Finite Group DatabasebetaFinite Group Databasebeta| order | 25154 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12577 |
| unambiguous semidirect product | C12577⋊C2 |
| Fitting, socle, derived, Sylow | C12577 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12577 | C2 |
| LCS | G ▷ C12577 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12577 |
| transitive degree | μt(G) = 12577 |
A minimal faithful permutation representation — 2 generators on 12577 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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,6744)(5836,6743)(5837,6742)(5838,6741)(5839,6740)(5840,6739)(5841,6738)(5842,6737)(5843,6736)(5844,6735)(5845,6734)(5846,6733)(5847,6732)(5848,6731)(5849,6730)(5850,6729)(5851,6728)(5852,6727)(5853,6726)(5854,6725)(5855,6724)(5856,6723)(5857,6722)(5858,6721)(5859,6720)(5860,6719)(5861,6718)(5862,6717)(5863,6716)(5864,6715)(5865,6714)(5866,6713)(5867,6712)(5868,6711)(5869,6710)(5870,6709)(5871,6708)(5872,6707)(5873,6706)(5874,6705)(5875,6704)(5876,6703)(5877,6702)(5878,6701)(5879,6700)(5880,6699)(5881,6698)(5882,6697)(5883,6696)(5884,6695)(5885,6694)(5886,6693)(5887,6692)(5888,6691)(5889,6690)(5890,6689)(5891,6688)(5892,6687)(5893,6686)(5894,6685)(5895,6684)(5896,6683)(5897,6682)(5898,6681)(5899,6680)(5900,6679)(5901,6678)(5902,6677)(5903,6676)(5904,6675)(5905,6674)(5906,6673)(5907,6672)(5908,6671)(5909,6670)(5910,6669)(5911,6668)(5912,6667)(5913,6666)(5914,6665)(5915,6664)(5916,6663)(5917,6662)(5918,6661)(5919,6660)(5920,6659)(5921,6658)(5922,6657)(5923,6656)(5924,6655)(5925,6654)(5926,6653)(5927,6652)(5928,6651)(5929,6650)(5930,6649)(5931,6648)(5932,6647)(5933,6646)(5934,6645)(5935,6644)(5936,6643)(5937,6642)(5938,6641)(5939,6640)(5940,6639)(5941,6638)(5942,6637)(5943,6636)(5944,6635)(5945,6634)(5946,6633)(5947,6632)(5948,6631)(5949,6630)(5950,6629)(5951,6628)(5952,6627)(5953,6626)(5954,6625)(5955,6624)(5956,6623)(5957,6622)(5958,6621)(5959,6620)(5960,6619)(5961,6618)(5962,6617)(5963,6616)(5964,6615)(5965,6614)(5966,6613)(5967,6612)(5968,6611)(5969,6610)(5970,6609)(5971,6608)(5972,6607)(5973,6606)(5974,6605)(5975,6604)(5976,6603)(5977,6602)(5978,6601)(5979,6600)(5980,6599)(5981,6598)(5982,6597)(5983,6596)(5984,6595)(5985,6594)(5986,6593)(5987,6592)(5988,6591)(5989,6590)(5990,6589)(5991,6588)(5992,6587)(5993,6586)(5994,6585)(5995,6584)(5996,6583)(5997,6582)(5998,6581)(5999,6580)(6000,6579)(6001,6578)(6002,6577)(6003,6576)(6004,6575)(6005,6574)(6006,6573)(6007,6572)(6008,6571)(6009,6570)(6010,6569)(6011,6568)(6012,6567)(6013,6566)(6014,6565)(6015,6564)(6016,6563)(6017,6562)(6018,6561)(6019,6560)(6020,6559)(6021,6558)(6022,6557)(6023,6556)(6024,6555)(6025,6554)(6026,6553)(6027,6552)(6028,6551)(6029,6550)(6030,6549)(6031,6548)(6032,6547)(6033,6546)(6034,6545)(6035,6544)(6036,6543)(6037,6542)(6038,6541)(6039,6540)(6040,6539)(6041,6538)(6042,6537)(6043,6536)(6044,6535)(6045,6534)(6046,6533)(6047,6532)(6048,6531)(6049,6530)(6050,6529)(6051,6528)(6052,6527)(6053,6526)(6054,6525)(6055,6524)(6056,6523)(6057,6522)(6058,6521)(6059,6520)(6060,6519)(6061,6518)(6062,6517)(6063,6516)(6064,6515)(6065,6514)(6066,6513)(6067,6512)(6068,6511)(6069,6510)(6070,6509)(6071,6508)(6072,6507)(6073,6506)(6074,6505)(6075,6504)(6076,6503)(6077,6502)(6078,6501)(6079,6500)(6080,6499)(6081,6498)(6082,6497)(6083,6496)(6084,6495)(6085,6494)(6086,6493)(6087,6492)(6088,6491)(6089,6490)(6090,6489)(6091,6488)(6092,6487)(6093,6486)(6094,6485)(6095,6484)(6096,6483)(6097,6482)(6098,6481)(6099,6480)(6100,6479)(6101,6478)(6102,6477)(6103,6476)(6104,6475)(6105,6474)(6106,6473)(6107,6472)(6108,6471)(6109,6470)(6110,6469)(6111,6468)(6112,6467)(6113,6466)(6114,6465)(6115,6464)(6116,6463)(6117,6462)(6118,6461)(6119,6460)(6120,6459)(6121,6458)(6122,6457)(6123,6456)(6124,6455)(6125,6454)(6126,6453)(6127,6452)(6128,6451)(6129,6450)(6130,6449)(6131,6448)(6132,6447)(6133,6446)(6134,6445)(6135,6444)(6136,6443)(6137,6442)(6138,6441)(6139,6440)(6140,6439)(6141,6438)(6142,6437)(6143,6436)(6144,6435)(6145,6434)(6146,6433)(6147,6432)(6148,6431)(6149,6430)(6150,6429)(6151,6428)(6152,6427)(6153,6426)(6154,6425)(6155,6424)(6156,6423)(6157,6422)(6158,6421)(6159,6420)(6160,6419)(6161,6418)(6162,6417)(6163,6416)(6164,6415)(6165,6414)(6166,6413)(6167,6412)(6168,6411)(6169,6410)(6170,6409)(6171,6408)(6172,6407)(6173,6406)(6174,6405)(6175,6404)(6176,6403)(6177,6402)(6178,6401)(6179,6400)(6180,6399)(6181,6398)(6182,6397)(6183,6396)(6184,6395)(6185,6394)(6186,6393)(6187,6392)(6188,6391)(6189,6390)(6190,6389)(6191,6388)(6192,6387)(6193,6386)(6194,6385)(6195,6384)(6196,6383)(6197,6382)(6198,6381)(6199,6380)(6200,6379)(6201,6378)(6202,6377)(6203,6376)(6204,6375)(6205,6374)(6206,6373)(6207,6372)(6208,6371)(6209,6370)(6210,6369)(6211,6368)(6212,6367)(6213,6366)(6214,6365)(6215,6364)(6216,6363)(6217,6362)(6218,6361)(6219,6360)(6220,6359)(6221,6358)(6222,6357)(6223,6356)(6224,6355)(6225,6354)(6226,6353)(6227,6352)(6228,6351)(6229,6350)(6230,6349)(6231,6348)(6232,6347)(6233,6346)(6234,6345)(6235,6344)(6236,6343)(6237,6342)(6238,6341)(6239,6340)(6240,6339)(6241,6338)(6242,6337)(6243,6336)(6244,6335)(6245,6334)(6246,6333)(6247,6332)(6248,6331)(6249,6330)(6250,6329)(6251,6328)(6252,6327)(6253,6326)(6254,6325)(6255,6324)(6256,6323)(6257,6322)(6258,6321)(6259,6320)(6260,6319)(6261,6318)(6262,6317)(6263,6316)(6264,6315)(6265,6314)(6266,6313)(6267,6312)(6268,6311)(6269,6310)(6270,6309)(6271,6308)(6272,6307)(6273,6306)(6274,6305)(6275,6304)(6276,6303)(6277,6302)(6278,6301)(6279,6300)(6280,6299)(6281,6298)(6282,6297)(6283,6296)(6284,6295)(6285,6294)(6286,6293)(6287,6292)(6288,6291)(6289,6290)Polycyclic presentation:
2,12577|b^a=b^125766290 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25154, 1);