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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '19360.h', 'ambient_counter': 8, 'ambient_order': 19360, 'ambient_tex': 'C_{11}^2:(C_{10}\\times \\SD_{16})', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2420, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '19360.h.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.g1.a1', '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': 4, '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': '4840.bb', 'subgroup_hash': 3459893620231323134, 'subgroup_order': 4840, 'subgroup_tex': 'C_{11}:(C_4\\times F_{11})', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '19360.h', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '9680.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.e1.b1', '20.g1.a1', '44.i1.a1', '44.i1.b1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7885, -1, 8483, -1, 7087, -1, 6663, -1], 'generators': [13415, 1760, 2, 9680, 4900, 40], 'label': '19360.h.4.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '4.g1.a1', 'projective_image': '9680.ba', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.y'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '40.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [20, 10, 110, 22, 2], 'aut_gens': [[1, 10, 440], [2096, 3705, 120], [4481, 290, 3520], [341, 2430, 3520], [3961, 670, 440], [221, 230, 440]], 'aut_group': '96800.d', 'aut_hash': 294072648738705471, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96800, 'aut_permdeg': 165, 'aut_perms': [26887946357653327241919148376253960444964022953138881121333315167910851311237867638038508343465278855659645917427530697090111809679564608748147464654050491784112815885876632924968018340763611690419883380376125912300262505652159382861957026655810145838830454635269673523792964937577420279568279968, 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14147136261014988421890402711149064071342216845866825911841715028956230240199386483335367978890651896136823671402361484980504720917058404237079924415650030869333919428965424770671007917279117087975448946058861999286457879673780519343577299561575244122910768792830593690339809263818563261], 'aut_phi_ratio': 55.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 2, 1], [4, 11, 4, 1], [5, 121, 1, 4], [10, 121, 1, 4], [10, 121, 2, 4], [11, 10, 2, 1], [11, 20, 5, 1], [20, 121, 4, 4], [22, 10, 2, 1], [22, 20, 5, 1], [44, 110, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}^2:D_4', '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': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [4, 11, 4], [5, 121, 4], [10, 121, 12], [11, 10, 2], [11, 20, 5], [20, 121, 16], [22, 10, 2], [22, 20, 5], [44, 110, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2420.x', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 28, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [4, 11, 2, 2], [5, 121, 4, 1], [10, 121, 4, 3], [11, 10, 1, 2], [11, 20, 1, 5], [20, 121, 8, 2], [22, 10, 1, 2], [22, 20, 1, 5], [44, 110, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 220, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 1, 5]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2420.x', 'hash': 3459893620231323134, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 22, 11], 'inner_gens': [[1, 2810, 2200], [2481, 10, 4400], [3081, 890, 440]], 'inner_hash': 3244222575460283753, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': True, 'inner_tex': 'D_{11}:F_{11}', 'inner_used': [1, 2], 'irrC_degree': 20, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 20, 'irrep_stats': [[1, 40], [10, 8], [20, 10]], 'label': '4840.bb', 'linC_count': 17, 'linC_degree': 20, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 5, 'linQ_dim': 20, 'linQ_dim_count': 5, 'linR_count': 5, 'linR_degree': 20, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11:(C4*F11)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 25, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 58, 'number_divisions': 28, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 114, 'number_subgroups': 2684, 'old_label': None, 'order': 4840, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [4, 44], [5, 484], [10, 1452], [11, 120], [20, 1936], [22, 120], [44, 440]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [10, 2, 2], 'outer_gen_pows': [0, 2, 0], 'outer_gens': [[221, 2510, 3520], [2096, 2225, 160], [221, 3730, 4400]], 'outer_group': '40.8', 'outer_hash': 8, 'outer_nilpotent': False, 'outer_order': 40, 'outer_permdeg': 9, 'outer_perms': [56887, 11536, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_5:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 26, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 4], [8, 2], [10, 4], [20, 12]], 'representations': {'PC': {'code': '1559576732850775616851097645465320498243561244934095030099', 'gens': [1, 3, 6], 'pres': [6, -2, -5, -2, -2, -11, -11, 12, 1327, 50582, 14138, 50, 8163, 729, 69, 7204, 1810, 79205, 23771, 15857]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [18418977602547828, 39041701844509573, 42218820227238581, 7265543269142274, 40451685466516614, 41772741070013040]}, 'Perm': {'d': 26, 'gens': [15566290944817027911473716, 16159914175745343942541805]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}:(C_4\\times F_{11})', 'transitive_degree': 44, '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': '40.14', '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, 20, 10, 10], 'aut_gens': [[1, 10, 40, 440], [7441, 6970, 160, 16280], [8821, 11010, 5360, 13760], [4001, 14430, 10720, 12760], [14721, 11030, 2080, 1320], [1461, 3990, 120, 18440], [7361, 430, 16080, 2200]], 'aut_group': None, 'aut_hash': 6924539337684527549, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 154880, 'aut_permdeg': 297, 'aut_perms': [7981763939924546360764279891347510331416028051802311028847405748176021680524974958531783888904297415942642717507862049004320161971518192380606189829014126901419378151500691435705692825142189827977482899335345661026196356140681289702115466714016403813301679339142257995200908295976626190142752212711359289214332096802111076306118650912566705768746356007094827711799656106570118824436596745765730865798697708593311306919335153594543640844757055614989677436085366858493607917271772680313331884311406446131646366380326636633464951693243285444197902735317485948319399453823001895992766097361809504528490888641636, 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4528487603208450142208928240749216875254352526615846622728539469391732956610921856863191929995510893736018080708174787260357438820087951294837650884171020647201396201989689341020569605391713888502451083826846031749174321205036116711210119471668157155920776469795612701621045531899689667973711732493306703468866248897677646835477184907015452131406051423467689628612754050421159248079677351492143914191653418257635681378756101437770536229159843793562701282230478680712604135297644680047754965206528357568592921686771910084471337320841592081598968746811124875662137491860540518840629936683234362646415211890435], 'aut_phi_ratio': 22.0, '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, 121, 1, 4], [8, 242, 4, 1], [10, 121, 1, 4], [10, 121, 2, 4], [10, 484, 2, 4], [11, 20, 1, 2], [11, 40, 1, 2], [20, 242, 1, 8], [20, 484, 2, 4], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 2, 1], [40, 242, 4, 4], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_2^3.C_5.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', '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, 121, 4], [8, 242, 4], [10, 121, 12], [10, 484, 8], [11, 20, 2], [11, 40, 2], [20, 242, 8], [20, 484, 8], [22, 20, 2], [22, 40, 2], [22, 440, 2], [40, 242, 16], [44, 40, 6], [44, 440, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, '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', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, '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, 121, 4, 1], [8, 242, 2, 2], [10, 121, 4, 3], [10, 484, 4, 2], [11, 20, 1, 2], [11, 40, 1, 2], [20, 242, 4, 2], [20, 484, 4, 2], [22, 20, 1, 2], [22, 40, 1, 2], [22, 440, 1, 2], [40, 242, 8, 2], [44, 40, 1, 2], [44, 40, 2, 2], [44, 440, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 15249024, 'exponent': 440, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[40, -1, 1], [40, 0, 4], [40, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '9680.ba', 'hash': 6161013968996120931, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 220, 'inner_gen_orders': [10, 4, 11, 22], 'inner_gens': [[1, 15870, 14440, 15400], [6181, 10, 12360, 9520], [5401, 7050, 40, 440], [4401, 10730, 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': 40, 'irrQ_dim': 40, 'irrR_degree': 40, 'irrep_stats': [[1, 40], [2, 30], [20, 8], [40, 10]], 'label': '19360.h', 'linC_count': 160, 'linC_degree': 22, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 24, 'linQ_degree_count': 16, 'linQ_dim': 24, 'linQ_dim_count': 16, 'linR_count': 80, 'linR_degree': 24, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C11^2:(C10*SD16)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 88, 'number_divisions': 40, 'number_normal_subgroups': 47, 'number_subgroup_autclasses': 182, 'number_subgroup_classes': 260, 'number_subgroups': 13840, 'old_label': None, 'order': 19360, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [4, 332], [5, 484], [8, 968], [10, 5324], [11, 120], [20, 5808], [22, 1000], [40, 3872], [44, 1120]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 4840, 0], 'outer_gens': [[4841, 4850, 40, 10120], [1, 9690, 40, 10120], [14521, 10, 40, 440], [12401, 16730, 400, 9240]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 415, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 30, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 10], [8, 2], [16, 2], [20, 8], [40, 6], [80, 2]], 'representations': {'PC': {'code': '237709070594190553847084917911028329208630051796201051475099379336692318935694701973809500934294955234405539276375703009009', 'gens': [1, 3, 5, 6], 'pres': [8, 2, 5, 2, 2, 11, 2, 2, 11, 16, 380882, 106210, 66, 86403, 203851, 15515, 577604, 3212, 49460, 828, 739205, 390733, 45717, 22205, 141, 640646, 369614, 104182, 51774, 166, 225287, 225295, 114199, 56351]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [10205032106821235, 10522401710269773, 3352440040187918, 28359274195767324, 16265167320216339, 39688262258321567, 40451685466516614, 41772741070013040]}, 'Perm': {'d': 30, 'gens': [10725617432828987907080673449809, 19932021658053053191376966091196, 29085808057853731426811931276437, 10192793457047840180283803040000, 36423478910311224388218174412800, 47009471610196414840525654366080, 56159299088347860887786997253751, 5329]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:(C_{10}\\times \\SD_{16})', 'transitive_degree': 88, 'wreath_data': None, 'wreath_product': False}
