← Prev (#28351989) Next (#28351991) →
Dic3446 #28351990
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1731 points:
(1,2,3,4)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)(10,1731)(11,1730)(12,1729)(13,1728)(14,1727)(15,1726)(16,1725)(17,1724)(18,1723)(19,1722)(20,1721)(21,1720)(22,1719)(23,1718)(24,1717)(25,1716)(26,1715)(27,1714)(28,1713)(29,1712)(30,1711)(31,1710)(32,1709)(33,1708)(34,1707)(35,1706)(36,1705)(37,1704)(38,1703)(39,1702)(40,1701)(41,1700)(42,1699)(43,1698)(44,1697)(45,1696)(46,1695)(47,1694)(48,1693)(49,1692)(50,1691)(51,1690)(52,1689)(53,1688)(54,1687)(55,1686)(56,1685)(57,1684)(58,1683)(59,1682)(60,1681)(61,1680)(62,1679)(63,1678)(64,1677)(65,1676)(66,1675)(67,1674)(68,1673)(69,1672)(70,1671)(71,1670)(72,1669)(73,1668)(74,1667)(75,1666)(76,1665)(77,1664)(78,1663)(79,1662)(80,1661)(81,1660)(82,1659)(83,1658)(84,1657)(85,1656)(86,1655)(87,1654)(88,1653)(89,1652)(90,1651)(91,1650)(92,1649)(93,1648)(94,1647)(95,1646)(96,1645)(97,1644)(98,1643)(99,1642)(100,1641)(101,1640)(102,1639)(103,1638)(104,1637)(105,1636)(106,1635)(107,1634)(108,1633)(109,1632)(110,1631)(111,1630)(112,1629)(113,1628)(114,1627)(115,1626)(116,1625)(117,1624)(118,1623)(119,1622)(120,1621)(121,1620)(122,1619)(123,1618)(124,1617)(125,1616)(126,1615)(127,1614)(128,1613)(129,1612)(130,1611)(131,1610)(132,1609)(133,1608)(134,1607)(135,1606)(136,1605)(137,1604)(138,1603)(139,1602)(140,1601)(141,1600)(142,1599)(143,1598)(144,1597)(145,1596)(146,1595)(147,1594)(148,1593)(149,1592)(150,1591)(151,1590)(152,1589)(153,1588)(154,1587)(155,1586)(156,1585)(157,1584)(158,1583)(159,1582)(160,1581)(161,1580)(162,1579)(163,1578)(164,1577)(165,1576)(166,1575)(167,1574)(168,1573)(169,1572)(170,1571)(171,1570)(172,1569)(173,1568)(174,1567)(175,1566)(176,1565)(177,1564)(178,1563)(179,1562)(180,1561)(181,1560)(182,1559)(183,1558)(184,1557)(185,1556)(186,1555)(187,1554)(188,1553)(189,1552)(190,1551)(191,1550)(192,1549)(193,1548)(194,1547)(195,1546)(196,1545)(197,1544)(198,1543)(199,1542)(200,1541)(201,1540)(202,1539)(203,1538)(204,1537)(205,1536)(206,1535)(207,1534)(208,1533)(209,1532)(210,1531)(211,1530)(212,1529)(213,1528)(214,1527)(215,1526)(216,1525)(217,1524)(218,1523)(219,1522)(220,1521)(221,1520)(222,1519)(223,1518)(224,1517)(225,1516)(226,1515)(227,1514)(228,1513)(229,1512)(230,1511)(231,1510)(232,1509)(233,1508)(234,1507)(235,1506)(236,1505)(237,1504)(238,1503)(239,1502)(240,1501)(241,1500)(242,1499)(243,1498)(244,1497)(245,1496)(246,1495)(247,1494)(248,1493)(249,1492)(250,1491)(251,1490)(252,1489)(253,1488)(254,1487)(255,1486)(256,1485)(257,1484)(258,1483)(259,1482)(260,1481)(261,1480)(262,1479)(263,1478)(264,1477)(265,1476)(266,1475)(267,1474)(268,1473)(269,1472)(270,1471)(271,1470)(272,1469)(273,1468)(274,1467)(275,1466)(276,1465)(277,1464)(278,1463)(279,1462)(280,1461)(281,1460)(282,1459)(283,1458)(284,1457)(285,1456)(286,1455)(287,1454)(288,1453)(289,1452)(290,1451)(291,1450)(292,1449)(293,1448)(294,1447)(295,1446)(296,1445)(297,1444)(298,1443)(299,1442)(300,1441)(301,1440)(302,1439)(303,1438)(304,1437)(305,1436)(306,1435)(307,1434)(308,1433)(309,1432)(310,1431)(311,1430)(312,1429)(313,1428)(314,1427)(315,1426)(316,1425)(317,1424)(318,1423)(319,1422)(320,1421)(321,1420)(322,1419)(323,1418)(324,1417)(325,1416)(326,1415)(327,1414)(328,1413)(329,1412)(330,1411)(331,1410)(332,1409)(333,1408)(334,1407)(335,1406)(336,1405)(337,1404)(338,1403)(339,1402)(340,1401)(341,1400)(342,1399)(343,1398)(344,1397)(345,1396)(346,1395)(347,1394)(348,1393)(349,1392)(350,1391)(351,1390)(352,1389)(353,1388)(354,1387)(355,1386)(356,1385)(357,1384)(358,1383)(359,1382)(360,1381)(361,1380)(362,1379)(363,1378)(364,1377)(365,1376)(366,1375)(367,1374)(368,1373)(369,1372)(370,1371)(371,1370)(372,1369)(373,1368)(374,1367)(375,1366)(376,1365)(377,1364)(378,1363)(379,1362)(380,1361)(381,1360)(382,1359)(383,1358)(384,1357)(385,1356)(386,1355)(387,1354)(388,1353)(389,1352)(390,1351)(391,1350)(392,1349)(393,1348)(394,1347)(395,1346)(396,1345)(397,1344)(398,1343)(399,1342)(400,1341)(401,1340)(402,1339)(403,1338)(404,1337)(405,1336)(406,1335)(407,1334)(408,1333)(409,1332)(410,1331)(411,1330)(412,1329)(413,1328)(414,1327)(415,1326)(416,1325)(417,1324)(418,1323)(419,1322)(420,1321)(421,1320)(422,1319)(423,1318)(424,1317)(425,1316)(426,1315)(427,1314)(428,1313)(429,1312)(430,1311)(431,1310)(432,1309)(433,1308)(434,1307)(435,1306)(436,1305)(437,1304)(438,1303)(439,1302)(440,1301)(441,1300)(442,1299)(443,1298)(444,1297)(445,1296)(446,1295)(447,1294)(448,1293)(449,1292)(450,1291)(451,1290)(452,1289)(453,1288)(454,1287)(455,1286)(456,1285)(457,1284)(458,1283)(459,1282)(460,1281)(461,1280)(462,1279)(463,1278)(464,1277)(465,1276)(466,1275)(467,1274)(468,1273)(469,1272)(470,1271)(471,1270)(472,1269)(473,1268)(474,1267)(475,1266)(476,1265)(477,1264)(478,1263)(479,1262)(480,1261)(481,1260)(482,1259)(483,1258)(484,1257)(485,1256)(486,1255)(487,1254)(488,1253)(489,1252)(490,1251)(491,1250)(492,1249)(493,1248)(494,1247)(495,1246)(496,1245)(497,1244)(498,1243)(499,1242)(500,1241)(501,1240)(502,1239)(503,1238)(504,1237)(505,1236)(506,1235)(507,1234)(508,1233)(509,1232)(510,1231)(511,1230)(512,1229)(513,1228)(514,1227)(515,1226)(516,1225)(517,1224)(518,1223)(519,1222)(520,1221)(521,1220)(522,1219)(523,1218)(524,1217)(525,1216)(526,1215)(527,1214)(528,1213)(529,1212)(530,1211)(531,1210)(532,1209)(533,1208)(534,1207)(535,1206)(536,1205)(537,1204)(538,1203)(539,1202)(540,1201)(541,1200)(542,1199)(543,1198)(544,1197)(545,1196)(546,1195)(547,1194)(548,1193)(549,1192)(550,1191)(551,1190)(552,1189)(553,1188)(554,1187)(555,1186)(556,1185)(557,1184)(558,1183)(559,1182)(560,1181)(561,1180)(562,1179)(563,1178)(564,1177)(565,1176)(566,1175)(567,1174)(568,1173)(569,1172)(570,1171)(571,1170)(572,1169)(573,1168)(574,1167)(575,1166)(576,1165)(577,1164)(578,1163)(579,1162)(580,1161)(581,1160)(582,1159)(583,1158)(584,1157)(585,1156)(586,1155)(587,1154)(588,1153)(589,1152)(590,1151)(591,1150)(592,1149)(593,1148)(594,1147)(595,1146)(596,1145)(597,1144)(598,1143)(599,1142)(600,1141)(601,1140)(602,1139)(603,1138)(604,1137)(605,1136)(606,1135)(607,1134)(608,1133)(609,1132)(610,1131)(611,1130)(612,1129)(613,1128)(614,1127)(615,1126)(616,1125)(617,1124)(618,1123)(619,1122)(620,1121)(621,1120)(622,1119)(623,1118)(624,1117)(625,1116)(626,1115)(627,1114)(628,1113)(629,1112)(630,1111)(631,1110)(632,1109)(633,1108)(634,1107)(635,1106)(636,1105)(637,1104)(638,1103)(639,1102)(640,1101)(641,1100)(642,1099)(643,1098)(644,1097)(645,1096)(646,1095)(647,1094)(648,1093)(649,1092)(650,1091)(651,1090)(652,1089)(653,1088)(654,1087)(655,1086)(656,1085)(657,1084)(658,1083)(659,1082)(660,1081)(661,1080)(662,1079)(663,1078)(664,1077)(665,1076)(666,1075)(667,1074)(668,1073)(669,1072)(670,1071)(671,1070)(672,1069)(673,1068)(674,1067)(675,1066)(676,1065)(677,1064)(678,1063)(679,1062)(680,1061)(681,1060)(682,1059)(683,1058)(684,1057)(685,1056)(686,1055)(687,1054)(688,1053)(689,1052)(690,1051)(691,1050)(692,1049)(693,1048)(694,1047)(695,1046)(696,1045)(697,1044)(698,1043)(699,1042)(700,1041)(701,1040)(702,1039)(703,1038)(704,1037)(705,1036)(706,1035)(707,1034)(708,1033)(709,1032)(710,1031)(711,1030)(712,1029)(713,1028)(714,1027)(715,1026)(716,1025)(717,1024)(718,1023)(719,1022)(720,1021)(721,1020)(722,1019)(723,1018)(724,1017)(725,1016)(726,1015)(727,1014)(728,1013)(729,1012)(730,1011)(731,1010)(732,1009)(733,1008)(734,1007)(735,1006)(736,1005)(737,1004)(738,1003)(739,1002)(740,1001)(741,1000)(742,999)(743,998)(744,997)(745,996)(746,995)(747,994)(748,993)(749,992)(750,991)(751,990)(752,989)(753,988)(754,987)(755,986)(756,985)(757,984)(758,983)(759,982)(760,981)(761,980)(762,979)(763,978)(764,977)(765,976)(766,975)(767,974)(768,973)(769,972)(770,971)(771,970)(772,969)(773,968)(774,967)(775,966)(776,965)(777,964)(778,963)(779,962)(780,961)(781,960)(782,959)(783,958)(784,957)(785,956)(786,955)(787,954)(788,953)(789,952)(790,951)(791,950)(792,949)(793,948)(794,947)(795,946)(796,945)(797,944)(798,943)(799,942)(800,941)(801,940)(802,939)(803,938)(804,937)(805,936)(806,935)(807,934)(808,933)(809,932)(810,931)(811,930)(812,929)(813,928)(814,927)(815,926)(816,925)(817,924)(818,923)(819,922)(820,921)(821,920)(822,919)(823,918)(824,917)(825,916)(826,915)(827,914)(828,913)(829,912)(830,911)(831,910)(832,909)(833,908)(834,907)(835,906)(836,905)(837,904)(838,903)(839,902)(840,901)(841,900)(842,899)(843,898)(844,897)(845,896)(846,895)(847,894)(848,893)(849,892)(850,891)(851,890)(852,889)(853,888)(854,887)(855,886)(856,885)(857,884)(858,883)(859,882)(860,881)(861,880)(862,879)(863,878)(864,877)(865,876)(866,875)(867,874)(868,873)(869,872)(870,871)
Polycyclic presentation:
2^3,1723|a^2=c,b^2=c,b^a=bc,d^b=d^1722
Conjugacy classes & character table
3449 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13784, 11);
Finite Group Databasebeta