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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '162000.o', 'ambient_counter': 15, 'ambient_order': 162000, 'ambient_tex': 'C_{15}^2.(F_5\\times S_3^2)', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 75, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '162000.o.180.cn1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '180.cn1', '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': 180, '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': '900.93', 'subgroup_hash': 93, 'subgroup_order': 900, 'subgroup_tex': 'C_3\\times C_5^2:D_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '162000.o', 'aut_centralizer_order': None, 'aut_label': '180.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54000.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1', '60.y1', '90.a1', '90.cq1', '90.cr1'], 'contains': ['360.bh1', '360.bz1', '360.de1', '540.cg1', '540.ct1', '4500.p1'], 'core': '2160.a1', 'coset_action_label': None, 'count': 45, 'diagramx': None, 'generators': [154123, 32400, 56400, 100088, 131244, 97920], 'label': '162000.o.180.cn1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '45.a1', 'old_label': '180.cn1', 'projective_image': '162000.o', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '180.cn1', 'subgroup_fusion': None, 'weyl_group': '1200.951'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [2, 24, 5, 10], 'aut_gens': [[1, 2, 12, 60], [1, 10, 396, 444], [3, 2, 576, 636], [205, 386, 12, 60], [205, 206, 12, 660]], 'aut_group': '2400.fv', 'aut_hash': 4902779705341075044, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2400, 'aut_permdeg': 32, 'aut_perms': [1583421087881593003708930125065027, 152926438882276026599170794009396334, 25704866177672373189020434174835468, 27729911718884309273675378547103874], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 15, 2, 1], [2, 25, 1, 1], [3, 1, 2, 1], [3, 50, 1, 1], [3, 50, 2, 1], [5, 6, 4, 1], [6, 15, 4, 1], [6, 25, 2, 1], [6, 50, 1, 1], [6, 50, 2, 1], [10, 30, 4, 1], [15, 6, 8, 1], [30, 30, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{25}:C_2^2', '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': 120, 'autcentquo_group': '1200.946', 'autcentquo_hash': 946, 'autcentquo_nilpotent': False, 'autcentquo_order': 1200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{25}:C_2', 'cc_stats': [[1, 1, 1], [2, 15, 2], [2, 25, 1], [3, 1, 2], [3, 50, 3], [5, 6, 4], [6, 15, 4], [6, 25, 2], [6, 50, 3], [10, 30, 4], [15, 6, 8], [30, 30, 8]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '300.25', 'commutator_count': 1, 'commutator_label': '75.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 93, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['300.25', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 15, 1, 2], [2, 25, 1, 1], [3, 1, 2, 1], [3, 50, 1, 1], [3, 50, 2, 1], [5, 6, 2, 2], [6, 15, 2, 2], [6, 25, 2, 1], [6, 50, 1, 1], [6, 50, 2, 1], [10, 30, 2, 2], [15, 6, 4, 2], [30, 30, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 30, 'exponents_of_order': [2, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 0, 16]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '900.93', 'hash': 93, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 6, 5, 5], 'inner_gens': [[1, 10, 564, 816], [5, 2, 564, 276], [409, 410, 12, 60], [205, 746, 12, 60]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 300, 'inner_split': False, 'inner_tex': 'C_5^2:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 6], [6, 24]], 'label': '900.93', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 16, 'linQ_dim': 14, 'linQ_dim_count': 16, 'linR_count': 32, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3*C5^2:D6', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 42, 'number_divisions': 20, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 64, 'number_subgroups': 852, 'old_label': None, 'order': 900, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 55], [3, 152], [5, 24], [6, 260], [10, 120], [15, 48], [30, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [0, 6], 'outer_gens': [[1, 2, 12, 660], [7, 2, 744, 828]], 'outer_group': '8.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2], [12, 4], [24, 4]], 'representations': {'PC': {'code': 75273635705562549151926080330108520884189732983, 'gens': [1, 2, 4, 5], 'pres': [6, 2, 2, 3, 5, 3, 5, 121, 31, 146, 13539, 6777, 3327, 24484, 4150, 6136, 118, 21173, 13835, 5309]}, 'Perm': {'d': 18, 'gens': [43191264414384, 45793772419680, 3, 402804167575080, 64531782975024, 781229798473104]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_5^2:D_6', 'transitive_degree': 45, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 180, 'aut_gen_orders': [12, 36, 12, 12, 30], 'aut_gens': [[1, 2, 24, 240, 3600, 10800], [101185, 84586, 40632, 103200, 7200, 60240], [22769, 107906, 150072, 104880, 55200, 116160], [131249, 70322, 31656, 161280, 108000, 10560], [97833, 38162, 160488, 19200, 6000, 138240], [102737, 5050, 61224, 58560, 2400, 69120]], 'aut_group': None, 'aut_hash': 451067231434280781, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1944000, 'aut_permdeg': 197, 'aut_perms': [38572661011479038609926156471396826338933413482967923867563001959410522727517999246916283971666042342616642958638541398183811305316970546790489492372138408583146247248745855337958746521672867291638032854949407772628911751095601926210865408774280652560176414981051830426608707671546971752596525879311568592672796455722575757039001512458508742081362723785258299520075962, 53152165146376026039225795694522276246765246003073483840145021479242829817816960843380976807675612906594517083973214929859931727589192910190230879890125237929249849881533804851452848904515478796414135818459118258130235298641303776780480314408907589557490225659051331794492440998317786402190266998670432816637951718615927996027034959304628834305564292147914628977838171, 50906981830444989487868655748846264542234636674963353789788878801743805239999830926409511651938650326759107423360756882238412623312113215099229877076139148360666947151234997675236125165692785945652406043250299855731350031521939422467545603819751619243828432531806055322996648400767812855583048983713834923008944473971299729238838384016458833464859788216740381697284985, 82763434439615435740057326939035960560290944183343455484294626304283485690223617295604785240385821803757701756241844903575913471421789595497563377281147331710232859232622490909600750065162683301280970147061185844289267421768753074592016118497155785780731468758232414389601592575214778082778138155571277288422633947996404223903754760978655016084471150262583823396875834, 1758136261793140517070192030916045321449838805674310446805132319114171499200015761453620688135946858475798541389983256589289925140128432543162561316312668869906656296219601860079033921868178287480691889185982381056933453419917745506160491108863806867430522732370793989369050592058593573918557198785310710101190615237046318521250895294789691015923187471175845532179482], 'aut_phi_ratio': 45.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 225, 1, 1], [2, 675, 1, 1], [2, 3375, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 6, 3, 1], [3, 450, 1, 1], [4, 125, 1, 2], [4, 1125, 1, 2], [4, 3375, 1, 4], [5, 4, 1, 1], [5, 12, 1, 2], [5, 12, 4, 1], [5, 24, 2, 1], [6, 90, 1, 1], [6, 90, 3, 1], [6, 250, 1, 1], [6, 270, 1, 1], [6, 450, 1, 1], [6, 450, 3, 1], [6, 750, 1, 1], [6, 750, 3, 1], [6, 1350, 1, 2], [6, 2250, 1, 1], [6, 6750, 1, 1], [9, 900, 1, 1], [10, 108, 1, 1], [10, 180, 1, 2], [10, 180, 4, 1], [10, 324, 1, 2], [10, 324, 4, 1], [10, 540, 1, 2], [10, 540, 4, 1], [10, 648, 2, 1], [10, 900, 1, 1], [10, 2700, 1, 1], [12, 250, 1, 2], [12, 750, 1, 2], [12, 750, 3, 2], [12, 2250, 1, 4], [12, 2250, 3, 2], [12, 6750, 1, 4], [15, 8, 1, 1], [15, 24, 1, 5], [15, 24, 3, 3], [15, 24, 4, 2], [15, 24, 12, 1], [15, 48, 1, 2], [15, 48, 2, 2], [15, 48, 3, 2], [15, 48, 4, 2], [15, 48, 6, 1], [15, 48, 12, 2], [15, 1800, 1, 1], [18, 4500, 1, 1], [30, 360, 1, 2], [30, 360, 3, 2], [30, 360, 4, 1], [30, 360, 12, 1], [30, 1080, 1, 2], [30, 1080, 4, 1], [30, 1800, 1, 1], [30, 1800, 3, 1], [30, 5400, 1, 2], [36, 4500, 1, 2], [45, 3600, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{15}^3.C_6^2.C_2^4', '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': 180, 'autcentquo_group': None, 'autcentquo_hash': 451067231434280781, 'autcentquo_nilpotent': False, 'autcentquo_order': 1944000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{15}^2.C_{15}.C_6^2.C_2^4', 'cc_stats': [[1, 1, 1], [2, 27, 1], [2, 45, 1], [2, 125, 1], [2, 135, 1], [2, 225, 1], [2, 675, 1], [2, 3375, 1], [3, 2, 1], [3, 6, 4], [3, 450, 1], [4, 125, 2], [4, 1125, 2], [4, 3375, 4], [5, 4, 1], [5, 12, 6], [5, 24, 2], [6, 90, 4], [6, 250, 1], [6, 270, 1], [6, 450, 4], [6, 750, 4], [6, 1350, 2], [6, 2250, 1], [6, 6750, 1], [9, 900, 1], [10, 108, 1], [10, 180, 6], [10, 324, 6], [10, 540, 6], [10, 648, 2], [10, 900, 1], [10, 2700, 1], [12, 250, 2], [12, 750, 8], [12, 2250, 10], [12, 6750, 4], [15, 8, 1], [15, 24, 34], [15, 48, 50], [15, 1800, 1], [18, 4500, 1], [30, 360, 24], [30, 1080, 6], [30, 1800, 4], [30, 5400, 2], [36, 4500, 2], [45, 3600, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '162000.o', 'commutator_count': 1, 'commutator_label': '10125.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 225, 1, 1], [2, 675, 1, 1], [2, 3375, 1, 1], [3, 2, 1, 1], [3, 6, 1, 4], [3, 450, 1, 1], [4, 125, 2, 1], [4, 1125, 2, 1], [4, 3375, 2, 2], [5, 4, 1, 1], [5, 12, 1, 6], [5, 24, 1, 2], [6, 90, 1, 4], [6, 250, 1, 1], [6, 270, 1, 1], [6, 450, 1, 4], [6, 750, 1, 4], [6, 1350, 1, 2], [6, 2250, 1, 1], [6, 6750, 1, 1], [9, 900, 1, 1], [10, 108, 1, 1], [10, 180, 1, 6], [10, 324, 1, 6], [10, 540, 1, 6], [10, 648, 1, 2], [10, 900, 1, 1], [10, 2700, 1, 1], [12, 250, 2, 1], [12, 750, 2, 4], [12, 2250, 2, 5], [12, 6750, 2, 2], [15, 8, 1, 1], [15, 24, 1, 34], [15, 48, 1, 50], [15, 1800, 1, 1], [18, 4500, 1, 1], [30, 360, 1, 24], [30, 1080, 1, 6], [30, 1800, 1, 4], [30, 5400, 1, 2], [36, 4500, 2, 1], [45, 3600, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 543449088, 'exponent': 180, 'exponents_of_order': [4, 4, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[24, 1, 24], [48, 1, 30]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '18000.c', 'hash': 7543864577875533143, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 180, 'inner_gen_orders': [12, 12, 10, 15, 3, 15], 'inner_gens': [[1, 142666, 130008, 73200, 3600, 116160], [18641, 2, 21768, 71520, 110400, 60240], [35857, 140498, 24, 2640, 7200, 118800], [103441, 105122, 1224, 240, 3600, 10800], [1, 58802, 7224, 240, 3600, 10800], [71041, 126962, 54024, 240, 3600, 10800]], 'inner_hash': 7543864577875533143, 'inner_nilpotent': False, 'inner_order': 162000, 'inner_split': True, 'inner_tex': 'C_{15}^2.(F_5\\times S_3^2)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 16], [2, 16], [4, 8], [6, 32], [8, 4], [12, 24], [16, 1], [24, 72], [48, 50]], 'label': '162000.o', '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': 'C15^2.(F5*S3^2)', 'ngens': 11, '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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 108, 'number_characteristic_subgroups': 74, 'number_conjugacy_classes': 223, 'number_divisions': 206, 'number_normal_subgroups': 74, 'number_subgroup_autclasses': 3040, 'number_subgroup_classes': 7344, 'number_subgroups': 1883024, 'old_label': None, 'order': 162000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 4607], [3, 476], [4, 16000], [5, 124], [6, 17380], [9, 900], [10, 11268], [12, 56000], [15, 5024], [18, 4500], [30, 33120], [36, 9000], [45, 3600]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [12], 'outer_gen_pows': [0], 'outer_gens': [[110641, 88082, 130344, 55920, 60000, 34800]], 'outer_group': '12.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [867], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{12}', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 10], [6, 16], [8, 5], [12, 32], [16, 1], [24, 72], [48, 50]], 'representations': {'PC': {'code': '1133118133375519551232108113717092079387401535181033850634152259597881437454107097197970557070111679183950338681939657550248544683791480960555469445326166796142650875112882192681414083219847189618740248489360196296166743231959', 'gens': [1, 2, 5, 7, 9, 10], 'pres': [11, 2, 2, 2, 3, 2, 5, 3, 5, 3, 3, 5, 1483284, 3138653, 56, 4199846, 90, 6938627, 7150444, 598635, 1461596, 841702, 158, 6611621, 3210784, 573435, 1069634, 5636406, 2753537, 2795128, 413529, 8520, 303, 2851207, 1520658, 2138429, 1100920, 5464819, 1514730, 683141, 29752, 12777609, 3313220, 3451831, 1626942, 544553, 438, 348490, 43581, 1045472, 32713]}, 'Perm': {'d': 24, 'gens': [28319724232008057378547, 1289445910380788890821, 29494112082756937997615]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}^2.(F_5\\times S_3^2)', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}
