponents_of_order': [1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [11], 'faithful_reps': [[1, 0, 10]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '11.1', 'hash': 1, 'hyperelementary': 11, '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': 10, 'irrQ_dim': 10, 'irrR_degree': 2, 'irrep_stats': [[1, 11]], 'label': '11.1', 'linC_count': 10, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 5, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11', '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': 11, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 11, 'order_factorization_type': 1, 'order_stats': [[1, 1], [11, 10]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [10], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '10.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 10, 'outer_permdeg': 7, 'outer_perms': [753], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{10}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 11, 'pgroup': 11, 'primary_abelian_invariants': [11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [10, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -11]}, 'Lie': [{'d': 1, 'q': 11, 'gens': [4037913], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 11, 'gens': [1343]}, 'Perm': {'d': 11, 'gens': [36288000]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [11], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}', 'transitive_degree': 11, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '33.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [10, 10, 20, 20], 'aut_gens': [[1, 33, 363], [2693, 957, 1617], [3818, 198, 2046], [2216, 1386, 825], [3572, 528, 2409]], 'aut_group': None, 'aut_hash': 918826766112171845, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 290400, 'aut_permdeg': 252, 'aut_perms': [29636313145691704291517294188584874896218751826283087193457911274349292167431043320267188235078467450542649545711782489292684062811471416555401726814196824690752479672013251555382104492589978436767944302825405251764689877888613618486055553143705722567299241169824817734429550387772579163344704591566862287707999068578957752203360747462933882209026783300487022767328880503128004471438964285443119678890255580366252282525943078977967034857714983522515804324995740595191298455399389534056519398994247, 88785984984210064693975808233413214609170928452490515548882308074464443758045527984302719718635377222704800038242461437296775187731890346401271812331419328547530120000981783614813563032209804694986898766519494655043294274072934622486558517150610009213528585544772656809069615768567051110951880819826191944767774386787154348183580691962949808291562927146342342480129558295146791211613718786528917196214591995987587035204865841607927101754200474084174162913253667614264021440709622084557959653921595, 72279343452914659324610768799936063551109931941583911029144385091727698211767655346293705554553223102744155963930229846683524911719854293827766321744898284328735263456708874994046677272798378141710653740677345770090933767505216964914441216858524085905449526117369245756605940482469820694103684393022244700738101409130781959066159332076258049962327966471354863760320195299259128970095000624849304440064968359004985417382250796327943385533810800591795331481540044814938619508179996142309430050846428, 78577254208074680388653909208999683013265317803877357021734386673447361428096978408153347167300055316013038431717623624686793533501708878401052300892370514572867298020710509821035287009921247006390562138010394028653713903811398478713209347719041163721844420041829653188696759344258115734555632482808089631807051668959632098297418408781984736348991373150959036206204466964649493047879827693561790891158932859274150197068577099451448658341285080793118104787091281691495403699380511985423092324624779], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 121, 2, 1], [11, 1, 10, 1], [11, 3, 40, 1], [11, 3, 400, 1], [33, 121, 20, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_5.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [3, 121, 2], [11, 1, 10], [11, 3, 440], [33, 121, 20]], 'center_label': '11.1', 'center_order': 11, 'central_product': True, 'central_quotient': '363.2', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '11.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['363.2', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 121, 2, 1], [11, 1, 10, 1], [11, 3, 10, 44], [33, 121, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 33, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [3, 11], 'faithful_reps': [[3, 0, 400]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3993.6', 'hash': 6, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 33, 'inner_gen_orders': [3, 11, 11], 'inner_gens': [[1, 660, 627], [3730, 33, 363], [100, 33, 363]], 'inner_hash': 2, 'inner_nilpotent': False, 'inner_order': 363, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 30, 'irrQ_dim': 30, 'irrR_degree': 6, 'irrep_stats': [[1, 33], [3, 440]], 'label': '3993.6', 'linC_count': 400, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 30, 'linQ_degree_count': 40, 'linQ_dim': 30, 'linQ_dim_count': 40, 'linR_count': 200, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11wrC3', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 473, 'number_divisions': 48, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 96, 'number_subgroups': 512, 'old_label': None, 'order': 3993, 'order_factorization_type': 31, 'order_stats': [[1, 1], [3, 242], [11, 1330], [33, 2420]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 40, 'outer_gen_orders': [2, 10, 40], 'outer_gen_pows': [32, 0, 0], 'outer_gens': [[10, 660, 627], [8, 660, 990], [1, 825, 3432]], 'outer_group': '800.952', 'outer_hash': 952, 'outer_nilpotent': True, 'outer_order': 800, 'outer_permdeg': 20, 'outer_perms': [39916800, 13516128494668890, 878906256441706080], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_8:C_{10}^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [3, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [10, 1], [20, 1], [30, 44]], 'representations': {'PC': {'code': '7185570867691999', 'gens': [1, 3, 4], 'pres': [4, -3, -11, -11, 11, 12, 7922, 10035]}, 'Lie': [{'d': 1, 'q': 1331, 'family': 'ASigmaL'}], 'GLZq': {'d': 2, 'q': 121, 'gens': [119507884, 120309146, 1757161, 1932613]}, 'Perm': {'d': 33, 'gens': [5975817900939513912271439485992960000, 1901394391467741686218740989968151616, 375563241578020631616, 2631308369336935812581601838730688000]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [33], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\wr C_3', 'transitive_degree': 33, 'wreath_data': ['C_{11}', 'C_3', '3T1'], 'wreath_product': True}
