← Prev (#16812476) Next (#16812478) →
D1741 #16812477
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1741 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438,1439,1440,1441,1442,1443,1444,1445,1446,1447,1448,1449,1450,1451,1452,1453,1454,1455,1456,1457,1458,1459,1460,1461,1462,1463,1464,1465,1466,1467,1468,1469,1470,1471,1472,1473,1474,1475,1476,1477,1478,1479,1480,1481,1482,1483,1484,1485,1486,1487,1488,1489,1490,1491,1492,1493,1494,1495,1496,1497,1498,1499,1500,1501,1502,1503,1504,1505,1506,1507,1508,1509,1510,1511,1512,1513,1514,1515,1516,1517,1518,1519,1520,1521,1522,1523,1524,1525,1526,1527,1528,1529,1530,1531,1532,1533,1534,1535,1536,1537,1538,1539,1540,1541,1542,1543,1544,1545,1546,1547,1548,1549,1550,1551,1552,1553,1554,1555,1556,1557,1558,1559,1560,1561,1562,1563,1564,1565,1566,1567,1568,1569,1570,1571,1572,1573,1574,1575,1576,1577,1578,1579,1580,1581,1582,1583,1584,1585,1586,1587,1588,1589,1590,1591,1592,1593,1594,1595,1596,1597,1598,1599,1600,1601,1602,1603,1604,1605,1606,1607,1608,1609,1610,1611,1612,1613,1614,1615,1616,1617,1618,1619,1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630,1631,1632,1633,1634,1635,1636,1637,1638,1639,1640,1641,1642,1643,1644,1645,1646,1647,1648,1649,1650,1651,1652,1653,1654,1655,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1666,1667,1668,1669,1670,1671,1672,1673,1674,1675,1676,1677,1678,1679,1680,1681,1682,1683,1684,1685,1686,1687,1688,1689,1690,1691,1692,1693,1694,1695,1696,1697,1698,1699,1700,1701,1702,1703,1704,1705,1706,1707,1708,1709,1710,1711,1712,1713,1714,1715,1716,1717,1718,1719,1720,1721,1722,1723,1724,1725,1726,1727,1728,1729,1730,1731,1732,1733,1734,1735,1736,1737,1738,1739,1740,1741);(2,1741)(3,1740)(4,1739)(5,1738)(6,1737)(7,1736)(8,1735)(9,1734)(10,1733)(11,1732)(12,1731)(13,1730)(14,1729)(15,1728)(16,1727)(17,1726)(18,1725)(19,1724)(20,1723)(21,1722)(22,1721)(23,1720)(24,1719)(25,1718)(26,1717)(27,1716)(28,1715)(29,1714)(30,1713)(31,1712)(32,1711)(33,1710)(34,1709)(35,1708)(36,1707)(37,1706)(38,1705)(39,1704)(40,1703)(41,1702)(42,1701)(43,1700)(44,1699)(45,1698)(46,1697)(47,1696)(48,1695)(49,1694)(50,1693)(51,1692)(52,1691)(53,1690)(54,1689)(55,1688)(56,1687)(57,1686)(58,1685)(59,1684)(60,1683)(61,1682)(62,1681)(63,1680)(64,1679)(65,1678)(66,1677)(67,1676)(68,1675)(69,1674)(70,1673)(71,1672)(72,1671)(73,1670)(74,1669)(75,1668)(76,1667)(77,1666)(78,1665)(79,1664)(80,1663)(81,1662)(82,1661)(83,1660)(84,1659)(85,1658)(86,1657)(87,1656)(88,1655)(89,1654)(90,1653)(91,1652)(92,1651)(93,1650)(94,1649)(95,1648)(96,1647)(97,1646)(98,1645)(99,1644)(100,1643)(101,1642)(102,1641)(103,1640)(104,1639)(105,1638)(106,1637)(107,1636)(108,1635)(109,1634)(110,1633)(111,1632)(112,1631)(113,1630)(114,1629)(115,1628)(116,1627)(117,1626)(118,1625)(119,1624)(120,1623)(121,1622)(122,1621)(123,1620)(124,1619)(125,1618)(126,1617)(127,1616)(128,1615)(129,1614)(130,1613)(131,1612)(132,1611)(133,1610)(134,1609)(135,1608)(136,1607)(137,1606)(138,1605)(139,1604)(140,1603)(141,1602)(142,1601)(143,1600)(144,1599)(145,1598)(146,1597)(147,1596)(148,1595)(149,1594)(150,1593)(151,1592)(152,1591)(153,1590)(154,1589)(155,1588)(156,1587)(157,1586)(158,1585)(159,1584)(160,1583)(161,1582)(162,1581)(163,1580)(164,1579)(165,1578)(166,1577)(167,1576)(168,1575)(169,1574)(170,1573)(171,1572)(172,1571)(173,1570)(174,1569)(175,1568)(176,1567)(177,1566)(178,1565)(179,1564)(180,1563)(181,1562)(182,1561)(183,1560)(184,1559)(185,1558)(186,1557)(187,1556)(188,1555)(189,1554)(190,1553)(191,1552)(192,1551)(193,1550)(194,1549)(195,1548)(196,1547)(197,1546)(198,1545)(199,1544)(200,1543)(201,1542)(202,1541)(203,1540)(204,1539)(205,1538)(206,1537)(207,1536)(208,1535)(209,1534)(210,1533)(211,1532)(212,1531)(213,1530)(214,1529)(215,1528)(216,1527)(217,1526)(218,1525)(219,1524)(220,1523)(221,1522)(222,1521)(223,1520)(224,1519)(225,1518)(226,1517)(227,1516)(228,1515)(229,1514)(230,1513)(231,1512)(232,1511)(233,1510)(234,1509)(235,1508)(236,1507)(237,1506)(238,1505)(239,1504)(240,1503)(241,1502)(242,1501)(243,1500)(244,1499)(245,1498)(246,1497)(247,1496)(248,1495)(249,1494)(250,1493)(251,1492)(252,1491)(253,1490)(254,1489)(255,1488)(256,1487)(257,1486)(258,1485)(259,1484)(260,1483)(261,1482)(262,1481)(263,1480)(264,1479)(265,1478)(266,1477)(267,1476)(268,1475)(269,1474)(270,1473)(271,1472)(272,1471)(273,1470)(274,1469)(275,1468)(276,1467)(277,1466)(278,1465)(279,1464)(280,1463)(281,1462)(282,1461)(283,1460)(284,1459)(285,1458)(286,1457)(287,1456)(288,1455)(289,1454)(290,1453)(291,1452)(292,1451)(293,1450)(294,1449)(295,1448)(296,1447)(297,1446)(298,1445)(299,1444)(300,1443)(301,1442)(302,1441)(303,1440)(304,1439)(305,1438)(306,1437)(307,1436)(308,1435)(309,1434)(310,1433)(311,1432)(312,1431)(313,1430)(314,1429)(315,1428)(316,1427)(317,1426)(318,1425)(319,1424)(320,1423)(321,1422)(322,1421)(323,1420)(324,1419)(325,1418)(326,1417)(327,1416)(328,1415)(329,1414)(330,1413)(331,1412)(332,1411)(333,1410)(334,1409)(335,1408)(336,1407)(337,1406)(338,1405)(339,1404)(340,1403)(341,1402)(342,1401)(343,1400)(344,1399)(345,1398)(346,1397)(347,1396)(348,1395)(349,1394)(350,1393)(351,1392)(352,1391)(353,1390)(354,1389)(355,1388)(356,1387)(357,1386)(358,1385)(359,1384)(360,1383)(361,1382)(362,1381)(363,1380)(364,1379)(365,1378)(366,1377)(367,1376)(368,1375)(369,1374)(370,1373)(371,1372)(372,1371)(373,1370)(374,1369)(375,1368)(376,1367)(377,1366)(378,1365)(379,1364)(380,1363)(381,1362)(382,1361)(383,1360)(384,1359)(385,1358)(386,1357)(387,1356)(388,1355)(389,1354)(390,1353)(391,1352)(392,1351)(393,1350)(394,1349)(395,1348)(396,1347)(397,1346)(398,1345)(399,1344)(400,1343)(401,1342)(402,1341)(403,1340)(404,1339)(405,1338)(406,1337)(407,1336)(408,1335)(409,1334)(410,1333)(411,1332)(412,1331)(413,1330)(414,1329)(415,1328)(416,1327)(417,1326)(418,1325)(419,1324)(420,1323)(421,1322)(422,1321)(423,1320)(424,1319)(425,1318)(426,1317)(427,1316)(428,1315)(429,1314)(430,1313)(431,1312)(432,1311)(433,1310)(434,1309)(435,1308)(436,1307)(437,1306)(438,1305)(439,1304)(440,1303)(441,1302)(442,1301)(443,1300)(444,1299)(445,1298)(446,1297)(447,1296)(448,1295)(449,1294)(450,1293)(451,1292)(452,1291)(453,1290)(454,1289)(455,1288)(456,1287)(457,1286)(458,1285)(459,1284)(460,1283)(461,1282)(462,1281)(463,1280)(464,1279)(465,1278)(466,1277)(467,1276)(468,1275)(469,1274)(470,1273)(471,1272)(472,1271)(473,1270)(474,1269)(475,1268)(476,1267)(477,1266)(478,1265)(479,1264)(480,1263)(481,1262)(482,1261)(483,1260)(484,1259)(485,1258)(486,1257)(487,1256)(488,1255)(489,1254)(490,1253)(491,1252)(492,1251)(493,1250)(494,1249)(495,1248)(496,1247)(497,1246)(498,1245)(499,1244)(500,1243)(501,1242)(502,1241)(503,1240)(504,1239)(505,1238)(506,1237)(507,1236)(508,1235)(509,1234)(510,1233)(511,1232)(512,1231)(513,1230)(514,1229)(515,1228)(516,1227)(517,1226)(518,1225)(519,1224)(520,1223)(521,1222)(522,1221)(523,1220)(524,1219)(525,1218)(526,1217)(527,1216)(528,1215)(529,1214)(530,1213)(531,1212)(532,1211)(533,1210)(534,1209)(535,1208)(536,1207)(537,1206)(538,1205)(539,1204)(540,1203)(541,1202)(542,1201)(543,1200)(544,1199)(545,1198)(546,1197)(547,1196)(548,1195)(549,1194)(550,1193)(551,1192)(552,1191)(553,1190)(554,1189)(555,1188)(556,1187)(557,1186)(558,1185)(559,1184)(560,1183)(561,1182)(562,1181)(563,1180)(564,1179)(565,1178)(566,1177)(567,1176)(568,1175)(569,1174)(570,1173)(571,1172)(572,1171)(573,1170)(574,1169)(575,1168)(576,1167)(577,1166)(578,1165)(579,1164)(580,1163)(581,1162)(582,1161)(583,1160)(584,1159)(585,1158)(586,1157)(587,1156)(588,1155)(589,1154)(590,1153)(591,1152)(592,1151)(593,1150)(594,1149)(595,1148)(596,1147)(597,1146)(598,1145)(599,1144)(600,1143)(601,1142)(602,1141)(603,1140)(604,1139)(605,1138)(606,1137)(607,1136)(608,1135)(609,1134)(610,1133)(611,1132)(612,1131)(613,1130)(614,1129)(615,1128)(616,1127)(617,1126)(618,1125)(619,1124)(620,1123)(621,1122)(622,1121)(623,1120)(624,1119)(625,1118)(626,1117)(627,1116)(628,1115)(629,1114)(630,1113)(631,1112)(632,1111)(633,1110)(634,1109)(635,1108)(636,1107)(637,1106)(638,1105)(639,1104)(640,1103)(641,1102)(642,1101)(643,1100)(644,1099)(645,1098)(646,1097)(647,1096)(648,1095)(649,1094)(650,1093)(651,1092)(652,1091)(653,1090)(654,1089)(655,1088)(656,1087)(657,1086)(658,1085)(659,1084)(660,1083)(661,1082)(662,1081)(663,1080)(664,1079)(665,1078)(666,1077)(667,1076)(668,1075)(669,1074)(670,1073)(671,1072)(672,1071)(673,1070)(674,1069)(675,1068)(676,1067)(677,1066)(678,1065)(679,1064)(680,1063)(681,1062)(682,1061)(683,1060)(684,1059)(685,1058)(686,1057)(687,1056)(688,1055)(689,1054)(690,1053)(691,1052)(692,1051)(693,1050)(694,1049)(695,1048)(696,1047)(697,1046)(698,1045)(699,1044)(700,1043)(701,1042)(702,1041)(703,1040)(704,1039)(705,1038)(706,1037)(707,1036)(708,1035)(709,1034)(710,1033)(711,1032)(712,1031)(713,1030)(714,1029)(715,1028)(716,1027)(717,1026)(718,1025)(719,1024)(720,1023)(721,1022)(722,1021)(723,1020)(724,1019)(725,1018)(726,1017)(727,1016)(728,1015)(729,1014)(730,1013)(731,1012)(732,1011)(733,1010)(734,1009)(735,1008)(736,1007)(737,1006)(738,1005)(739,1004)(740,1003)(741,1002)(742,1001)(743,1000)(744,999)(745,998)(746,997)(747,996)(748,995)(749,994)(750,993)(751,992)(752,991)(753,990)(754,989)(755,988)(756,987)(757,986)(758,985)(759,984)(760,983)(761,982)(762,981)(763,980)(764,979)(765,978)(766,977)(767,976)(768,975)(769,974)(770,973)(771,972)(772,971)(773,970)(774,969)(775,968)(776,967)(777,966)(778,965)(779,964)(780,963)(781,962)(782,961)(783,960)(784,959)(785,958)(786,957)(787,956)(788,955)(789,954)(790,953)(791,952)(792,951)(793,950)(794,949)(795,948)(796,947)(797,946)(798,945)(799,944)(800,943)(801,942)(802,941)(803,940)(804,939)(805,938)(806,937)(807,936)(808,935)(809,934)(810,933)(811,932)(812,931)(813,930)(814,929)(815,928)(816,927)(817,926)(818,925)(819,924)(820,923)(821,922)(822,921)(823,920)(824,919)(825,918)(826,917)(827,916)(828,915)(829,914)(830,913)(831,912)(832,911)(833,910)(834,909)(835,908)(836,907)(837,906)(838,905)(839,904)(840,903)(841,902)(842,901)(843,900)(844,899)(845,898)(846,897)(847,896)(848,895)(849,894)(850,893)(851,892)(852,891)(853,890)(854,889)(855,888)(856,887)(857,886)(858,885)(859,884)(860,883)(861,882)(862,881)(863,880)(864,879)(865,878)(866,877)(867,876)(868,875)(869,874)(870,873)(871,872)
Polycyclic presentation:
2,1741|b^a=b^1740
Conjugacy classes & character table
872 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3482, 1);
Finite Group Databasebeta