Finite Group DatabasebetaFinite Group Databasebeta| order | 26662 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D13331 |
| unambiguous semidirect product | C13331⋊C2 |
| Fitting, socle, derived, Sylow | C13331 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13331 | C2 |
| LCS | G ▷ C13331 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13331 |
| transitive degree | μt(G) = 13331 |
A minimal faithful permutation representation — 2 generators on 13331 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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69)(6265,7068)(6266,7067)(6267,7066)(6268,7065)(6269,7064)(6270,7063)(6271,7062)(6272,7061)(6273,7060)(6274,7059)(6275,7058)(6276,7057)(6277,7056)(6278,7055)(6279,7054)(6280,7053)(6281,7052)(6282,7051)(6283,7050)(6284,7049)(6285,7048)(6286,7047)(6287,7046)(6288,7045)(6289,7044)(6290,7043)(6291,7042)(6292,7041)(6293,7040)(6294,7039)(6295,7038)(6296,7037)(6297,7036)(6298,7035)(6299,7034)(6300,7033)(6301,7032)(6302,7031)(6303,7030)(6304,7029)(6305,7028)(6306,7027)(6307,7026)(6308,7025)(6309,7024)(6310,7023)(6311,7022)(6312,7021)(6313,7020)(6314,7019)(6315,7018)(6316,7017)(6317,7016)(6318,7015)(6319,7014)(6320,7013)(6321,7012)(6322,7011)(6323,7010)(6324,7009)(6325,7008)(6326,7007)(6327,7006)(6328,7005)(6329,7004)(6330,7003)(6331,7002)(6332,7001)(6333,7000)(6334,6999)(6335,6998)(6336,6997)(6337,6996)(6338,6995)(6339,6994)(6340,6993)(6341,6992)(6342,6991)(6343,6990)(6344,6989)(6345,6988)(6346,6987)(6347,6986)(6348,6985)(6349,6984)(6350,6983)(6351,6982)(6352,6981)(6353,6980)(6354,6979)(6355,6978)(6356,6977)(6357,6976)(6358,6975)(6359,6974)(6360,6973)(6361,6972)(6362,6971)(6363,6970)(6364,6969)(6365,6968)(6366,6967)(6367,6966)(6368,6965)(6369,6964)(6370,6963)(6371,6962)(6372,6961)(6373,6960)(6374,6959)(6375,6958)(6376,6957)(6377,6956)(6378,6955)(6379,6954)(6380,6953)(6381,6952)(6382,6951)(6383,6950)(6384,6949)(6385,6948)(6386,6947)(6387,6946)(6388,6945)(6389,6944)(6390,6943)(6391,6942)(6392,6941)(6393,6940)(6394,6939)(6395,6938)(6396,6937)(6397,6936)(6398,6935)(6399,6934)(6400,6933)(6401,6932)(6402,6931)(6403,6930)(6404,6929)(6405,6928)(6406,6927)(6407,6926)(6408,6925)(6409,6924)(6410,6923)(6411,6922)(6412,6921)(6413,6920)(6414,6919)(6415,6918)(6416,6917)(6417,6916)(6418,6915)(6419,6914)(6420,6913)(6421,6912)(6422,6911)(6423,6910)(6424,6909)(6425,6908)(6426,6907)(6427,6906)(6428,6905)(6429,6904)(6430,6903)(6431,6902)(6432,6901)(6433,6900)(6434,6899)(6435,6898)(6436,6897)(6437,6896)(6438,6895)(6439,6894)(6440,6893)(6441,6892)(6442,6891)(6443,6890)(6444,6889)(6445,6888)(6446,6887)(6447,6886)(6448,6885)(6449,6884)(6450,6883)(6451,6882)(6452,6881)(6453,6880)(6454,6879)(6455,6878)(6456,6877)(6457,6876)(6458,6875)(6459,6874)(6460,6873)(6461,6872)(6462,6871)(6463,6870)(6464,6869)(6465,6868)(6466,6867)(6467,6866)(6468,6865)(6469,6864)(6470,6863)(6471,6862)(6472,6861)(6473,6860)(6474,6859)(6475,6858)(6476,6857)(6477,6856)(6478,6855)(6479,6854)(6480,6853)(6481,6852)(6482,6851)(6483,6850)(6484,6849)(6485,6848)(6486,6847)(6487,6846)(6488,6845)(6489,6844)(6490,6843)(6491,6842)(6492,6841)(6493,6840)(6494,6839)(6495,6838)(6496,6837)(6497,6836)(6498,6835)(6499,6834)(6500,6833)(6501,6832)(6502,6831)(6503,6830)(6504,6829)(6505,6828)(6506,6827)(6507,6826)(6508,6825)(6509,6824)(6510,6823)(6511,6822)(6512,6821)(6513,6820)(6514,6819)(6515,6818)(6516,6817)(6517,6816)(6518,6815)(6519,6814)(6520,6813)(6521,6812)(6522,6811)(6523,6810)(6524,6809)(6525,6808)(6526,6807)(6527,6806)(6528,6805)(6529,6804)(6530,6803)(6531,6802)(6532,6801)(6533,6800)(6534,6799)(6535,6798)(6536,6797)(6537,6796)(6538,6795)(6539,6794)(6540,6793)(6541,6792)(6542,6791)(6543,6790)(6544,6789)(6545,6788)(6546,6787)(6547,6786)(6548,6785)(6549,6784)(6550,6783)(6551,6782)(6552,6781)(6553,6780)(6554,6779)(6555,6778)(6556,6777)(6557,6776)(6558,6775)(6559,6774)(6560,6773)(6561,6772)(6562,6771)(6563,6770)(6564,6769)(6565,6768)(6566,6767)(6567,6766)(6568,6765)(6569,6764)(6570,6763)(6571,6762)(6572,6761)(6573,6760)(6574,6759)(6575,6758)(6576,6757)(6577,6756)(6578,6755)(6579,6754)(6580,6753)(6581,6752)(6582,6751)(6583,6750)(6584,6749)(6585,6748)(6586,6747)(6587,6746)(6588,6745)(6589,6744)(6590,6743)(6591,6742)(6592,6741)(6593,6740)(6594,6739)(6595,6738)(6596,6737)(6597,6736)(6598,6735)(6599,6734)(6600,6733)(6601,6732)(6602,6731)(6603,6730)(6604,6729)(6605,6728)(6606,6727)(6607,6726)(6608,6725)(6609,6724)(6610,6723)(6611,6722)(6612,6721)(6613,6720)(6614,6719)(6615,6718)(6616,6717)(6617,6716)(6618,6715)(6619,6714)(6620,6713)(6621,6712)(6622,6711)(6623,6710)(6624,6709)(6625,6708)(6626,6707)(6627,6706)(6628,6705)(6629,6704)(6630,6703)(6631,6702)(6632,6701)(6633,6700)(6634,6699)(6635,6698)(6636,6697)(6637,6696)(6638,6695)(6639,6694)(6640,6693)(6641,6692)(6642,6691)(6643,6690)(6644,6689)(6645,6688)(6646,6687)(6647,6686)(6648,6685)(6649,6684)(6650,6683)(6651,6682)(6652,6681)(6653,6680)(6654,6679)(6655,6678)(6656,6677)(6657,6676)(6658,6675)(6659,6674)(6660,6673)(6661,6672)(6662,6671)(6663,6670)(6664,6669)(6665,6668)(6666,6667)Polycyclic presentation:
2,13331|b^a=b^133306667 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26662, 1);