Finite Group DatabasebetaFinite Group Databasebeta| order | 25054 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12527 |
| unambiguous semidirect product | C12527⋊C2 |
| Fitting, socle, derived, Sylow | C12527 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12527 | C2 |
| LCS | G ▷ C12527 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12527 |
| transitive degree | μt(G) = 12527 |
A minimal faithful permutation representation — 2 generators on 12527 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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67,6662)(5868,6661)(5869,6660)(5870,6659)(5871,6658)(5872,6657)(5873,6656)(5874,6655)(5875,6654)(5876,6653)(5877,6652)(5878,6651)(5879,6650)(5880,6649)(5881,6648)(5882,6647)(5883,6646)(5884,6645)(5885,6644)(5886,6643)(5887,6642)(5888,6641)(5889,6640)(5890,6639)(5891,6638)(5892,6637)(5893,6636)(5894,6635)(5895,6634)(5896,6633)(5897,6632)(5898,6631)(5899,6630)(5900,6629)(5901,6628)(5902,6627)(5903,6626)(5904,6625)(5905,6624)(5906,6623)(5907,6622)(5908,6621)(5909,6620)(5910,6619)(5911,6618)(5912,6617)(5913,6616)(5914,6615)(5915,6614)(5916,6613)(5917,6612)(5918,6611)(5919,6610)(5920,6609)(5921,6608)(5922,6607)(5923,6606)(5924,6605)(5925,6604)(5926,6603)(5927,6602)(5928,6601)(5929,6600)(5930,6599)(5931,6598)(5932,6597)(5933,6596)(5934,6595)(5935,6594)(5936,6593)(5937,6592)(5938,6591)(5939,6590)(5940,6589)(5941,6588)(5942,6587)(5943,6586)(5944,6585)(5945,6584)(5946,6583)(5947,6582)(5948,6581)(5949,6580)(5950,6579)(5951,6578)(5952,6577)(5953,6576)(5954,6575)(5955,6574)(5956,6573)(5957,6572)(5958,6571)(5959,6570)(5960,6569)(5961,6568)(5962,6567)(5963,6566)(5964,6565)(5965,6564)(5966,6563)(5967,6562)(5968,6561)(5969,6560)(5970,6559)(5971,6558)(5972,6557)(5973,6556)(5974,6555)(5975,6554)(5976,6553)(5977,6552)(5978,6551)(5979,6550)(5980,6549)(5981,6548)(5982,6547)(5983,6546)(5984,6545)(5985,6544)(5986,6543)(5987,6542)(5988,6541)(5989,6540)(5990,6539)(5991,6538)(5992,6537)(5993,6536)(5994,6535)(5995,6534)(5996,6533)(5997,6532)(5998,6531)(5999,6530)(6000,6529)(6001,6528)(6002,6527)(6003,6526)(6004,6525)(6005,6524)(6006,6523)(6007,6522)(6008,6521)(6009,6520)(6010,6519)(6011,6518)(6012,6517)(6013,6516)(6014,6515)(6015,6514)(6016,6513)(6017,6512)(6018,6511)(6019,6510)(6020,6509)(6021,6508)(6022,6507)(6023,6506)(6024,6505)(6025,6504)(6026,6503)(6027,6502)(6028,6501)(6029,6500)(6030,6499)(6031,6498)(6032,6497)(6033,6496)(6034,6495)(6035,6494)(6036,6493)(6037,6492)(6038,6491)(6039,6490)(6040,6489)(6041,6488)(6042,6487)(6043,6486)(6044,6485)(6045,6484)(6046,6483)(6047,6482)(6048,6481)(6049,6480)(6050,6479)(6051,6478)(6052,6477)(6053,6476)(6054,6475)(6055,6474)(6056,6473)(6057,6472)(6058,6471)(6059,6470)(6060,6469)(6061,6468)(6062,6467)(6063,6466)(6064,6465)(6065,6464)(6066,6463)(6067,6462)(6068,6461)(6069,6460)(6070,6459)(6071,6458)(6072,6457)(6073,6456)(6074,6455)(6075,6454)(6076,6453)(6077,6452)(6078,6451)(6079,6450)(6080,6449)(6081,6448)(6082,6447)(6083,6446)(6084,6445)(6085,6444)(6086,6443)(6087,6442)(6088,6441)(6089,6440)(6090,6439)(6091,6438)(6092,6437)(6093,6436)(6094,6435)(6095,6434)(6096,6433)(6097,6432)(6098,6431)(6099,6430)(6100,6429)(6101,6428)(6102,6427)(6103,6426)(6104,6425)(6105,6424)(6106,6423)(6107,6422)(6108,6421)(6109,6420)(6110,6419)(6111,6418)(6112,6417)(6113,6416)(6114,6415)(6115,6414)(6116,6413)(6117,6412)(6118,6411)(6119,6410)(6120,6409)(6121,6408)(6122,6407)(6123,6406)(6124,6405)(6125,6404)(6126,6403)(6127,6402)(6128,6401)(6129,6400)(6130,6399)(6131,6398)(6132,6397)(6133,6396)(6134,6395)(6135,6394)(6136,6393)(6137,6392)(6138,6391)(6139,6390)(6140,6389)(6141,6388)(6142,6387)(6143,6386)(6144,6385)(6145,6384)(6146,6383)(6147,6382)(6148,6381)(6149,6380)(6150,6379)(6151,6378)(6152,6377)(6153,6376)(6154,6375)(6155,6374)(6156,6373)(6157,6372)(6158,6371)(6159,6370)(6160,6369)(6161,6368)(6162,6367)(6163,6366)(6164,6365)(6165,6364)(6166,6363)(6167,6362)(6168,6361)(6169,6360)(6170,6359)(6171,6358)(6172,6357)(6173,6356)(6174,6355)(6175,6354)(6176,6353)(6177,6352)(6178,6351)(6179,6350)(6180,6349)(6181,6348)(6182,6347)(6183,6346)(6184,6345)(6185,6344)(6186,6343)(6187,6342)(6188,6341)(6189,6340)(6190,6339)(6191,6338)(6192,6337)(6193,6336)(6194,6335)(6195,6334)(6196,6333)(6197,6332)(6198,6331)(6199,6330)(6200,6329)(6201,6328)(6202,6327)(6203,6326)(6204,6325)(6205,6324)(6206,6323)(6207,6322)(6208,6321)(6209,6320)(6210,6319)(6211,6318)(6212,6317)(6213,6316)(6214,6315)(6215,6314)(6216,6313)(6217,6312)(6218,6311)(6219,6310)(6220,6309)(6221,6308)(6222,6307)(6223,6306)(6224,6305)(6225,6304)(6226,6303)(6227,6302)(6228,6301)(6229,6300)(6230,6299)(6231,6298)(6232,6297)(6233,6296)(6234,6295)(6235,6294)(6236,6293)(6237,6292)(6238,6291)(6239,6290)(6240,6289)(6241,6288)(6242,6287)(6243,6286)(6244,6285)(6245,6284)(6246,6283)(6247,6282)(6248,6281)(6249,6280)(6250,6279)(6251,6278)(6252,6277)(6253,6276)(6254,6275)(6255,6274)(6256,6273)(6257,6272)(6258,6271)(6259,6270)(6260,6269)(6261,6268)(6262,6267)(6263,6266)(6264,6265)Polycyclic presentation:
2,12527|b^a=b^125266265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25054, 1);