Finite Group DatabasebetaFinite Group Databasebeta| order | 24086 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12043 |
| unambiguous semidirect product | C12043⋊C2 |
| Fitting, socle, derived, Sylow | C12043 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12043 | C2 |
| LCS | G ▷ C12043 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12043 |
| transitive degree | μt(G) = 12043 |
A minimal faithful permutation representation — 2 generators on 12043 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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25)(5721,6324)(5722,6323)(5723,6322)(5724,6321)(5725,6320)(5726,6319)(5727,6318)(5728,6317)(5729,6316)(5730,6315)(5731,6314)(5732,6313)(5733,6312)(5734,6311)(5735,6310)(5736,6309)(5737,6308)(5738,6307)(5739,6306)(5740,6305)(5741,6304)(5742,6303)(5743,6302)(5744,6301)(5745,6300)(5746,6299)(5747,6298)(5748,6297)(5749,6296)(5750,6295)(5751,6294)(5752,6293)(5753,6292)(5754,6291)(5755,6290)(5756,6289)(5757,6288)(5758,6287)(5759,6286)(5760,6285)(5761,6284)(5762,6283)(5763,6282)(5764,6281)(5765,6280)(5766,6279)(5767,6278)(5768,6277)(5769,6276)(5770,6275)(5771,6274)(5772,6273)(5773,6272)(5774,6271)(5775,6270)(5776,6269)(5777,6268)(5778,6267)(5779,6266)(5780,6265)(5781,6264)(5782,6263)(5783,6262)(5784,6261)(5785,6260)(5786,6259)(5787,6258)(5788,6257)(5789,6256)(5790,6255)(5791,6254)(5792,6253)(5793,6252)(5794,6251)(5795,6250)(5796,6249)(5797,6248)(5798,6247)(5799,6246)(5800,6245)(5801,6244)(5802,6243)(5803,6242)(5804,6241)(5805,6240)(5806,6239)(5807,6238)(5808,6237)(5809,6236)(5810,6235)(5811,6234)(5812,6233)(5813,6232)(5814,6231)(5815,6230)(5816,6229)(5817,6228)(5818,6227)(5819,6226)(5820,6225)(5821,6224)(5822,6223)(5823,6222)(5824,6221)(5825,6220)(5826,6219)(5827,6218)(5828,6217)(5829,6216)(5830,6215)(5831,6214)(5832,6213)(5833,6212)(5834,6211)(5835,6210)(5836,6209)(5837,6208)(5838,6207)(5839,6206)(5840,6205)(5841,6204)(5842,6203)(5843,6202)(5844,6201)(5845,6200)(5846,6199)(5847,6198)(5848,6197)(5849,6196)(5850,6195)(5851,6194)(5852,6193)(5853,6192)(5854,6191)(5855,6190)(5856,6189)(5857,6188)(5858,6187)(5859,6186)(5860,6185)(5861,6184)(5862,6183)(5863,6182)(5864,6181)(5865,6180)(5866,6179)(5867,6178)(5868,6177)(5869,6176)(5870,6175)(5871,6174)(5872,6173)(5873,6172)(5874,6171)(5875,6170)(5876,6169)(5877,6168)(5878,6167)(5879,6166)(5880,6165)(5881,6164)(5882,6163)(5883,6162)(5884,6161)(5885,6160)(5886,6159)(5887,6158)(5888,6157)(5889,6156)(5890,6155)(5891,6154)(5892,6153)(5893,6152)(5894,6151)(5895,6150)(5896,6149)(5897,6148)(5898,6147)(5899,6146)(5900,6145)(5901,6144)(5902,6143)(5903,6142)(5904,6141)(5905,6140)(5906,6139)(5907,6138)(5908,6137)(5909,6136)(5910,6135)(5911,6134)(5912,6133)(5913,6132)(5914,6131)(5915,6130)(5916,6129)(5917,6128)(5918,6127)(5919,6126)(5920,6125)(5921,6124)(5922,6123)(5923,6122)(5924,6121)(5925,6120)(5926,6119)(5927,6118)(5928,6117)(5929,6116)(5930,6115)(5931,6114)(5932,6113)(5933,6112)(5934,6111)(5935,6110)(5936,6109)(5937,6108)(5938,6107)(5939,6106)(5940,6105)(5941,6104)(5942,6103)(5943,6102)(5944,6101)(5945,6100)(5946,6099)(5947,6098)(5948,6097)(5949,6096)(5950,6095)(5951,6094)(5952,6093)(5953,6092)(5954,6091)(5955,6090)(5956,6089)(5957,6088)(5958,6087)(5959,6086)(5960,6085)(5961,6084)(5962,6083)(5963,6082)(5964,6081)(5965,6080)(5966,6079)(5967,6078)(5968,6077)(5969,6076)(5970,6075)(5971,6074)(5972,6073)(5973,6072)(5974,6071)(5975,6070)(5976,6069)(5977,6068)(5978,6067)(5979,6066)(5980,6065)(5981,6064)(5982,6063)(5983,6062)(5984,6061)(5985,6060)(5986,6059)(5987,6058)(5988,6057)(5989,6056)(5990,6055)(5991,6054)(5992,6053)(5993,6052)(5994,6051)(5995,6050)(5996,6049)(5997,6048)(5998,6047)(5999,6046)(6000,6045)(6001,6044)(6002,6043)(6003,6042)(6004,6041)(6005,6040)(6006,6039)(6007,6038)(6008,6037)(6009,6036)(6010,6035)(6011,6034)(6012,6033)(6013,6032)(6014,6031)(6015,6030)(6016,6029)(6017,6028)(6018,6027)(6019,6026)(6020,6025)(6021,6024)(6022,6023)Polycyclic presentation:
2,12043|b^a=b^120426023 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24086, 1);