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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '16464.bn', 'ambient_counter': 40, 'ambient_order': 16464, 'ambient_tex': '\\He_7:(C_6\\times D_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 686, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '16464.bn.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', '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': 12, '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': '1372.16', 'subgroup_hash': 16, 'subgroup_order': 1372, 'subgroup_tex': 'C_7^2:D_{14}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '16464.bn', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8232.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.e1', '6.a1'], 'contains': ['24.c1', '24.d1', '84.f1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [4531, -1, 5982, -1], 'generators': [30120347594583, 31392350697539, 16807270434870, 13420387588825, 23092195706753], 'label': '16464.bn.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.e1', 'projective_image': '16464.bn', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '4116.t'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 84, 'aut_gen_orders': [6, 21, 14, 14, 3, 7, 7, 7], 'aut_gens': [[18902558, 34720862, 21401649, 473244, 4590980], [12798007, 34720862, 39726573, 39650299, 34709006], [20488867, 16014990, 38915967, 3767423, 2943915], [13608270, 16915566, 31161565, 22135981, 31946124], [38887498, 25779729, 21344756, 31061818, 24120759], [10724142, 34720862, 20562789, 24944316, 27414938], [18902558, 2132214, 31122789, 31061818, 9061382], [13608270, 7426523, 577821, 473244, 4590980], [18902558, 5426393, 25872394, 473244, 4590980]], 'aut_group': '24696.h', 'aut_hash': 6460325027391172650, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24696, 'aut_permdeg': 98, 'aut_perms': [8072462525763657423887702027775695715895911117012154301568510614420364347434964987387663919598489908873577320738018286916069031332376005551658206645729583, 7973648044450685043766907102563357622158175401158398038833872247406603965313357925888178547807405946748680004035352917984094022637058134928651307645734741, 1428268859122317160947749691118549436577039933412273933878834232153973079329249071523242759989445452823232247092715339107999061863736166820493591591302153, 1860361354981565449877489976347257140588715883857436270573222205710148967594623653328624922147802799243547750636093363357310266993960960854884468429478447, 7676531147824910761918749237926645851807486595443180145442589715217405723186553033782241772019173118153767963289078074522216544364221428802813419935666361, 4575999928770365575849865302600576453160207894551106387879418952403947478088452135214139955763337048549178957105409835376759985509964387298863877118247217, 13068746034600252549823024523116571394016353712986496744692036808617792947706406641231233336445456949362420625037565073409918239101557244158316633431889, 5649811286836169354106838724954916597346818334812051447262000409334644962152457333418638353733818312182114119765610158294913505064463473153936500717640202], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 49, 1, 1], [2, 49, 2, 1], [7, 2, 3, 1], [7, 14, 6, 1], [7, 28, 9, 1], [14, 98, 3, 1], [14, 98, 6, 1]], 'aut_supersolvable': False, 'aut_tex': '\\He_7:C_6\\wr C_2', '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': 84, 'autcentquo_group': '24696.h', 'autcentquo_hash': 6460325027391172650, 'autcentquo_nilpotent': False, 'autcentquo_order': 24696, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_7:C_6\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 49, 3], [7, 2, 3], [7, 14, 6], [7, 28, 9], [14, 98, 9]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1372.16', 'commutator_count': 1, 'commutator_label': '343.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '7.1', '7.1', '7.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 49, 1, 3], [7, 2, 3, 1], [7, 14, 3, 2], [7, 28, 3, 3], [14, 98, 3, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 21, 'exponent': 14, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[14, 1, 6]], 'familial': False, 'frattini_label': '7.1', 'frattini_quotient': '196.9', 'hash': 16, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [7, 2, 14, 7, 7], 'inner_gens': [[18902558, 14367925, 21296951, 21297079, 14355719], [4667088, 34720862, 2224935, 11885048, 13532162], [38887498, 13544368, 21401649, 21297079, 29414704], [3843531, 23309058, 577821, 473244, 4590980], [8314276, 25779729, 31166388, 473244, 4590980]], 'inner_hash': 16, 'inner_nilpotent': False, 'inner_order': 1372, 'inner_split': True, 'inner_tex': 'C_7^2:D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 14, 'irrQ_degree': 42, 'irrQ_dim': 42, 'irrR_degree': 14, 'irrep_stats': [[1, 4], [2, 12], [4, 9], [14, 6]], 'label': '1372.16', 'linC_count': 6, 'linC_degree': 14, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 2, 'linQ_dim': 42, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C7^2:D14', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 31, 'number_divisions': 13, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 47, 'number_subgroups': 1109, 'old_label': None, 'order': 1372, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 147], [7, 342], [14, 882]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [5767203, 9896923], 'outer_gens': [[16018136, 36355943, 16910743, 1344312, 26695785], [33637138, 34720862, 39697976, 4590980, 5414537]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [652, 373], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 49, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [6, 4], [12, 3], [42, 2]], 'representations': {'PC': {'code': 1702653240871935217080098711, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -7, -7, -7, 261, 26, 362, 13448, 2113, 29404, 14709]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [18902558, 34720862, 21401649, 473244, 4590980]}, 'Perm': {'d': 49, 'gens': [1315490939820261104781241293384898516680185382247095762872399, 1315490941020389297941406270674321266170870307462847850030879, 532482879537830020389456268526937482059870595614507008000000000, 200715159680502423232357683145854231081788001750633, 74483493555417151184854488523683573561511365457240384149969120]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_7^2:D_{14}', 'transitive_degree': 49, '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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 168, 'aut_gen_orders': [6, 6, 6, 56], 'aut_gens': [[11018540921774, 22165580522919, 31377278699738, 28487064012000, 30151566904449, 17233820802337, 31584908075045, 28186167033742], [26377799597348, 11223694496079, 32190091856054, 28487064012000, 22701035052169, 2191285665337, 16405766752913, 13544849055836], [23368903172831, 20936473845264, 29533374098248, 28487064012000, 26952098254183, 23031355981478, 15744975985122, 1487683265364], [25283580852192, 4879503254529, 14326661126192, 28487064012000, 32706530809565, 8771305970127, 31210976847291, 31460169900330], [27268668745004, 4247988231682, 23161326075938, 28487064012000, 8301731496668, 31369705569094, 23092195706753, 28186167033742]], 'aut_group': None, 'aut_hash': 7665760530828185436, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 65856, 'aut_permdeg': 735, 'aut_perms': 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'aut_phi_ratio': 14.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 49, 1, 2], [2, 98, 4, 1], [3, 343, 1, 2], [4, 98, 2, 1], [6, 343, 1, 6], [6, 686, 4, 2], [7, 6, 1, 1], [7, 84, 2, 1], [7, 168, 1, 1], [12, 686, 2, 2], [14, 6, 1, 1], [14, 84, 2, 1], [14, 168, 1, 1], [14, 294, 1, 2], [14, 588, 4, 1], [28, 294, 2, 2]], 'aut_supersolvable': False, 'aut_tex': '\\He_7.C_4.C_6.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': 168, 'autcentquo_group': '16464.n', 'autcentquo_hash': 1800759200399241800, 'autcentquo_nilpotent': False, 'autcentquo_order': 16464, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\He_7:(C_3\\times D_8)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 49, 2], [2, 98, 4], [3, 343, 2], [4, 98, 2], [6, 343, 6], [6, 686, 8], [7, 6, 1], [7, 84, 2], [7, 168, 1], [12, 686, 4], [14, 6, 1], [14, 84, 2], [14, 168, 1], [14, 294, 2], [14, 588, 4], [28, 294, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '8232.n', 'commutator_count': 1, 'commutator_label': '686.8', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1', '7.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 40, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['8232.n', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 49, 1, 2], [2, 98, 1, 4], [3, 343, 2, 1], [4, 98, 1, 2], [6, 343, 2, 3], [6, 686, 2, 4], [7, 6, 1, 1], [7, 84, 1, 2], [7, 168, 1, 1], [12, 686, 2, 2], [14, 6, 1, 1], [14, 84, 1, 2], [14, 168, 1, 1], [14, 294, 1, 2], [14, 588, 1, 4], [28, 294, 2, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 21403200, 'exponent': 84, 'exponents_of_order': [4, 3, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[42, 1, 4]], 'familial': False, 'frattini_label': '7.1', 'frattini_quotient': '2352.cj', 'hash': 3296812974421571037, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 84, 'inner_gen_orders': [6, 28, 7, 1, 14, 3, 7, 7], 'inner_gens': [[11018540921774, 25704147918924, 2314493528002, 28487064012000, 30131457909962, 17233820802337, 16405766752913, 13544849055836], [29335370513620, 22165580522919, 31404845388797, 28487064012000, 9366638703006, 5714485256721, 19129880664018, 28186167033742], [553714237083, 22188695395191, 31377278699738, 28487064012000, 18772301494870, 22477870518051, 12894152318439, 28186167033742], [11018540921774, 22165580522919, 31377278699738, 28487064012000, 30151566904449, 17233820802337, 31584908075045, 28186167033742], [29736826687990, 17346860986158, 15153603003366, 28487064012000, 30151566904449, 20784868992736, 8729897272937, 20081273301458], [11018540921774, 18650127881593, 22777577527895, 28487064012000, 30431334483305, 17233820802337, 13018890495555, 16807270434870], [11447856643305, 14442735852675, 13461669732500, 28487064012000, 31735860906964, 23893010137776, 31584908075045, 28186167033742], [26349952524075, 22165580522919, 31377278699738, 28487064012000, 289809863892, 5866788149510, 31584908075045, 28186167033742]], 'inner_hash': 4617446893275312164, 'inner_nilpotent': False, 'inner_order': 8232, 'inner_split': True, 'inner_tex': '\\He_7:(C_3\\times D_4)', 'inner_used': [1, 2, 5], 'irrC_degree': 42, 'irrQ_degree': 42, 'irrQ_dim': 42, 'irrR_degree': 42, 'irrep_stats': [[1, 24], [2, 6], [12, 8], [24, 2], [42, 8]], 'label': '16464.bn', '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': 'He7:(C6*D4)', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 29, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 48, 'number_divisions': 36, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 152, 'number_subgroup_classes': 310, 'number_subgroups': 28494, 'old_label': None, 'order': 16464, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 491], [3, 686], [4, 196], [6, 7546], [7, 342], [12, 2744], [14, 3282], [28, 1176]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [4747844002000, 20458852240163], 'outer_gens': [[11018540921774, 16605889332983, 31377278699738, 28487064012000, 30151566904449, 17233820802337, 31584908075045, 28186167033742], [11018540921774, 2628976185664, 27470050935670, 28487064012000, 12826181150771, 17233820802337, 26217807438680, 16807270434870]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 100, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 2], [12, 8], [24, 2], [42, 4], [84, 2]], 'representations': {'PC': {'code': '3309310532067307875576318670136127846580931799600242890504703170312509412862997031975610642303880237764667756316571', 'gens': [1, 3, 5, 6, 8], 'pres': [8, 2, 3, 2, 2, 7, 2, 7, 7, 16, 221042, 1810, 66, 398211, 120011, 25115, 286084, 283212, 13780, 39708, 138245, 205645, 120789, 55805, 14485, 141, 585990, 413966, 104630, 42366, 33750, 752647, 301071]}, 'GLFp': {'d': 4, 'p': 7, 'gens': [11018540921774, 22165580522919, 31377278699738, 28487064012000, 30151566904449, 17233820802337, 31584908075045, 28186167033742]}, 'Perm': {'d': 100, 'gens': [48209493897084131340663584552221395836861305430353447573214596121858612758608598170262565245077661365283757443453667134451431619809597071579195320672703961, 990995744307732092891762720366078925993382298319084996115249279925858199512357275656156617239714351878656136054092052504329803112069577005604416902188615649, 1933782035407652184675948602934075679658743852555505012224077523902987501120375724535575222359588174795868232810513703641041173383381389298753616233866014744, 2876568328345683846676341726766183936060664570302020384454599164194207249510322072847344914256350303620446399697889802844852448335985257680637197250456244950, 1, 3819354588771467411031207403788306312051261127097788009258624918943621181849660453483811735691876487338546164606227267674866496935777966592794598935612339560, 95830045992340945384982746139692703087263622588610783450807901089013448274933830255904590500044446825001580165083103213590207302186764569405829438697569344, 4771664901357795743831811993641175512382207244008111721198452492160563398140309665537741243941469792910605409513419259403224665604906921376014386601482024121]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '\\He_7:(C_6\\times D_4)', 'transitive_degree': 196, 'wreath_data': None, 'wreath_product': False}
