Formats: - HTML - YAML - JSON - 2026-07-20T15:34:59.021657
  • gps_subgroup_search • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '22674816.mj', 'ambient_counter': 322, 'ambient_order': 22674816, 'ambient_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 11337408, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '22674816.mj.2.B', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '11337408.lq', 'subgroup_hash': 1146316497117696609, 'subgroup_order': 11337408, 'subgroup_tex': 'C_3^7.S_3\\wr C_2^2', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '22674816.mj', 'aut_centralizer_order': None, 'aut_label': '2.B', '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': '2.B', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [148311879831258572617263545887398359486134, 271353676394454377792702129150099764, 10872818880982496732313752133, 109900955613340922550081068540160, 8222838669689168581034339899808375, 8223143542522570255320234346169784, 10628380765426167900161457350544321177603, 418802671169936714973312003, 191469869419146555635461657520918225014892, 6790244583891749623177323607624408918, 51704034189144853017744, 17683942790150574557177061504243, 116402028737842036772929287354544384054773, 8223143542522567700438361122524824, 8222838654177955983155394012802560, 10333156189529703288896251288337297841869, 2554547282942135043], 'label': '22674816.mj.2.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.B', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.B', 'subgroup_fusion': None, 'weyl_group': None}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 18, 36], 'aut_gens': [[1, 6, 36, 216, 3888, 69984, 1259712], [1925254, 4750095, 7341972, 1811916, 10100160, 5062932, 3456], [4369621, 9408822, 9272196, 4949532, 2296404, 7261704, 1275264], [10298086, 8352771, 4959696, 9571932, 1924128, 962280, 1275264]], 'aut_group': '22674816.mj', 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 2016, 'aut_perms': 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157464, 1, 2], [12, 157464, 2, 3], [12, 236196, 2, 1], [18, 216, 1, 3], [18, 216, 2, 3], [18, 432, 1, 6], [18, 432, 2, 6], [18, 648, 2, 18], [18, 864, 1, 3], [18, 864, 2, 3], [18, 1296, 1, 3], [18, 1296, 2, 30], [18, 1944, 1, 3], [18, 1944, 2, 30], [18, 2592, 1, 3], [18, 2592, 2, 12], [18, 3888, 1, 3], [18, 3888, 2, 39], [18, 5832, 1, 3], [18, 5832, 2, 36], [18, 7776, 1, 1], [18, 7776, 2, 13], [18, 11664, 1, 8], [18, 11664, 2, 14], [18, 17496, 1, 1], [18, 17496, 2, 13], [18, 23328, 1, 2], [18, 23328, 2, 2], [18, 34992, 1, 4], [18, 34992, 2, 8], [18, 69984, 1, 4], [18, 69984, 2, 2], [18, 104976, 2, 2], [36, 104976, 1, 2], [36, 104976, 2, 8], [36, 314928, 1, 1], [36, 314928, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [11, 6], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 64], [24, 1, 8], [48, 0, 96], [48, 1, 12], [72, 0, 16], [72, 1, 12], [96, 0, 48], [96, 1, 6], [144, 0, 6], [144, 1, 5], [192, 0, 8], [192, 1, 1], [288, 0, 20], [288, 1, 12], [432, 1, 4], [576, 1, 1], [864, 1, 4], [1728, 1, 1]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '139968.bv', 'hash': 1146316497117696609, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [18, 36, 6, 18, 18, 18, 9], 'inner_gens': [[1, 10612614, 4082436, 232740, 1331424, 11092464, 979776], [817717, 6, 1875492, 4951692, 7312788, 7259112, 8856864], [8584705, 11262318, 36, 3688200, 7601040, 2869344, 6298560], [10473949, 8000106, 8983044, 216, 625968, 4968864, 10077696], [6374593, 4081866, 3810276, 707832, 3888, 6228576, 1259712], [11162449, 6072846, 9797796, 7698456, 6442416, 69984, 10077696], [1539649, 3810246, 6298596, 2519640, 3888, 2589408, 1259712]], 'inner_hash': 1146316497117696609, 'inner_nilpotent': False, 'inner_order': 11337408, 'inner_split': True, 'inner_tex': 'C_3^7.S_3\\wr C_2^2', 'inner_used': [1, 2, 4], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 66], [4, 90], [8, 300], [16, 153], [24, 72], [32, 66], [48, 108], [64, 3], [72, 28], [96, 54], [144, 11], [192, 9], [288, 32], [432, 4], [576, 1], [864, 4], [1728, 1]], 'label': '11337408.lq', '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': 'C3^7.S3wrC2^2', 'ngens': 17, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 611, 'number_characteristic_subgroups': 41, 'number_conjugacy_classes': 1026, 'number_divisions': 585, 'number_normal_subgroups': 125, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 11337408, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 14859], [3, 2186], [4, 481140], [6, 779022], [9, 174960], [12, 3061800], [18, 3989088], [36, 2834352]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[374290, 8228811, 4221408, 8001720, 5697864, 5676480, 1259712]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 22], [4, 36], [8, 60], [16, 159], [24, 8], [32, 73], [48, 44], [64, 31], [72, 12], [96, 54], [128, 1], [144, 13], [192, 25], [288, 15], [384, 4], [432, 4], [576, 11], [864, 4], [1728, 1]], 'representations': {'PC': {'code': '87872021495828688998845464471946453170743544580200687724041557926678090147533058938370075103282472426752011398322343941375849994268077370792691399659604557553271797644797183872561912330634779755905580752900544622819288201446173493667564357237939426701114782798644598183272859340046703303323414893067972150589164794843373266963256863285635061413681844681037146286593101370753082460079846146969274826403436353737626857834430917547415977838946158467805914632885268424697742963910706132728491397857406195133296551519178140212735635280499538347996054477054450253973625493899694850593982249555725446052258577497406711096890415969988284385059611517223367433432369834962672448183645954496997780597058292927105510255', 'gens': [1, 3, 5, 7, 10, 13, 16], 'pres': [17, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 34, 71383698, 541243316, 208492660, 138, 480615027, 343435244, 49421502, 347007064, 476994351, 26569508, 36980410, 242, 42837557, 214154734, 7934007, 39669284, 27696066, 167962811, 98208598, 47593155, 12191624, 6944812, 346, 693743623, 22208297, 34330, 3339, 3356, 534, 585346184, 10707594, 11092, 226342089, 702270026, 207195703, 8206980, 35893877, 17965354, 492771, 502, 26820298, 354076299, 79006796, 605941, 19711374, 9896135, 53968, 741, 86189195, 258567597, 793214, 264463, 44177, 2451434556, 796522925, 267377338, 194619735, 17614664, 13103629, 5083998, 354207, 288587, 72466, 658, 2098680205, 66624798, 17183, 19432288, 4626801, 3238802, 1233907, 68710, 948, 963679694, 55128, 5948722, 991556, 55247, 266499087, 685283360, 401511217, 142767426, 47589203, 33312484, 12690549, 39387, 1086, 121352272, 184275698, 182028451, 60676212, 10112806, 31432]}, 'Perm': {'d': 36, 'gens': [159556224623760164928697900143247054898163, 265626768539161335327960573900821253882238, 351025007822651663201027327447747742014012]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^7.S_3\\wr C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 72, 'aut_gen_orders': [18, 18, 36], 'aut_gens': [[10341559710233054493134541928070270514932, 116402028737842036772929287354544384054773, 297539038794244101560037845226962645183757], [10341559710237248103881856892595945932535, 42247319343021719307074191646154195549813, 244048435616148696543643428893473878692668], [191468494787246195873979803215743350179345, 95735732914962282284234659076128213673970, 95733848183496167046094071919977363471504], [339786086637375768470520602767931290460163, 159556232855746276054893328282476031099587, 159557591096606382292863491650499145519507]], 'aut_group': '22674816.mj', 'aut_hash': 8826279076269810851, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 22674816, 'aut_permdeg': 2124, 'aut_perms': 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104976, 2, 4], [36, 209952, 1, 1], [36, 209952, 2, 4], [36, 314928, 1, 1], [36, 314928, 2, 1], [36, 629856, 1, 1], [36, 629856, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [11, 7], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 0, 16], [24, 1, 8], [48, 0, 32], [48, 1, 10], [72, 1, 8], [96, 0, 52], [96, 1, 11], [144, 0, 12], [144, 1, 10], [192, 0, 24], [192, 1, 6], [288, 0, 10], [288, 1, 9], [384, 0, 2], [384, 1, 1], [432, 1, 4], [576, 0, 8], [576, 1, 6], [864, 1, 9], [1728, 1, 2]], 'familial': False, 'frattini_label': '81.15', 'frattini_quotient': '279936.u', 'hash': 8826279076269810851, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 72, 'inner_gen_orders': [18, 18, 36], 'inner_gens': [[10341559710233054493134541928070270514932, 42542017731129522868572191379389885566655, 96031254153417223945134656449944120505411], [201801116326817428051637866875376806869615, 116402028737842036772929287354544384054773, 116402851945042948313084818602476764612295], [329449408073640901719775972431899375328028, 297534141504575641997075264153031179734796, 297539038794244101560037845226962645183757]], 'inner_hash': 8826279076269810851, 'inner_nilpotent': False, 'inner_order': 22674816, 'inner_split': True, 'inner_tex': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 24], [2, 18], [4, 90], [8, 126], [16, 180], [24, 24], [32, 99], [48, 42], [64, 30], [72, 8], [96, 63], [144, 22], [192, 30], [288, 19], [384, 3], [432, 4], [576, 14], [864, 9], [1728, 2]], 'label': '22674816.mj', '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': 'C3^6.(C3*S3wrD4)', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 807, 'number_characteristic_subgroups': 71, 'number_conjugacy_classes': 807, 'number_divisions': 492, 'number_normal_subgroups': 71, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 22674816, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 25659], [3, 2186], [4, 683316], [6, 1188126], [8, 944784], [9, 174960], [12, 5064120], [18, 6403536], [24, 1889568], [36, 6298560]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 14], [4, 24], [8, 56], [16, 77], [24, 8], [32, 89], [48, 18], [64, 50], [72, 8], [96, 27], [128, 12], [144, 10], [192, 32], [288, 15], [384, 13], [432, 4], [576, 11], [768, 1], [864, 9], [1152, 4], [1728, 2]], 'representations': {'PC': {'code': '204753924464296186969946519059962375052652655475942633568214243427490136073407930074016560457401090758537159028231590404130482766329098938130388729837530391094828875584511118200227703157844612941215182329908480334752322883765913875948411016494417544765931299291642024743845676310532080892374929434764549838331695343823269578187068826408567792155284713829628961499749037323627366548038341873190493293365599438982450894799256332546048845508911613530946071784879863941886876707819948508685463361930474072589461315775216445223007363038598937475536066547926401390585134985878227548532034793956994513598410894989156133140369601191232459037995320970281916461416661527939855296155230678890617507301750322135724738672420720413495878018377795647746822981001316894306571013552751651583865453982375687948007991113346077794474868874988118590632861002409256968891022415042539068708390634273870401527472460447232081372665331661649351332922367', 'gens': [1, 3, 5, 7, 8, 10, 12, 13, 15, 16, 17, 18], 'pres': [18, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 36, 1679635, 555220334, 292450358, 146, 814548963, 552531909, 109755705, 540771124, 140746702, 291605440, 78564118, 256, 1427264069, 992655671, 31362377, 137729003, 28942367, 1298977350, 968460216, 421241226, 80104812, 52837926, 34423548, 1351842, 2239411975, 228690457, 178789291, 177591229, 5941519, 1824289, 1584403, 421, 3346168328, 445969178, 205213868, 357758, 37332656, 18478466, 13082588, 1338596, 3280988169, 725787, 613993005, 307008063, 153530001, 34659, 9990117, 8775, 711, 1053119242, 3079342, 87760000, 43880050, 28612, 14374, 7264, 2302193675, 2208135197, 82991, 192596033, 559955, 886565, 46236215, 23013209, 221825, 2518304268, 25474206, 798490416, 211476162, 104828340, 99773958, 26535720, 13002582, 930, 223388977, 429141955, 214571029, 490009, 2218026254, 1360488992, 394865330, 5326646, 75096824, 7105442, 11547500, 7086038, 9932, 87710, 5455392783, 3063619617, 340402227, 515082309, 271019607, 114794601, 2820219, 29958477, 15959103, 979953, 28725, 197223, 2512705552, 2013019810, 947199796, 7314694, 5948728, 65479210, 914452, 16656334, 10484638, 77326, 129670, 6622166033, 1103881013, 5132231, 2612825, 86920235, 51018461, 30705623]}, 'Perm': {'d': 36, 'gens': [10341559710233054493134541928070270514932, 297539038794244101560037845226962645183757, 116402028737842036772929287354544384054773]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6.(C_3\\times S_3\\wr D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '2.1', 'center_order': 2, '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'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, 'wreath_data': None, 'wreath_product': False}