Finite Group DatabasebetaFinite Group Databasebeta| order | 24226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12113 |
| unambiguous semidirect product | C12113⋊C2 |
| Fitting, socle, derived, Sylow | C12113 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12113 | C2 |
| LCS | G ▷ C12113 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12113 |
| transitive degree | μt(G) = 12113 |
A minimal faithful permutation representation — 2 generators on 12113 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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676,6439)(5677,6438)(5678,6437)(5679,6436)(5680,6435)(5681,6434)(5682,6433)(5683,6432)(5684,6431)(5685,6430)(5686,6429)(5687,6428)(5688,6427)(5689,6426)(5690,6425)(5691,6424)(5692,6423)(5693,6422)(5694,6421)(5695,6420)(5696,6419)(5697,6418)(5698,6417)(5699,6416)(5700,6415)(5701,6414)(5702,6413)(5703,6412)(5704,6411)(5705,6410)(5706,6409)(5707,6408)(5708,6407)(5709,6406)(5710,6405)(5711,6404)(5712,6403)(5713,6402)(5714,6401)(5715,6400)(5716,6399)(5717,6398)(5718,6397)(5719,6396)(5720,6395)(5721,6394)(5722,6393)(5723,6392)(5724,6391)(5725,6390)(5726,6389)(5727,6388)(5728,6387)(5729,6386)(5730,6385)(5731,6384)(5732,6383)(5733,6382)(5734,6381)(5735,6380)(5736,6379)(5737,6378)(5738,6377)(5739,6376)(5740,6375)(5741,6374)(5742,6373)(5743,6372)(5744,6371)(5745,6370)(5746,6369)(5747,6368)(5748,6367)(5749,6366)(5750,6365)(5751,6364)(5752,6363)(5753,6362)(5754,6361)(5755,6360)(5756,6359)(5757,6358)(5758,6357)(5759,6356)(5760,6355)(5761,6354)(5762,6353)(5763,6352)(5764,6351)(5765,6350)(5766,6349)(5767,6348)(5768,6347)(5769,6346)(5770,6345)(5771,6344)(5772,6343)(5773,6342)(5774,6341)(5775,6340)(5776,6339)(5777,6338)(5778,6337)(5779,6336)(5780,6335)(5781,6334)(5782,6333)(5783,6332)(5784,6331)(5785,6330)(5786,6329)(5787,6328)(5788,6327)(5789,6326)(5790,6325)(5791,6324)(5792,6323)(5793,6322)(5794,6321)(5795,6320)(5796,6319)(5797,6318)(5798,6317)(5799,6316)(5800,6315)(5801,6314)(5802,6313)(5803,6312)(5804,6311)(5805,6310)(5806,6309)(5807,6308)(5808,6307)(5809,6306)(5810,6305)(5811,6304)(5812,6303)(5813,6302)(5814,6301)(5815,6300)(5816,6299)(5817,6298)(5818,6297)(5819,6296)(5820,6295)(5821,6294)(5822,6293)(5823,6292)(5824,6291)(5825,6290)(5826,6289)(5827,6288)(5828,6287)(5829,6286)(5830,6285)(5831,6284)(5832,6283)(5833,6282)(5834,6281)(5835,6280)(5836,6279)(5837,6278)(5838,6277)(5839,6276)(5840,6275)(5841,6274)(5842,6273)(5843,6272)(5844,6271)(5845,6270)(5846,6269)(5847,6268)(5848,6267)(5849,6266)(5850,6265)(5851,6264)(5852,6263)(5853,6262)(5854,6261)(5855,6260)(5856,6259)(5857,6258)(5858,6257)(5859,6256)(5860,6255)(5861,6254)(5862,6253)(5863,6252)(5864,6251)(5865,6250)(5866,6249)(5867,6248)(5868,6247)(5869,6246)(5870,6245)(5871,6244)(5872,6243)(5873,6242)(5874,6241)(5875,6240)(5876,6239)(5877,6238)(5878,6237)(5879,6236)(5880,6235)(5881,6234)(5882,6233)(5883,6232)(5884,6231)(5885,6230)(5886,6229)(5887,6228)(5888,6227)(5889,6226)(5890,6225)(5891,6224)(5892,6223)(5893,6222)(5894,6221)(5895,6220)(5896,6219)(5897,6218)(5898,6217)(5899,6216)(5900,6215)(5901,6214)(5902,6213)(5903,6212)(5904,6211)(5905,6210)(5906,6209)(5907,6208)(5908,6207)(5909,6206)(5910,6205)(5911,6204)(5912,6203)(5913,6202)(5914,6201)(5915,6200)(5916,6199)(5917,6198)(5918,6197)(5919,6196)(5920,6195)(5921,6194)(5922,6193)(5923,6192)(5924,6191)(5925,6190)(5926,6189)(5927,6188)(5928,6187)(5929,6186)(5930,6185)(5931,6184)(5932,6183)(5933,6182)(5934,6181)(5935,6180)(5936,6179)(5937,6178)(5938,6177)(5939,6176)(5940,6175)(5941,6174)(5942,6173)(5943,6172)(5944,6171)(5945,6170)(5946,6169)(5947,6168)(5948,6167)(5949,6166)(5950,6165)(5951,6164)(5952,6163)(5953,6162)(5954,6161)(5955,6160)(5956,6159)(5957,6158)(5958,6157)(5959,6156)(5960,6155)(5961,6154)(5962,6153)(5963,6152)(5964,6151)(5965,6150)(5966,6149)(5967,6148)(5968,6147)(5969,6146)(5970,6145)(5971,6144)(5972,6143)(5973,6142)(5974,6141)(5975,6140)(5976,6139)(5977,6138)(5978,6137)(5979,6136)(5980,6135)(5981,6134)(5982,6133)(5983,6132)(5984,6131)(5985,6130)(5986,6129)(5987,6128)(5988,6127)(5989,6126)(5990,6125)(5991,6124)(5992,6123)(5993,6122)(5994,6121)(5995,6120)(5996,6119)(5997,6118)(5998,6117)(5999,6116)(6000,6115)(6001,6114)(6002,6113)(6003,6112)(6004,6111)(6005,6110)(6006,6109)(6007,6108)(6008,6107)(6009,6106)(6010,6105)(6011,6104)(6012,6103)(6013,6102)(6014,6101)(6015,6100)(6016,6099)(6017,6098)(6018,6097)(6019,6096)(6020,6095)(6021,6094)(6022,6093)(6023,6092)(6024,6091)(6025,6090)(6026,6089)(6027,6088)(6028,6087)(6029,6086)(6030,6085)(6031,6084)(6032,6083)(6033,6082)(6034,6081)(6035,6080)(6036,6079)(6037,6078)(6038,6077)(6039,6076)(6040,6075)(6041,6074)(6042,6073)(6043,6072)(6044,6071)(6045,6070)(6046,6069)(6047,6068)(6048,6067)(6049,6066)(6050,6065)(6051,6064)(6052,6063)(6053,6062)(6054,6061)(6055,6060)(6056,6059)(6057,6058)Polycyclic presentation:
2,12113|b^a=b^121126058 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24226, 1);