Finite Group DatabasebetaFinite Group Databasebeta| order | 25562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12781 |
| unambiguous semidirect product | C12781⋊C2 |
| Fitting, socle, derived, Sylow | C12781 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12781 | C2 |
| LCS | G ▷ C12781 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12781 |
| transitive degree | μt(G) = 12781 |
A minimal faithful permutation representation — 2 generators on 12781 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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160,6623)(6161,6622)(6162,6621)(6163,6620)(6164,6619)(6165,6618)(6166,6617)(6167,6616)(6168,6615)(6169,6614)(6170,6613)(6171,6612)(6172,6611)(6173,6610)(6174,6609)(6175,6608)(6176,6607)(6177,6606)(6178,6605)(6179,6604)(6180,6603)(6181,6602)(6182,6601)(6183,6600)(6184,6599)(6185,6598)(6186,6597)(6187,6596)(6188,6595)(6189,6594)(6190,6593)(6191,6592)(6192,6591)(6193,6590)(6194,6589)(6195,6588)(6196,6587)(6197,6586)(6198,6585)(6199,6584)(6200,6583)(6201,6582)(6202,6581)(6203,6580)(6204,6579)(6205,6578)(6206,6577)(6207,6576)(6208,6575)(6209,6574)(6210,6573)(6211,6572)(6212,6571)(6213,6570)(6214,6569)(6215,6568)(6216,6567)(6217,6566)(6218,6565)(6219,6564)(6220,6563)(6221,6562)(6222,6561)(6223,6560)(6224,6559)(6225,6558)(6226,6557)(6227,6556)(6228,6555)(6229,6554)(6230,6553)(6231,6552)(6232,6551)(6233,6550)(6234,6549)(6235,6548)(6236,6547)(6237,6546)(6238,6545)(6239,6544)(6240,6543)(6241,6542)(6242,6541)(6243,6540)(6244,6539)(6245,6538)(6246,6537)(6247,6536)(6248,6535)(6249,6534)(6250,6533)(6251,6532)(6252,6531)(6253,6530)(6254,6529)(6255,6528)(6256,6527)(6257,6526)(6258,6525)(6259,6524)(6260,6523)(6261,6522)(6262,6521)(6263,6520)(6264,6519)(6265,6518)(6266,6517)(6267,6516)(6268,6515)(6269,6514)(6270,6513)(6271,6512)(6272,6511)(6273,6510)(6274,6509)(6275,6508)(6276,6507)(6277,6506)(6278,6505)(6279,6504)(6280,6503)(6281,6502)(6282,6501)(6283,6500)(6284,6499)(6285,6498)(6286,6497)(6287,6496)(6288,6495)(6289,6494)(6290,6493)(6291,6492)(6292,6491)(6293,6490)(6294,6489)(6295,6488)(6296,6487)(6297,6486)(6298,6485)(6299,6484)(6300,6483)(6301,6482)(6302,6481)(6303,6480)(6304,6479)(6305,6478)(6306,6477)(6307,6476)(6308,6475)(6309,6474)(6310,6473)(6311,6472)(6312,6471)(6313,6470)(6314,6469)(6315,6468)(6316,6467)(6317,6466)(6318,6465)(6319,6464)(6320,6463)(6321,6462)(6322,6461)(6323,6460)(6324,6459)(6325,6458)(6326,6457)(6327,6456)(6328,6455)(6329,6454)(6330,6453)(6331,6452)(6332,6451)(6333,6450)(6334,6449)(6335,6448)(6336,6447)(6337,6446)(6338,6445)(6339,6444)(6340,6443)(6341,6442)(6342,6441)(6343,6440)(6344,6439)(6345,6438)(6346,6437)(6347,6436)(6348,6435)(6349,6434)(6350,6433)(6351,6432)(6352,6431)(6353,6430)(6354,6429)(6355,6428)(6356,6427)(6357,6426)(6358,6425)(6359,6424)(6360,6423)(6361,6422)(6362,6421)(6363,6420)(6364,6419)(6365,6418)(6366,6417)(6367,6416)(6368,6415)(6369,6414)(6370,6413)(6371,6412)(6372,6411)(6373,6410)(6374,6409)(6375,6408)(6376,6407)(6377,6406)(6378,6405)(6379,6404)(6380,6403)(6381,6402)(6382,6401)(6383,6400)(6384,6399)(6385,6398)(6386,6397)(6387,6396)(6388,6395)(6389,6394)(6390,6393)(6391,6392)Polycyclic presentation:
2,12781|b^a=b^127806392 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25562, 1);