Finite Group DatabasebetaFinite Group Databasebeta| order | 36454 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18227 |
| unambiguous semidirect product | C11⋊D1657 |
| unambiguous semidirect product | C1657⋊D11 |
| Fitting, socle, derived, Hall | C11×C1657 ⋊ C2 |
| Sylow | C1657 ⋊ D11 |
| Sylow | C11 ⋊ D1657 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C11×C1657 | C2 |
| LCS | G ▷ C11×C1657 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1668 |
| transitive degree | μt(G) = 18227 |
A minimal faithful permutation representation — 2 generators on 1668 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1668)(14,1667)(15,1666)(16,1665)(17,1664)(18,1663)(19,1662)(20,1661)(21,1660)(22,1659)(23,1658)(24,1657)(25,1656)(26,1655)(27,1654)(28,1653)(29,1652)(30,1651)(31,1650)(32,1649)(33,1648)(34,1647)(35,1646)(36,1645)(37,1644)(38,1643)(39,1642)(40,1641)(41,1640)(42,1639)(43,1638)(44,1637)(45,1636)(46,1635)(47,1634)(48,1633)(49,1632)(50,1631)(51,1630)(52,1629)(53,1628)(54,1627)(55,1626)(56,1625)(57,1624)(58,1623)(59,1622)(60,1621)(61,1620)(62,1619)(63,1618)(64,1617)(65,1616)(66,1615)(67,1614)(68,1613)(69,1612)(70,1611)(71,1610)(72,1609)(73,1608)(74,1607)(75,1606)(76,1605)(77,1604)(78,1603)(79,1602)(80,1601)(81,1600)(82,1599)(83,1598)(84,1597)(85,1596)(86,1595)(87,1594)(88,1593)(89,1592)(90,1591)(91,1590)(92,1589)(93,1588)(94,1587)(95,1586)(96,1585)(97,1584)(98,1583)(99,1582)(100,1581)(101,1580)(102,1579)(103,1578)(104,1577)(105,1576)(106,1575)(107,1574)(108,1573)(109,1572)(110,1571)(111,1570)(112,1569)(113,1568)(114,1567)(115,1566)(116,1565)(117,1564)(118,1563)(119,1562)(120,1561)(121,1560)(122,1559)(123,1558)(124,1557)(125,1556)(126,1555)(127,1554)(128,1553)(129,1552)(130,1551)(131,1550)(132,1549)(133,1548)(134,1547)(135,1546)(136,1545)(137,1544)(138,1543)(139,1542)(140,1541)(141,1540)(142,1539)(143,1538)(144,1537)(145,1536)(146,1535)(147,1534)(148,1533)(149,1532)(150,1531)(151,1530)(152,1529)(153,1528)(154,1527)(155,1526)(156,1525)(157,1524)(158,1523)(159,1522)(160,1521)(161,1520)(162,1519)(163,1518)(164,1517)(165,1516)(166,1515)(167,1514)(168,1513)(169,1512)(170,1511)(171,1510)(172,1509)(173,1508)(174,1507)(175,1506)(176,1505)(177,1504)(178,1503)(179,1502)(180,1501)(181,1500)(182,1499)(183,1498)(184,1497)(185,1496)(186,1495)(187,1494)(188,1493)(189,1492)(190,1491)(191,1490)(192,1489)(193,1488)(194,1487)(195,1486)(196,1485)(197,1484)(198,1483)(199,1482)(200,1481)(201,1480)(202,1479)(203,1478)(204,1477)(205,1476)(206,1475)(207,1474)(208,1473)(209,1472)(210,1471)(211,1470)(212,1469)(213,1468)(214,1467)(215,1466)(216,1465)(217,1464)(218,1463)(219,1462)(220,1461)(221,1460)(222,1459)(223,1458)(224,1457)(225,1456)(226,1455)(227,1454)(228,1453)(229,1452)(230,1451)(231,1450)(232,1449)(233,1448)(234,1447)(235,1446)(236,1445)(237,1444)(238,1443)(239,1442)(240,1441)(241,1440)(242,1439)(243,1438)(244,1437)(245,1436)(246,1435)(247,1434)(248,1433)(249,1432)(250,1431)(251,1430)(252,1429)(253,1428)(254,1427)(255,1426)(256,1425)(257,1424)(258,1423)(259,1422)(260,1421)(261,1420)(262,1419)(263,1418)(264,1417)(265,1416)(266,1415)(267,1414)(268,1413)(269,1412)(270,1411)(271,1410)(272,1409)(273,1408)(274,1407)(275,1406)(276,1405)(277,1404)(278,1403)(279,1402)(280,1401)(281,1400)(282,1399)(283,1398)(284,1397)(285,1396)(286,1395)(287,1394)(288,1393)(289,1392)(290,1391)(291,1390)(292,1389)(293,1388)(294,1387)(295,1386)(296,1385)(297,1384)(298,1383)(299,1382)(300,1381)(301,1380)(302,1379)(303,1378)(304,1377)(305,1376)(306,1375)(307,1374)(308,1373)(309,1372)(310,1371)(311,1370)(312,1369)(313,1368)(314,1367)(315,1366)(316,1365)(317,1364)(318,1363)(319,1362)(320,1361)(321,1360)(322,1359)(323,1358)(324,1357)(325,1356)(326,1355)(327,1354)(328,1353)(329,1352)(330,1351)(331,1350)(332,1349)(333,1348)(334,1347)(335,1346)(336,1345)(337,1344)(338,1343)(339,1342)(340,1341)(341,1340)(342,1339)(343,1338)(344,1337)(345,1336)(346,1335)(347,1334)(348,1333)(349,1332)(350,1331)(351,1330)(352,1329)(353,1328)(354,1327)(355,1326)(356,1325)(357,1324)(358,1323)(359,1322)(360,1321)(361,1320)(362,1319)(363,1318)(364,1317)(365,1316)(366,1315)(367,1314)(368,1313)(369,1312)(370,1311)(371,1310)(372,1309)(373,1308)(374,1307)(375,1306)(376,1305)(377,1304)(378,1303)(379,1302)(380,1301)(381,1300)(382,1299)(383,1298)(384,1297)(385,1296)(386,1295)(387,1294)(388,1293)(389,1292)(390,1291)(391,1290)(392,1289)(393,1288)(394,1287)(395,1286)(396,1285)(397,1284)(398,1283)(399,1282)(400,1281)(401,1280)(402,1279)(403,1278)(404,1277)(405,1276)(406,1275)(407,1274)(408,1273)(409,1272)(410,1271)(411,1270)(412,1269)(413,1268)(414,1267)(415,1266)(416,1265)(417,1264)(418,1263)(419,1262)(420,1261)(421,1260)(422,1259)(423,1258)(424,1257)(425,1256)(426,1255)(427,1254)(428,1253)(429,1252)(430,1251)(431,1250)(432,1249)(433,1248)(434,1247)(435,1246)(436,1245)(437,1244)(438,1243)(439,1242)(440,1241)(441,1240)(442,1239)(443,1238)(444,1237)(445,1236)(446,1235)(447,1234)(448,1233)(449,1232)(450,1231)(451,1230)(452,1229)(453,1228)(454,1227)(455,1226)(456,1225)(457,1224)(458,1223)(459,1222)(460,1221)(461,1220)(462,1219)(463,1218)(464,1217)(465,1216)(466,1215)(467,1214)(468,1213)(469,1212)(470,1211)(471,1210)(472,1209)(473,1208)(474,1207)(475,1206)(476,1205)(477,1204)(478,1203)(479,1202)(480,1201)(481,1200)(482,1199)(483,1198)(484,1197)(485,1196)(486,1195)(487,1194)(488,1193)(489,1192)(490,1191)(491,1190)(492,1189)(493,1188)(494,1187)(495,1186)(496,1185)(497,1184)(498,1183)(499,1182)(500,1181)(501,1180)(502,1179)(503,1178)(504,1177)(505,1176)(506,1175)(507,1174)(508,1173)(509,1172)(510,1171)(511,1170)(512,1169)(513,1168)(514,1167)(515,1166)(516,1165)(517,1164)(518,1163)(519,1162)(520,1161)(521,1160)(522,1159)(523,1158)(524,1157)(525,1156)(526,1155)(527,1154)(528,1153)(529,1152)(530,1151)(531,1150)(532,1149)(533,1148)(534,1147)(535,1146)(536,1145)(537,1144)(538,1143)(539,1142)(540,1141)(541,1140)(542,1139)(543,1138)(544,1137)(545,1136)(546,1135)(547,1134)(548,1133)(549,1132)(550,1131)(551,1130)(552,1129)(553,1128)(554,1127)(555,1126)(556,1125)(557,1124)(558,1123)(559,1122)(560,1121)(561,1120)(562,1119)(563,1118)(564,1117)(565,1116)(566,1115)(567,1114)(568,1113)(569,1112)(570,1111)(571,1110)(572,1109)(573,1108)(574,1107)(575,1106)(576,1105)(577,1104)(578,1103)(579,1102)(580,1101)(581,1100)(582,1099)(583,1098)(584,1097)(585,1096)(586,1095)(587,1094)(588,1093)(589,1092)(590,1091)(591,1090)(592,1089)(593,1088)(594,1087)(595,1086)(596,1085)(597,1084)(598,1083)(599,1082)(600,1081)(601,1080)(602,1079)(603,1078)(604,1077)(605,1076)(606,1075)(607,1074)(608,1073)(609,1072)(610,1071)(611,1070)(612,1069)(613,1068)(614,1067)(615,1066)(616,1065)(617,1064)(618,1063)(619,1062)(620,1061)(621,1060)(622,1059)(623,1058)(624,1057)(625,1056)(626,1055)(627,1054)(628,1053)(629,1052)(630,1051)(631,1050)(632,1049)(633,1048)(634,1047)(635,1046)(636,1045)(637,1044)(638,1043)(639,1042)(640,1041)(641,1040)(642,1039)(643,1038)(644,1037)(645,1036)(646,1035)(647,1034)(648,1033)(649,1032)(650,1031)(651,1030)(652,1029)(653,1028)(654,1027)(655,1026)(656,1025)(657,1024)(658,1023)(659,1022)(660,1021)(661,1020)(662,1019)(663,1018)(664,1017)(665,1016)(666,1015)(667,1014)(668,1013)(669,1012)(670,1011)(671,1010)(672,1009)(673,1008)(674,1007)(675,1006)(676,1005)(677,1004)(678,1003)(679,1002)(680,1001)(681,1000)(682,999)(683,998)(684,997)(685,996)(686,995)(687,994)(688,993)(689,992)(690,991)(691,990)(692,989)(693,988)(694,987)(695,986)(696,985)(697,984)(698,983)(699,982)(700,981)(701,980)(702,979)(703,978)(704,977)(705,976)(706,975)(707,974)(708,973)(709,972)(710,971)(711,970)(712,969)(713,968)(714,967)(715,966)(716,965)(717,964)(718,963)(719,962)(720,961)(721,960)(722,959)(723,958)(724,957)(725,956)(726,955)(727,954)(728,953)(729,952)(730,951)(731,950)(732,949)(733,948)(734,947)(735,946)(736,945)(737,944)(738,943)(739,942)(740,941)(741,940)(742,939)(743,938)(744,937)(745,936)(746,935)(747,934)(748,933)(749,932)(750,931)(751,930)(752,929)(753,928)(754,927)(755,926)(756,925)(757,924)(758,923)(759,922)(760,921)(761,920)(762,919)(763,918)(764,917)(765,916)(766,915)(767,914)(768,913)(769,912)(770,911)(771,910)(772,909)(773,908)(774,907)(775,906)(776,905)(777,904)(778,903)(779,902)(780,901)(781,900)(782,899)(783,898)(784,897)(785,896)(786,895)(787,894)(788,893)(789,892)(790,891)(791,890)(792,889)(793,888)(794,887)(795,886)(796,885)(797,884)(798,883)(799,882)(800,881)(801,880)(802,879)(803,878)(804,877)(805,876)(806,875)(807,874)(808,873)(809,872)(810,871)(811,870)(812,869)(813,868)(814,867)(815,866)(816,865)(817,864)(818,863)(819,862)(820,861)(821,860)(822,859)(823,858)(824,857)(825,856)(826,855)(827,854)(828,853)(829,852)(830,851)(831,850)(832,849)(833,848)(834,847)(835,846)(836,845)(837,844)(838,843)(839,842)(840,841)Polycyclic presentation:
2,11,1657|b^a=b^10,c^a=c^16569115 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36454, 3);