-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '46080.bx', 'ambient_counter': 50, 'ambient_order': 46080, 'ambient_tex': '(S_5\\times \\GL(2,\\mathbb{Z}/4)).C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 11520, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '46080.bx.4.J', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': False, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11520.gg', 'subgroup_hash': 5751830915595786420, 'subgroup_order': 11520, 'subgroup_tex': 'C_2^4.D_6\\times A_5', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '46080.bx', 'aut_centralizer_order': None, 'aut_label': '4.J', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '4.J', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [367920, 12973323017, 11647, 1617960, 88177029257, 7, 5040, 11662, 5160], 'label': '46080.bx.4.J', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.J', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '11520.cv', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.J', 'subgroup_fusion': None, 'weyl_group': '5760.co'}
-
gps_groups • Show schema
Hide schema
{'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': 60, 'aut_gen_orders': [12, 30, 30, 4, 20, 30], 'aut_gens': [[13414475808, 362886, 2424528, 363479, 5167, 5040, 349234870729, 5046, 23455], [88177385520, 367920, 2787535, 599, 363007, 127, 181065387295, 362886, 2431014], [193077947929, 5046, 2787414, 363592, 368041, 362880, 960790729, 367920, 811446], [355938496854, 5046, 2782368, 5758, 368041, 362880, 7227723295, 367920, 1169407], [19681418569, 362886, 2782489, 363479, 5167, 5161, 181583942809, 5046, 391369], [180624694447, 367920, 829855, 368513, 5167, 127, 6707215135, 5046, 386335], [193077589974, 5046, 2787535, 5639, 368041, 363001, 262016662729, 367920, 1169280]], 'aut_group': None, 'aut_hash': 4437775753756993605, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 92160, 'aut_permdeg': 43, 'aut_perms': [9487843131095715647020549962000951060847497174563785, 6718087790565018029539248374348318875170876448277532, 30123228239962710872282657825735289635289754893789774, 53920544571657926427197500745954323869152290655872362, 48641219246627072314906816934269941268684747829579077, 31295890765641092449038872286281097081434106838705578], 'aut_phi_ratio': 30.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 4, 1], [2, 15, 1, 2], [2, 15, 2, 1], [2, 45, 1, 2], [2, 45, 2, 1], [2, 90, 4, 1], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 1, 4, 1], [4, 3, 4, 1], [4, 6, 4, 3], [4, 15, 4, 1], [4, 45, 4, 1], [4, 90, 4, 3], [5, 12, 2, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 60, 1, 2], [6, 60, 2, 1], [6, 120, 1, 2], [6, 120, 2, 1], [6, 120, 4, 1], [6, 160, 1, 1], [6, 160, 2, 1], [10, 12, 2, 1], [10, 12, 4, 1], [10, 36, 2, 2], [10, 36, 4, 1], [10, 72, 8, 1], [12, 8, 4, 1], [12, 20, 4, 1], [12, 60, 4, 1], [12, 120, 4, 4], [12, 160, 4, 1], [15, 96, 2, 1], [20, 12, 8, 1], [20, 36, 8, 1], [20, 72, 8, 3], [30, 96, 2, 1], [30, 96, 4, 1], [60, 96, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_2^3\\times A_4).C_2^3.S_5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '2880.dv', 'autcentquo_hash': 409072078557532110, 'autcentquo_nilpotent': False, 'autcentquo_order': 2880, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 3, 4], [2, 6, 4], [2, 15, 4], [2, 45, 4], [2, 90, 4], [3, 8, 1], [3, 20, 1], [3, 160, 1], [4, 1, 4], [4, 3, 4], [4, 6, 12], [4, 15, 4], [4, 45, 4], [4, 90, 12], [5, 12, 2], [6, 8, 3], [6, 20, 3], [6, 60, 4], [6, 120, 8], [6, 160, 3], [10, 12, 6], [10, 36, 8], [10, 72, 8], [12, 8, 4], [12, 20, 4], [12, 60, 4], [12, 120, 16], [12, 160, 4], [15, 96, 2], [20, 12, 8], [20, 36, 8], [20, 72, 24], [30, 96, 6], [60, 96, 8]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '1440.5848', 'commutator_count': 1, 'commutator_label': '720.768', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '60.5'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 163, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['24.12', 1], ['4.1', 1], ['60.5', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 3, 1, 4], [2, 6, 1, 4], [2, 15, 1, 4], [2, 45, 1, 4], [2, 90, 1, 4], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 1, 2, 2], [4, 3, 2, 2], [4, 6, 1, 4], [4, 6, 2, 4], [4, 15, 2, 2], [4, 45, 2, 2], [4, 90, 1, 4], [4, 90, 2, 4], [5, 12, 2, 1], [6, 8, 1, 3], [6, 20, 1, 3], [6, 60, 1, 4], [6, 120, 1, 8], [6, 160, 1, 3], [10, 12, 2, 3], [10, 36, 2, 4], [10, 72, 2, 4], [12, 8, 2, 2], [12, 20, 2, 2], [12, 60, 2, 2], [12, 120, 1, 4], [12, 120, 2, 6], [12, 160, 2, 2], [15, 96, 2, 1], [20, 12, 4, 2], [20, 36, 4, 2], [20, 72, 2, 4], [20, 72, 4, 4], [30, 96, 2, 3], [60, 96, 4, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 4203360, 'exponent': 60, 'exponents_of_order': [8, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '5760.eb', 'hash': 5751830915595786420, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 3, 2, 2, 2, 3, 2, 4], 'inner_gens': [[13414475808, 362886, 834768, 363479, 368041, 5040, 181063439695, 367920, 1169401], [13414475808, 362886, 2419494, 363479, 5167, 5040, 349234865695, 5046, 28489], [13412068128, 5046, 2424528, 5639, 368041, 362880, 349234507855, 367920, 1169401], [13414475808, 362886, 2419494, 363479, 5167, 5040, 349234865695, 5046, 28489], [13414838694, 362886, 2782368, 363479, 5167, 5040, 349234502809, 5046, 23455], [13414475808, 362886, 2419494, 363479, 5167, 5040, 349234865695, 5046, 28489], [274467945174, 5046, 2787414, 5639, 368041, 362880, 349234870729, 367920, 1169401], [13414838694, 362886, 2782368, 363479, 5167, 5040, 349234502809, 5046, 23455], [13413219120, 367920, 1197654, 368513, 5167, 6, 349232918095, 5046, 23455]], 'inner_hash': 5848, 'inner_nilpotent': False, 'inner_order': 1440, 'inner_split': True, 'inner_tex': 'S_4\\times A_5', 'inner_used': [1, 2, 3, 7], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 8], [3, 48], [4, 16], [5, 16], [6, 16], [8, 8], [9, 32], [10, 8], [12, 16], [15, 16]], 'label': '11520.gg', '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': False, 'name': 'C2^4.D6*A5', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 64, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 200, 'number_divisions': 120, 'number_normal_subgroups': 86, 'number_subgroup_autclasses': 2622, 'number_subgroup_classes': 6669, 'number_subgroups': 257978, 'old_label': None, 'order': 11520, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 639], [3, 188], [4, 1408], [5, 24], [6, 1764], [10, 936], [12, 2912], [15, 192], [20, 2112], [30, 576], [60, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 87218208121, 0, 0], 'outer_gens': [[13414843734, 362886, 2424528, 5633, 5167, 5040, 349234870729, 5046, 391369], [13414475808, 362886, 2424528, 5633, 5167, 5040, 349234870729, 5046, 23455], [274470347808, 362886, 2424528, 363479, 5167, 5040, 12975747529, 5046, 23455], [13414475929, 362886, 2424528, 363598, 5167, 5040, 349234870729, 5046, 23334], [13414475929, 362886, 2424649, 5633, 5167, 5161, 349234870729, 5046, 23455]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [5040, 5041, 127, 367920, 1169422], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [5, 8], [6, 12], [8, 8], [10, 8], [12, 16], [15, 8], [16, 2], [18, 8], [20, 2], [24, 6], [30, 4], [36, 4]], 'representations': {'Perm': {'d': 15, 'gens': [13414475808, 362886, 2424528, 363479, 5167, 5040, 349234870729, 5046, 23455]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4.D_6\\times A_5', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.51', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 60, 'aut_gen_orders': [4, 12, 6, 4, 60, 4, 12, 12], 'aut_gens': [[5182, 87178291200, 1, 274508656560, 379441, 362886, 5040, 5167, 1980721, 5047], [5182, 997920007, 16, 193038825607, 16576, 362903, 5040, 5167, 1975816, 5047], [5057, 87178659240, 23, 274947736327, 1629503, 5063, 127, 363007, 1612823, 120], [5177, 180583971240, 23, 87699190320, 16583, 362896, 120, 5167, 1180943, 127], [5057, 6227388847, 368063, 280257828607, 1987223, 363016, 362880, 363007, 1180823, 362887], [367942, 268240896000, 368041, 367914331567, 1169401, 367921, 362887, 367927, 1980841, 362880], [363017, 12933043200, 16, 106859254440, 1992263, 5063, 362880, 363007, 817936, 362887], [367942, 12933411247, 368063, 174398117167, 811463, 367936, 5040, 367927, 818063, 5047], [5062, 12933411247, 368056, 349712270640, 1987223, 363016, 127, 363007, 1975696, 120]], 'aut_group': '5324.b', 'aut_hash': 1498025544026746074, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2949120, 'aut_permdeg': 72, 'aut_perms': [27580687975010528451747829805971456366911360196643516149077234171095951900897571371581422285496072628934, 47409030395766859491598704199925642911736143705848966988354386671121284834674986152461722376659393661602, 15490094713799895665984897391090641408054859658874626110346525732118630815177293580283579304212340621373, 8820959368020426612459619884184736086442176908084906118507288553555539591886091705303651445695961204180, 2663203322531614739421532032490855889695284337228644736957538384115056392683997405047082173334052085095, 40620093035525175677028449972866022490518021781327432852525285719306939524013754710376250035060566498996, 48416115253608868795596252409092745307227784751122457648887020923352809606984000556957495840401603764513, 47350271729643409959749594242400586438085557684487607069912783680844598988528561732272652658474817684009], 'aut_phi_ratio': 240.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 4, 1], [2, 3, 1, 2], [2, 3, 2, 1], [2, 6, 4, 2], [2, 10, 4, 1], [2, 12, 4, 1], [2, 15, 1, 2], [2, 15, 2, 1], [2, 20, 4, 1], [2, 30, 4, 2], [2, 45, 1, 2], [2, 45, 2, 1], [2, 60, 4, 2], [2, 90, 4, 2], [2, 120, 4, 1], [2, 180, 4, 1], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [4, 6, 4, 1], [4, 12, 2, 2], [4, 12, 4, 1], [4, 20, 2, 1], [4, 30, 2, 1], [4, 30, 4, 1], [4, 60, 2, 2], [4, 60, 4, 2], [4, 90, 2, 1], [4, 90, 4, 2], [4, 120, 2, 2], [4, 120, 4, 1], [4, 180, 2, 3], [4, 180, 4, 4], [4, 360, 2, 2], [4, 360, 4, 2], [5, 24, 1, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 16, 4, 1], [6, 20, 1, 1], [6, 20, 2, 1], [6, 20, 4, 1], [6, 40, 4, 2], [6, 60, 1, 2], [6, 60, 2, 1], [6, 60, 4, 1], [6, 80, 4, 1], [6, 120, 1, 2], [6, 120, 2, 1], [6, 120, 4, 4], [6, 160, 1, 1], [6, 160, 2, 1], [6, 160, 4, 2], [6, 240, 4, 3], [6, 320, 4, 2], [10, 24, 1, 1], [10, 24, 2, 1], [10, 48, 4, 1], [10, 72, 1, 2], [10, 72, 2, 1], [10, 144, 4, 2], [10, 288, 4, 1], [12, 16, 2, 1], [12, 40, 2, 2], [12, 120, 2, 2], [12, 120, 4, 2], [12, 160, 2, 1], [12, 240, 2, 5], [12, 240, 4, 3], [12, 320, 2, 2], [12, 480, 2, 1], [12, 480, 4, 1], [15, 192, 1, 1], [20, 48, 2, 1], [20, 144, 2, 1], [20, 144, 4, 1], [20, 288, 2, 2], [20, 288, 4, 1], [30, 192, 1, 1], [30, 192, 2, 1], [30, 384, 4, 1], [60, 384, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2:C_{44}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '512.6249567', 'autcent_hash': 6452065007057432321, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '5760.co', 'autcentquo_hash': 6537139331229567448, 'autcentquo_nilpotent': False, 'autcentquo_order': 5760, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2\\times S_4\\times S_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 4], [2, 3, 4], [2, 6, 8], [2, 10, 4], [2, 12, 4], [2, 15, 4], [2, 20, 4], [2, 30, 8], [2, 45, 4], [2, 60, 8], [2, 90, 8], [2, 120, 4], [2, 180, 4], [3, 8, 1], [3, 20, 1], [3, 160, 1], [4, 2, 2], [4, 6, 6], [4, 12, 8], [4, 20, 2], [4, 30, 6], [4, 60, 12], [4, 90, 10], [4, 120, 8], [4, 180, 22], [4, 360, 12], [5, 24, 1], [6, 8, 3], [6, 16, 4], [6, 20, 7], [6, 40, 8], [6, 60, 8], [6, 80, 4], [6, 120, 20], [6, 160, 11], [6, 240, 12], [6, 320, 8], [10, 24, 3], [10, 48, 4], [10, 72, 4], [10, 144, 8], [10, 288, 4], [12, 16, 2], [12, 40, 4], [12, 120, 12], [12, 160, 2], [12, 240, 22], [12, 320, 4], [12, 480, 6], [15, 192, 1], [20, 48, 2], [20, 144, 6], [20, 288, 8], [30, 192, 3], [30, 384, 4], [60, 384, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '11520.cv', 'commutator_count': 1, 'commutator_label': '1440.5850', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '60.5'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 50, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['120.34', 1], ['2.1', 1], ['24.12', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 4], [2, 3, 1, 4], [2, 6, 1, 8], [2, 10, 1, 4], [2, 12, 1, 4], [2, 15, 1, 4], [2, 20, 1, 4], [2, 30, 1, 8], [2, 45, 1, 4], [2, 60, 1, 8], [2, 90, 1, 8], [2, 120, 1, 4], [2, 180, 1, 4], [3, 8, 1, 1], [3, 20, 1, 1], [3, 160, 1, 1], [4, 2, 1, 2], [4, 6, 1, 6], [4, 12, 1, 8], [4, 20, 1, 2], [4, 30, 1, 6], [4, 60, 1, 12], [4, 90, 1, 10], [4, 120, 1, 8], [4, 180, 1, 22], [4, 360, 1, 12], [5, 24, 1, 1], [6, 8, 1, 3], [6, 16, 1, 4], [6, 20, 1, 7], [6, 40, 1, 8], [6, 60, 1, 8], [6, 80, 1, 4], [6, 120, 1, 20], [6, 160, 1, 11], [6, 240, 1, 12], [6, 320, 1, 8], [10, 24, 1, 3], [10, 48, 1, 4], [10, 72, 1, 4], [10, 144, 1, 8], [10, 288, 1, 4], [12, 16, 1, 2], [12, 40, 1, 4], [12, 120, 1, 12], [12, 160, 1, 2], [12, 240, 1, 22], [12, 320, 1, 4], [12, 480, 1, 6], [15, 192, 1, 1], [20, 48, 1, 2], [20, 144, 1, 6], [20, 288, 1, 8], [30, 192, 1, 3], [30, 384, 1, 4], [60, 384, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 60, 'exponents_of_order': [10, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '23040.dx', 'hash': 2275311098820581292, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 2, 6, 4, 2, 2, 2, 6, 2], 'inner_gens': [[5182, 87178291200, 6, 274509019560, 379446, 362881, 5040, 5167, 1612806, 5047], [5182, 87178291200, 1, 186851363760, 379441, 362886, 5040, 5167, 1980721, 5047], [5177, 87178291200, 1, 274508656560, 379441, 362886, 5040, 5167, 1980721, 5047], [363022, 479001600, 1, 274508656560, 1992241, 5046, 120, 363007, 1980721, 127], [5177, 87178291200, 1, 274509451440, 379441, 362886, 120, 5167, 823081, 127], [5177, 87178291200, 1, 274509019560, 379441, 362886, 5040, 5167, 1612801, 5047], [5182, 87178291200, 1, 274509014400, 374521, 362886, 5040, 5167, 1975801, 5047], [5182, 87178291200, 1, 274509019560, 379441, 362886, 5040, 5167, 1612801, 5047], [367937, 87178291200, 1, 274508656560, 811561, 126, 362880, 367927, 1980721, 362887], [5182, 87178291200, 1, 274509014400, 374521, 362886, 5040, 5167, 1975801, 5047]], 'inner_hash': 6978133608943699788, 'inner_nilpotent': False, 'inner_order': 11520, 'inner_split': None, 'inner_tex': 'C_2^2\\times S_4\\times S_5', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 24], [3, 32], [4, 36], [5, 32], [6, 24], [8, 24], [10, 24], [12, 44], [15, 32], [16, 4], [18, 16], [20, 4], [24, 10], [30, 8], [36, 4]], 'label': '46080.bx', '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': False, 'name': '(S5*GL(2,Z/4)).C2^2', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 129, 'number_characteristic_subgroups': 69, 'number_conjugacy_classes': 350, 'number_divisions': 350, 'number_normal_subgroups': 697, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 46080, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 3119], [3, 188], [4, 11216], [5, 24], [6, 10948], [10, 2856], [12, 11392], [15, 192], [20, 3264], [30, 2112], [60, 768]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4, 4], 'outer_gen_pows': [120, 5040, 0, 181063422847, 0, 193516646400], 'outer_gens': [[5057, 39916800, 368041, 100591953840, 1987206, 363006, 362880, 363007, 1180801, 362887], [367942, 180583603207, 6, 274509809287, 811446, 121, 5040, 367927, 1185846, 5047], [5177, 87178659247, 368046, 187810524727, 16566, 5161, 120, 5167, 822966, 127], [367942, 12933043200, 1, 88137480360, 1169406, 126, 362880, 367927, 1612801, 362887], [142, 355459104000, 16, 88138270080, 1169423, 143, 5040, 367927, 1185856, 5047], [5182, 479369640, 1, 186852158767, 379446, 362881, 127, 5167, 1185841, 120]], 'outer_group': '256.29080', 'outer_hash': 29080, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 32, 'outer_perms': [110467608229479963527059411837717686, 99072684852539574567778755576442273, 130358200347157157614330189505199497, 105451893236067592593923422312047840, 186049904670522636374605049370916510, 169816384704163038045614524566115729], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2:D_4^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 24], [3, 32], [4, 36], [5, 32], [6, 24], [8, 24], [10, 24], [12, 44], [15, 32], [16, 4], [18, 16], [20, 4], [24, 10], [30, 8], [36, 4]], 'representations': {'Perm': {'d': 15, 'gens': [5182, 87178291200, 1, 274508656560, 379441, 362886, 5040, 5167, 1980721, 5047]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 36, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(S_5\\times \\GL(2,\\mathbb{Z}/4)).C_2^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
