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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '4632.h', 'ambient_counter': 8, 'ambient_order': 4632, 'ambient_tex': 'C_{1544}:C_3', 'central': False, 'central_factor': True, 'centralizer_order': 8, 'characteristic': True, 'core_order': 579, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 579, 'label': '4632.h.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '579.1', 'subgroup_hash': 1, 'subgroup_order': 579, 'subgroup_tex': 'C_{193}:C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4632.h', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '37056.a', 'aut_weyl_index': 4, 'centralizer': '579.a1.a1', 'complements': ['579.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.a1.a1', '1544.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1106, 1952, 8251, 8557, 1765, 2609, 1765, 7391], 'generators': [8, 24], 'label': '4632.h.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '4632.h', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.1', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '579.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [192, 193], 'aut_gens': [[1, 3], [1, 114], [445, 3]], 'aut_group': '37056.a', 'aut_hash': 1432757702296672986, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 37056, 'aut_permdeg': 193, 'aut_perms': [39053339670721327572543569039395005031096653245802774324204298263788953285647090763476541643345676324473056783378543774660072842471514711015868302482279618194714261105949788702112347134548908091797187306612050281053946057960581089182560863568602379974419627409015496038525465690691519350455551181816446171767151758025418672254963521648341121096265656543605694, 27537046770698028029509447452483255633857520585283838421883440607221768231104384860166214394878916709368227289860720561987161029954363059081082583776521393368876604263321802053274125013685434525755757109968295753899028688290909515762484435944252483952769187280784953622110633939104871157686235761278347542756654691358393510201744955724775767189520816064076473], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 193, 1, 2], [193, 3, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{193}', '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': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [3, 193, 2], [193, 3, 64]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '579.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '193.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 193, 2, 1], [193, 3, 64, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8, 'exponent': 579, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [3, 193], 'faithful_reps': [[3, 0, 64]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '579.1', 'hash': 1, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 579, 'inner_gen_orders': [3, 193], 'inner_gens': [[1, 252], [331, 3]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 579, 'inner_split': True, 'inner_tex': 'C_{193}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 192, 'irrQ_dim': 192, 'irrR_degree': 6, 'irrep_stats': [[1, 3], [3, 64]], 'label': '579.1', 'linC_count': 64, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 192, 'linQ_degree_count': 1, 'linQ_dim': 192, 'linQ_dim_count': 1, 'linR_count': 32, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C193:C3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, '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': 3, 'number_conjugacy_classes': 67, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 196, 'old_label': None, 'order': 579, 'order_factorization_type': 11, 'order_stats': [[1, 1], [3, 386], [193, 192]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 64, 'outer_gen_orders': [64], 'outer_gen_pows': [2], 'outer_gens': [[1, 447]], 'outer_group': '64.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [2014594330940748694500315964401030837224914941382363373987443624058107002128920420940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{64}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 193, 'pgroup': 0, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [192, 1]], 'representations': {'PC': {'code': 12312959, 'gens': [1, 2], 'pres': [2, -3, -193, 1009]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 603880789]}, 'Perm': {'d': 193, 'gens': [155072081769025479153068005764655310398056985534484553249510570014180068596765767602220702796160851423904603713380353967374496827693048038873577863314427425322295450355127868085281304176469528282592426059218603719048013636231661630498986145587733965119292349387964516295495591000760117599793495606069314966880735163520645227705730930758607614125986326901066, 68159384284216415434244229769722897785298203470789342442007462716964519312047994015473537393503254737883254692840162175520283792238796194464802516244938515792342454228783658226402112128483243230028631870556954631033853483990335822197126471859553676149202878029250924171717175622127511797106029233701101543903723520000000000000000000000000000000000000000000000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{193}:C_3', 'transitive_degree': 193, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '24.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [2, 2, 192, 193], 'aut_gens': [[1, 24], [13, 4608], [19, 4608], [1, 1272], [2041, 24]], 'aut_group': None, 'aut_hash': 8288488061211764452, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 148224, 'aut_permdeg': 197, 'aut_perms': [93950995934672498602014885739827793369191982430654947752704005025075964880363237794908477402156944430695186657636851919402113077802396200410797215890646609374031170568204240844428494424177121709499292054938490225802435983274845867025453208901315592780028314629525870308858747915751390410829956992255020135141101786914011346395121933154324366342003697656628955476172799, 93950995934672498602014885739827793369191982430654947752704005025075964880363237794908625664658430464659212197376182026277213214565537821667276564547946524895218165626625871229060514031631936038461357787531059941615973985545260394233420592493461853518804348677795600409418421915601229630495702154896117468445297236265650450864870958086521695959752307385140955476172799, 75707557534274704080871876537150422808537139720767445973246633736970041799219657874011086569320606893667780439444347258056692521655313308688241155513980213510497970709594884747377679250642792759010902514105503983500226324274473112825558863665328844943456065680623176402075601117250760763361378138388968936865958054123014184053607531738892276798590672558647440900104440, 44423719958210338989845316928497838416454396378310757629869133207000078463195955479349122363803202713612757154184584479606915190653066150875636912977875222364800858249203665229822710777067975068282078124144521498174178995706119066423642561071919063224795668692059832271462143573727014186300267239887168153946881483094295591930754072145330644264696772820992000000000000], 'aut_phi_ratio': 96.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 193, 1, 2], [4, 1, 2, 1], [6, 193, 1, 2], [8, 1, 4, 1], [12, 193, 2, 2], [24, 193, 4, 2], [193, 3, 64, 1], [386, 3, 64, 1], [772, 3, 128, 1], [1544, 3, 256, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{193}.C_{96}.C_2^3', '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': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 193, 2], [4, 1, 2], [6, 193, 2], [8, 1, 4], [12, 193, 4], [24, 193, 8], [193, 3, 64], [386, 3, 64], [772, 3, 128], [1544, 3, 256]], 'center_label': '8.1', 'center_order': 8, 'central_product': True, 'central_quotient': '579.1', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '193.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['579.1', 1], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 193, 2, 1], [4, 1, 2, 1], [6, 193, 2, 1], [8, 1, 4, 1], [12, 193, 4, 1], [24, 193, 8, 1], [193, 3, 64, 1], [386, 3, 64, 1], [772, 3, 128, 1], [1544, 3, 256, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 96, 'exponent': 4632, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[3, 0, 256]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '1158.2', 'hash': 8204311627663605522, 'hyperelementary': 3, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 579, 'inner_gen_orders': [3, 193], 'inner_gens': [[1, 2592], [2065, 24]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 579, 'inner_split': True, 'inner_tex': 'C_{193}:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 768, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [3, 512]], 'label': '4632.h', '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': True, 'metacyclic': True, 'monomial': True, 'name': 'C1544:C3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 536, 'number_divisions': 12, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 16, 'number_subgroups': 784, 'old_label': None, 'order': 4632, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1], [3, 386], [4, 2], [6, 386], [8, 4], [12, 772], [24, 1544], [193, 192], [386, 192], [772, 384], [1544, 768]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 64, 'outer_gen_orders': [2, 2, 64], 'outer_gen_pows': [0, 0, 1], 'outer_gens': [[13, 4608], [19, 4608], [1, 1272]], 'outer_group': '256.6723', 'outer_hash': 6723, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 68, 'outer_perms': [36471110918188685288249859096605464427167635314049524593701628500267962436943872000000000000000, 8247650592082470666723170306785496252186258551345437492922123134388955774976000000000000000, 2014594330940748694500315964401030837224914941382363373987443624058107002128920420940313], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{64}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 201, 'pgroup': 0, 'primary_abelian_invariants': [8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 3], [4, 2], [8, 1], [192, 2], [384, 1], [768, 1]], 'representations': {'PC': {'code': '3505390083541057249433941476449439449471', 'gens': [1, 5], 'pres': [5, -2, -2, -2, -3, -193, 10, 26, 42, 64804, 25209, 16214, 6319]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1380299136, 115025096]}, 'Perm': {'d': 201, 'gens': [6783, 796545049056815003502813766629553711575829478957297699696105025376355177141876404071375381063554972542590027903667279993404622226657716863963567237582700914999273039319032281414137764337661627384871464382304636538787184162021362830278891742796318882532344577047251041908262615766169209196924584172988126534240477688882932764512081847856183094843861943353759895714619540625280, 11909832180610594894758345313088294246632692139472813493214472070049706077774066529739016640914964401035491750799234300560207250061878446361157041324973898815897459679998213336883264018487417952212075225687872373068483743657967945333331129464201716992404148503650009404397211771225236602645740612071528148745429924486882397856738283243458167407996231290359548603708373183516]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [24], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{1544}:C_3', 'transitive_degree': 1544, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2, 2], 'aut_gens': [[1], [5], [3]], 'aut_group': '4.2', 'aut_hash': 2, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [1, 6], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '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': 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], [4, 1, 2], [8, 1, 4]], 'center_label': '8.1', 'center_order': 8, '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', '2.1', '2.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1], [8, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 8, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '4.1', '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 8]], 'label': '8.1', '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': 'C8', 'ngens': 1, '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': 8, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 1], [4, 2], [8, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[5], [3]], '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': 1, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [4, 1]], 'representations': {'PC': {'code': 323, 'gens': [1], 'pres': [3, -2, -2, -2, 6, 16]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26315074]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [77]}, 'Perm': {'d': 8, 'gens': [40176, 16582, 5167]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_8', 'transitive_degree': 8, 'wreath_data': None, 'wreath_product': False}
