Finite Group DatabasebetaFinite Group Databasebeta| order | 24218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12109 |
| unambiguous semidirect product | C12109⋊C2 |
| Fitting, socle, derived, Sylow | C12109 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12109 | C2 |
| LCS | G ▷ C12109 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12109 |
| transitive degree | μt(G) = 12109 |
A minimal faithful permutation representation — 2 generators on 12109 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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33)(5679,6432)(5680,6431)(5681,6430)(5682,6429)(5683,6428)(5684,6427)(5685,6426)(5686,6425)(5687,6424)(5688,6423)(5689,6422)(5690,6421)(5691,6420)(5692,6419)(5693,6418)(5694,6417)(5695,6416)(5696,6415)(5697,6414)(5698,6413)(5699,6412)(5700,6411)(5701,6410)(5702,6409)(5703,6408)(5704,6407)(5705,6406)(5706,6405)(5707,6404)(5708,6403)(5709,6402)(5710,6401)(5711,6400)(5712,6399)(5713,6398)(5714,6397)(5715,6396)(5716,6395)(5717,6394)(5718,6393)(5719,6392)(5720,6391)(5721,6390)(5722,6389)(5723,6388)(5724,6387)(5725,6386)(5726,6385)(5727,6384)(5728,6383)(5729,6382)(5730,6381)(5731,6380)(5732,6379)(5733,6378)(5734,6377)(5735,6376)(5736,6375)(5737,6374)(5738,6373)(5739,6372)(5740,6371)(5741,6370)(5742,6369)(5743,6368)(5744,6367)(5745,6366)(5746,6365)(5747,6364)(5748,6363)(5749,6362)(5750,6361)(5751,6360)(5752,6359)(5753,6358)(5754,6357)(5755,6356)(5756,6355)(5757,6354)(5758,6353)(5759,6352)(5760,6351)(5761,6350)(5762,6349)(5763,6348)(5764,6347)(5765,6346)(5766,6345)(5767,6344)(5768,6343)(5769,6342)(5770,6341)(5771,6340)(5772,6339)(5773,6338)(5774,6337)(5775,6336)(5776,6335)(5777,6334)(5778,6333)(5779,6332)(5780,6331)(5781,6330)(5782,6329)(5783,6328)(5784,6327)(5785,6326)(5786,6325)(5787,6324)(5788,6323)(5789,6322)(5790,6321)(5791,6320)(5792,6319)(5793,6318)(5794,6317)(5795,6316)(5796,6315)(5797,6314)(5798,6313)(5799,6312)(5800,6311)(5801,6310)(5802,6309)(5803,6308)(5804,6307)(5805,6306)(5806,6305)(5807,6304)(5808,6303)(5809,6302)(5810,6301)(5811,6300)(5812,6299)(5813,6298)(5814,6297)(5815,6296)(5816,6295)(5817,6294)(5818,6293)(5819,6292)(5820,6291)(5821,6290)(5822,6289)(5823,6288)(5824,6287)(5825,6286)(5826,6285)(5827,6284)(5828,6283)(5829,6282)(5830,6281)(5831,6280)(5832,6279)(5833,6278)(5834,6277)(5835,6276)(5836,6275)(5837,6274)(5838,6273)(5839,6272)(5840,6271)(5841,6270)(5842,6269)(5843,6268)(5844,6267)(5845,6266)(5846,6265)(5847,6264)(5848,6263)(5849,6262)(5850,6261)(5851,6260)(5852,6259)(5853,6258)(5854,6257)(5855,6256)(5856,6255)(5857,6254)(5858,6253)(5859,6252)(5860,6251)(5861,6250)(5862,6249)(5863,6248)(5864,6247)(5865,6246)(5866,6245)(5867,6244)(5868,6243)(5869,6242)(5870,6241)(5871,6240)(5872,6239)(5873,6238)(5874,6237)(5875,6236)(5876,6235)(5877,6234)(5878,6233)(5879,6232)(5880,6231)(5881,6230)(5882,6229)(5883,6228)(5884,6227)(5885,6226)(5886,6225)(5887,6224)(5888,6223)(5889,6222)(5890,6221)(5891,6220)(5892,6219)(5893,6218)(5894,6217)(5895,6216)(5896,6215)(5897,6214)(5898,6213)(5899,6212)(5900,6211)(5901,6210)(5902,6209)(5903,6208)(5904,6207)(5905,6206)(5906,6205)(5907,6204)(5908,6203)(5909,6202)(5910,6201)(5911,6200)(5912,6199)(5913,6198)(5914,6197)(5915,6196)(5916,6195)(5917,6194)(5918,6193)(5919,6192)(5920,6191)(5921,6190)(5922,6189)(5923,6188)(5924,6187)(5925,6186)(5926,6185)(5927,6184)(5928,6183)(5929,6182)(5930,6181)(5931,6180)(5932,6179)(5933,6178)(5934,6177)(5935,6176)(5936,6175)(5937,6174)(5938,6173)(5939,6172)(5940,6171)(5941,6170)(5942,6169)(5943,6168)(5944,6167)(5945,6166)(5946,6165)(5947,6164)(5948,6163)(5949,6162)(5950,6161)(5951,6160)(5952,6159)(5953,6158)(5954,6157)(5955,6156)(5956,6155)(5957,6154)(5958,6153)(5959,6152)(5960,6151)(5961,6150)(5962,6149)(5963,6148)(5964,6147)(5965,6146)(5966,6145)(5967,6144)(5968,6143)(5969,6142)(5970,6141)(5971,6140)(5972,6139)(5973,6138)(5974,6137)(5975,6136)(5976,6135)(5977,6134)(5978,6133)(5979,6132)(5980,6131)(5981,6130)(5982,6129)(5983,6128)(5984,6127)(5985,6126)(5986,6125)(5987,6124)(5988,6123)(5989,6122)(5990,6121)(5991,6120)(5992,6119)(5993,6118)(5994,6117)(5995,6116)(5996,6115)(5997,6114)(5998,6113)(5999,6112)(6000,6111)(6001,6110)(6002,6109)(6003,6108)(6004,6107)(6005,6106)(6006,6105)(6007,6104)(6008,6103)(6009,6102)(6010,6101)(6011,6100)(6012,6099)(6013,6098)(6014,6097)(6015,6096)(6016,6095)(6017,6094)(6018,6093)(6019,6092)(6020,6091)(6021,6090)(6022,6089)(6023,6088)(6024,6087)(6025,6086)(6026,6085)(6027,6084)(6028,6083)(6029,6082)(6030,6081)(6031,6080)(6032,6079)(6033,6078)(6034,6077)(6035,6076)(6036,6075)(6037,6074)(6038,6073)(6039,6072)(6040,6071)(6041,6070)(6042,6069)(6043,6068)(6044,6067)(6045,6066)(6046,6065)(6047,6064)(6048,6063)(6049,6062)(6050,6061)(6051,6060)(6052,6059)(6053,6058)(6054,6057)(6055,6056)Polycyclic presentation:
2,12109|b^a=b^121086056 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24218, 1);