Finite Group DatabasebetaFinite Group Databasebeta| order | 21878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D10939 |
| unambiguous semidirect product | C10939⋊C2 |
| Fitting, socle, derived, Sylow | C10939 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C10939 | C2 |
| LCS | G ▷ C10939 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 10939 |
| transitive degree | μt(G) = 10939 |
A minimal faithful permutation representation — 2 generators on 10939 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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882)(5060,5881)(5061,5880)(5062,5879)(5063,5878)(5064,5877)(5065,5876)(5066,5875)(5067,5874)(5068,5873)(5069,5872)(5070,5871)(5071,5870)(5072,5869)(5073,5868)(5074,5867)(5075,5866)(5076,5865)(5077,5864)(5078,5863)(5079,5862)(5080,5861)(5081,5860)(5082,5859)(5083,5858)(5084,5857)(5085,5856)(5086,5855)(5087,5854)(5088,5853)(5089,5852)(5090,5851)(5091,5850)(5092,5849)(5093,5848)(5094,5847)(5095,5846)(5096,5845)(5097,5844)(5098,5843)(5099,5842)(5100,5841)(5101,5840)(5102,5839)(5103,5838)(5104,5837)(5105,5836)(5106,5835)(5107,5834)(5108,5833)(5109,5832)(5110,5831)(5111,5830)(5112,5829)(5113,5828)(5114,5827)(5115,5826)(5116,5825)(5117,5824)(5118,5823)(5119,5822)(5120,5821)(5121,5820)(5122,5819)(5123,5818)(5124,5817)(5125,5816)(5126,5815)(5127,5814)(5128,5813)(5129,5812)(5130,5811)(5131,5810)(5132,5809)(5133,5808)(5134,5807)(5135,5806)(5136,5805)(5137,5804)(5138,5803)(5139,5802)(5140,5801)(5141,5800)(5142,5799)(5143,5798)(5144,5797)(5145,5796)(5146,5795)(5147,5794)(5148,5793)(5149,5792)(5150,5791)(5151,5790)(5152,5789)(5153,5788)(5154,5787)(5155,5786)(5156,5785)(5157,5784)(5158,5783)(5159,5782)(5160,5781)(5161,5780)(5162,5779)(5163,5778)(5164,5777)(5165,5776)(5166,5775)(5167,5774)(5168,5773)(5169,5772)(5170,5771)(5171,5770)(5172,5769)(5173,5768)(5174,5767)(5175,5766)(5176,5765)(5177,5764)(5178,5763)(5179,5762)(5180,5761)(5181,5760)(5182,5759)(5183,5758)(5184,5757)(5185,5756)(5186,5755)(5187,5754)(5188,5753)(5189,5752)(5190,5751)(5191,5750)(5192,5749)(5193,5748)(5194,5747)(5195,5746)(5196,5745)(5197,5744)(5198,5743)(5199,5742)(5200,5741)(5201,5740)(5202,5739)(5203,5738)(5204,5737)(5205,5736)(5206,5735)(5207,5734)(5208,5733)(5209,5732)(5210,5731)(5211,5730)(5212,5729)(5213,5728)(5214,5727)(5215,5726)(5216,5725)(5217,5724)(5218,5723)(5219,5722)(5220,5721)(5221,5720)(5222,5719)(5223,5718)(5224,5717)(5225,5716)(5226,5715)(5227,5714)(5228,5713)(5229,5712)(5230,5711)(5231,5710)(5232,5709)(5233,5708)(5234,5707)(5235,5706)(5236,5705)(5237,5704)(5238,5703)(5239,5702)(5240,5701)(5241,5700)(5242,5699)(5243,5698)(5244,5697)(5245,5696)(5246,5695)(5247,5694)(5248,5693)(5249,5692)(5250,5691)(5251,5690)(5252,5689)(5253,5688)(5254,5687)(5255,5686)(5256,5685)(5257,5684)(5258,5683)(5259,5682)(5260,5681)(5261,5680)(5262,5679)(5263,5678)(5264,5677)(5265,5676)(5266,5675)(5267,5674)(5268,5673)(5269,5672)(5270,5671)(5271,5670)(5272,5669)(5273,5668)(5274,5667)(5275,5666)(5276,5665)(5277,5664)(5278,5663)(5279,5662)(5280,5661)(5281,5660)(5282,5659)(5283,5658)(5284,5657)(5285,5656)(5286,5655)(5287,5654)(5288,5653)(5289,5652)(5290,5651)(5291,5650)(5292,5649)(5293,5648)(5294,5647)(5295,5646)(5296,5645)(5297,5644)(5298,5643)(5299,5642)(5300,5641)(5301,5640)(5302,5639)(5303,5638)(5304,5637)(5305,5636)(5306,5635)(5307,5634)(5308,5633)(5309,5632)(5310,5631)(5311,5630)(5312,5629)(5313,5628)(5314,5627)(5315,5626)(5316,5625)(5317,5624)(5318,5623)(5319,5622)(5320,5621)(5321,5620)(5322,5619)(5323,5618)(5324,5617)(5325,5616)(5326,5615)(5327,5614)(5328,5613)(5329,5612)(5330,5611)(5331,5610)(5332,5609)(5333,5608)(5334,5607)(5335,5606)(5336,5605)(5337,5604)(5338,5603)(5339,5602)(5340,5601)(5341,5600)(5342,5599)(5343,5598)(5344,5597)(5345,5596)(5346,5595)(5347,5594)(5348,5593)(5349,5592)(5350,5591)(5351,5590)(5352,5589)(5353,5588)(5354,5587)(5355,5586)(5356,5585)(5357,5584)(5358,5583)(5359,5582)(5360,5581)(5361,5580)(5362,5579)(5363,5578)(5364,5577)(5365,5576)(5366,5575)(5367,5574)(5368,5573)(5369,5572)(5370,5571)(5371,5570)(5372,5569)(5373,5568)(5374,5567)(5375,5566)(5376,5565)(5377,5564)(5378,5563)(5379,5562)(5380,5561)(5381,5560)(5382,5559)(5383,5558)(5384,5557)(5385,5556)(5386,5555)(5387,5554)(5388,5553)(5389,5552)(5390,5551)(5391,5550)(5392,5549)(5393,5548)(5394,5547)(5395,5546)(5396,5545)(5397,5544)(5398,5543)(5399,5542)(5400,5541)(5401,5540)(5402,5539)(5403,5538)(5404,5537)(5405,5536)(5406,5535)(5407,5534)(5408,5533)(5409,5532)(5410,5531)(5411,5530)(5412,5529)(5413,5528)(5414,5527)(5415,5526)(5416,5525)(5417,5524)(5418,5523)(5419,5522)(5420,5521)(5421,5520)(5422,5519)(5423,5518)(5424,5517)(5425,5516)(5426,5515)(5427,5514)(5428,5513)(5429,5512)(5430,5511)(5431,5510)(5432,5509)(5433,5508)(5434,5507)(5435,5506)(5436,5505)(5437,5504)(5438,5503)(5439,5502)(5440,5501)(5441,5500)(5442,5499)(5443,5498)(5444,5497)(5445,5496)(5446,5495)(5447,5494)(5448,5493)(5449,5492)(5450,5491)(5451,5490)(5452,5489)(5453,5488)(5454,5487)(5455,5486)(5456,5485)(5457,5484)(5458,5483)(5459,5482)(5460,5481)(5461,5480)(5462,5479)(5463,5478)(5464,5477)(5465,5476)(5466,5475)(5467,5474)(5468,5473)(5469,5472)(5470,5471)Polycyclic presentation:
2,10939|b^a=b^109385471 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21878, 1);