Finite Group DatabasebetaFinite Group Databasebeta| order | 24314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12157 |
| unambiguous semidirect product | C12157⋊C2 |
| Fitting, socle, derived, Sylow | C12157 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12157 | C2 |
| LCS | G ▷ C12157 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12157 |
| transitive degree | μt(G) = 12157 |
A minimal faithful permutation representation — 2 generators on 12157 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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648,6511)(5649,6510)(5650,6509)(5651,6508)(5652,6507)(5653,6506)(5654,6505)(5655,6504)(5656,6503)(5657,6502)(5658,6501)(5659,6500)(5660,6499)(5661,6498)(5662,6497)(5663,6496)(5664,6495)(5665,6494)(5666,6493)(5667,6492)(5668,6491)(5669,6490)(5670,6489)(5671,6488)(5672,6487)(5673,6486)(5674,6485)(5675,6484)(5676,6483)(5677,6482)(5678,6481)(5679,6480)(5680,6479)(5681,6478)(5682,6477)(5683,6476)(5684,6475)(5685,6474)(5686,6473)(5687,6472)(5688,6471)(5689,6470)(5690,6469)(5691,6468)(5692,6467)(5693,6466)(5694,6465)(5695,6464)(5696,6463)(5697,6462)(5698,6461)(5699,6460)(5700,6459)(5701,6458)(5702,6457)(5703,6456)(5704,6455)(5705,6454)(5706,6453)(5707,6452)(5708,6451)(5709,6450)(5710,6449)(5711,6448)(5712,6447)(5713,6446)(5714,6445)(5715,6444)(5716,6443)(5717,6442)(5718,6441)(5719,6440)(5720,6439)(5721,6438)(5722,6437)(5723,6436)(5724,6435)(5725,6434)(5726,6433)(5727,6432)(5728,6431)(5729,6430)(5730,6429)(5731,6428)(5732,6427)(5733,6426)(5734,6425)(5735,6424)(5736,6423)(5737,6422)(5738,6421)(5739,6420)(5740,6419)(5741,6418)(5742,6417)(5743,6416)(5744,6415)(5745,6414)(5746,6413)(5747,6412)(5748,6411)(5749,6410)(5750,6409)(5751,6408)(5752,6407)(5753,6406)(5754,6405)(5755,6404)(5756,6403)(5757,6402)(5758,6401)(5759,6400)(5760,6399)(5761,6398)(5762,6397)(5763,6396)(5764,6395)(5765,6394)(5766,6393)(5767,6392)(5768,6391)(5769,6390)(5770,6389)(5771,6388)(5772,6387)(5773,6386)(5774,6385)(5775,6384)(5776,6383)(5777,6382)(5778,6381)(5779,6380)(5780,6379)(5781,6378)(5782,6377)(5783,6376)(5784,6375)(5785,6374)(5786,6373)(5787,6372)(5788,6371)(5789,6370)(5790,6369)(5791,6368)(5792,6367)(5793,6366)(5794,6365)(5795,6364)(5796,6363)(5797,6362)(5798,6361)(5799,6360)(5800,6359)(5801,6358)(5802,6357)(5803,6356)(5804,6355)(5805,6354)(5806,6353)(5807,6352)(5808,6351)(5809,6350)(5810,6349)(5811,6348)(5812,6347)(5813,6346)(5814,6345)(5815,6344)(5816,6343)(5817,6342)(5818,6341)(5819,6340)(5820,6339)(5821,6338)(5822,6337)(5823,6336)(5824,6335)(5825,6334)(5826,6333)(5827,6332)(5828,6331)(5829,6330)(5830,6329)(5831,6328)(5832,6327)(5833,6326)(5834,6325)(5835,6324)(5836,6323)(5837,6322)(5838,6321)(5839,6320)(5840,6319)(5841,6318)(5842,6317)(5843,6316)(5844,6315)(5845,6314)(5846,6313)(5847,6312)(5848,6311)(5849,6310)(5850,6309)(5851,6308)(5852,6307)(5853,6306)(5854,6305)(5855,6304)(5856,6303)(5857,6302)(5858,6301)(5859,6300)(5860,6299)(5861,6298)(5862,6297)(5863,6296)(5864,6295)(5865,6294)(5866,6293)(5867,6292)(5868,6291)(5869,6290)(5870,6289)(5871,6288)(5872,6287)(5873,6286)(5874,6285)(5875,6284)(5876,6283)(5877,6282)(5878,6281)(5879,6280)(5880,6279)(5881,6278)(5882,6277)(5883,6276)(5884,6275)(5885,6274)(5886,6273)(5887,6272)(5888,6271)(5889,6270)(5890,6269)(5891,6268)(5892,6267)(5893,6266)(5894,6265)(5895,6264)(5896,6263)(5897,6262)(5898,6261)(5899,6260)(5900,6259)(5901,6258)(5902,6257)(5903,6256)(5904,6255)(5905,6254)(5906,6253)(5907,6252)(5908,6251)(5909,6250)(5910,6249)(5911,6248)(5912,6247)(5913,6246)(5914,6245)(5915,6244)(5916,6243)(5917,6242)(5918,6241)(5919,6240)(5920,6239)(5921,6238)(5922,6237)(5923,6236)(5924,6235)(5925,6234)(5926,6233)(5927,6232)(5928,6231)(5929,6230)(5930,6229)(5931,6228)(5932,6227)(5933,6226)(5934,6225)(5935,6224)(5936,6223)(5937,6222)(5938,6221)(5939,6220)(5940,6219)(5941,6218)(5942,6217)(5943,6216)(5944,6215)(5945,6214)(5946,6213)(5947,6212)(5948,6211)(5949,6210)(5950,6209)(5951,6208)(5952,6207)(5953,6206)(5954,6205)(5955,6204)(5956,6203)(5957,6202)(5958,6201)(5959,6200)(5960,6199)(5961,6198)(5962,6197)(5963,6196)(5964,6195)(5965,6194)(5966,6193)(5967,6192)(5968,6191)(5969,6190)(5970,6189)(5971,6188)(5972,6187)(5973,6186)(5974,6185)(5975,6184)(5976,6183)(5977,6182)(5978,6181)(5979,6180)(5980,6179)(5981,6178)(5982,6177)(5983,6176)(5984,6175)(5985,6174)(5986,6173)(5987,6172)(5988,6171)(5989,6170)(5990,6169)(5991,6168)(5992,6167)(5993,6166)(5994,6165)(5995,6164)(5996,6163)(5997,6162)(5998,6161)(5999,6160)(6000,6159)(6001,6158)(6002,6157)(6003,6156)(6004,6155)(6005,6154)(6006,6153)(6007,6152)(6008,6151)(6009,6150)(6010,6149)(6011,6148)(6012,6147)(6013,6146)(6014,6145)(6015,6144)(6016,6143)(6017,6142)(6018,6141)(6019,6140)(6020,6139)(6021,6138)(6022,6137)(6023,6136)(6024,6135)(6025,6134)(6026,6133)(6027,6132)(6028,6131)(6029,6130)(6030,6129)(6031,6128)(6032,6127)(6033,6126)(6034,6125)(6035,6124)(6036,6123)(6037,6122)(6038,6121)(6039,6120)(6040,6119)(6041,6118)(6042,6117)(6043,6116)(6044,6115)(6045,6114)(6046,6113)(6047,6112)(6048,6111)(6049,6110)(6050,6109)(6051,6108)(6052,6107)(6053,6106)(6054,6105)(6055,6104)(6056,6103)(6057,6102)(6058,6101)(6059,6100)(6060,6099)(6061,6098)(6062,6097)(6063,6096)(6064,6095)(6065,6094)(6066,6093)(6067,6092)(6068,6091)(6069,6090)(6070,6089)(6071,6088)(6072,6087)(6073,6086)(6074,6085)(6075,6084)(6076,6083)(6077,6082)(6078,6081)(6079,6080)Polycyclic presentation:
2,12157|b^a=b^121566080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24314, 1);