D₁₀₄₈₇ #35230495

order	20974
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₀₄₈₇
unambiguous semidirect product	C₁₀₄₈₇⋊C₂

Splittings

Fitting, socle, derived, Sylow

C₁₀₄₈₇ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₀₄₈₇	C₂
LCS	G ▷ C₁₀₄₈₇
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 10487
transitive degree	μ_t(G) = 10487

A minimal faithful permutation representation — 2 generators on 10487 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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97)(4893,5596)(4894,5595)(4895,5594)(4896,5593)(4897,5592)(4898,5591)(4899,5590)(4900,5589)(4901,5588)(4902,5587)(4903,5586)(4904,5585)(4905,5584)(4906,5583)(4907,5582)(4908,5581)(4909,5580)(4910,5579)(4911,5578)(4912,5577)(4913,5576)(4914,5575)(4915,5574)(4916,5573)(4917,5572)(4918,5571)(4919,5570)(4920,5569)(4921,5568)(4922,5567)(4923,5566)(4924,5565)(4925,5564)(4926,5563)(4927,5562)(4928,5561)(4929,5560)(4930,5559)(4931,5558)(4932,5557)(4933,5556)(4934,5555)(4935,5554)(4936,5553)(4937,5552)(4938,5551)(4939,5550)(4940,5549)(4941,5548)(4942,5547)(4943,5546)(4944,5545)(4945,5544)(4946,5543)(4947,5542)(4948,5541)(4949,5540)(4950,5539)(4951,5538)(4952,5537)(4953,5536)(4954,5535)(4955,5534)(4956,5533)(4957,5532)(4958,5531)(4959,5530)(4960,5529)(4961,5528)(4962,5527)(4963,5526)(4964,5525)(4965,5524)(4966,5523)(4967,5522)(4968,5521)(4969,5520)(4970,5519)(4971,5518)(4972,5517)(4973,5516)(4974,5515)(4975,5514)(4976,5513)(4977,5512)(4978,5511)(4979,5510)(4980,5509)(4981,5508)(4982,5507)(4983,5506)(4984,5505)(4985,5504)(4986,5503)(4987,5502)(4988,5501)(4989,5500)(4990,5499)(4991,5498)(4992,5497)(4993,5496)(4994,5495)(4995,5494)(4996,5493)(4997,5492)(4998,5491)(4999,5490)(5000,5489)(5001,5488)(5002,5487)(5003,5486)(5004,5485)(5005,5484)(5006,5483)(5007,5482)(5008,5481)(5009,5480)(5010,5479)(5011,5478)(5012,5477)(5013,5476)(5014,5475)(5015,5474)(5016,5473)(5017,5472)(5018,5471)(5019,5470)(5020,5469)(5021,5468)(5022,5467)(5023,5466)(5024,5465)(5025,5464)(5026,5463)(5027,5462)(5028,5461)(5029,5460)(5030,5459)(5031,5458)(5032,5457)(5033,5456)(5034,5455)(5035,5454)(5036,5453)(5037,5452)(5038,5451)(5039,5450)(5040,5449)(5041,5448)(5042,5447)(5043,5446)(5044,5445)(5045,5444)(5046,5443)(5047,5442)(5048,5441)(5049,5440)(5050,5439)(5051,5438)(5052,5437)(5053,5436)(5054,5435)(5055,5434)(5056,5433)(5057,5432)(5058,5431)(5059,5430)(5060,5429)(5061,5428)(5062,5427)(5063,5426)(5064,5425)(5065,5424)(5066,5423)(5067,5422)(5068,5421)(5069,5420)(5070,5419)(5071,5418)(5072,5417)(5073,5416)(5074,5415)(5075,5414)(5076,5413)(5077,5412)(5078,5411)(5079,5410)(5080,5409)(5081,5408)(5082,5407)(5083,5406)(5084,5405)(5085,5404)(5086,5403)(5087,5402)(5088,5401)(5089,5400)(5090,5399)(5091,5398)(5092,5397)(5093,5396)(5094,5395)(5095,5394)(5096,5393)(5097,5392)(5098,5391)(5099,5390)(5100,5389)(5101,5388)(5102,5387)(5103,5386)(5104,5385)(5105,5384)(5106,5383)(5107,5382)(5108,5381)(5109,5380)(5110,5379)(5111,5378)(5112,5377)(5113,5376)(5114,5375)(5115,5374)(5116,5373)(5117,5372)(5118,5371)(5119,5370)(5120,5369)(5121,5368)(5122,5367)(5123,5366)(5124,5365)(5125,5364)(5126,5363)(5127,5362)(5128,5361)(5129,5360)(5130,5359)(5131,5358)(5132,5357)(5133,5356)(5134,5355)(5135,5354)(5136,5353)(5137,5352)(5138,5351)(5139,5350)(5140,5349)(5141,5348)(5142,5347)(5143,5346)(5144,5345)(5145,5344)(5146,5343)(5147,5342)(5148,5341)(5149,5340)(5150,5339)(5151,5338)(5152,5337)(5153,5336)(5154,5335)(5155,5334)(5156,5333)(5157,5332)(5158,5331)(5159,5330)(5160,5329)(5161,5328)(5162,5327)(5163,5326)(5164,5325)(5165,5324)(5166,5323)(5167,5322)(5168,5321)(5169,5320)(5170,5319)(5171,5318)(5172,5317)(5173,5316)(5174,5315)(5175,5314)(5176,5313)(5177,5312)(5178,5311)(5179,5310)(5180,5309)(5181,5308)(5182,5307)(5183,5306)(5184,5305)(5185,5304)(5186,5303)(5187,5302)(5188,5301)(5189,5300)(5190,5299)(5191,5298)(5192,5297)(5193,5296)(5194,5295)(5195,5294)(5196,5293)(5197,5292)(5198,5291)(5199,5290)(5200,5289)(5201,5288)(5202,5287)(5203,5286)(5204,5285)(5205,5284)(5206,5283)(5207,5282)(5208,5281)(5209,5280)(5210,5279)(5211,5278)(5212,5277)(5213,5276)(5214,5275)(5215,5274)(5216,5273)(5217,5272)(5218,5271)(5219,5270)(5220,5269)(5221,5268)(5222,5267)(5223,5266)(5224,5265)(5225,5264)(5226,5263)(5227,5262)(5228,5261)(5229,5260)(5230,5259)(5231,5258)(5232,5257)(5233,5256)(5234,5255)(5235,5254)(5236,5253)(5237,5252)(5238,5251)(5239,5250)(5240,5249)(5241,5248)(5242,5247)(5243,5246)(5244,5245)

Polycyclic presentation:

2,10487|b^a=b^10486

Conjugacy classes & character table

5245 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20974, 1);

D10487 #35230495