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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1611 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,378)(284,331,332,374)(288,335,336,370)(292,339,340,366)(296,343,344,362)(300,347,348,358)(304,351,352,354)(308,355,356,350)(312,359,360,346)(316,363,364,342)(320,367,368,338)(324,371,372,334)(326,375,376,330)(329,380,381,435)(333,384,385,431)(337,388,389,427)(341,392,393,423)(345,396,397,419)(349,400,401,415)(353,404,405,411)(357,408,409,407)(361,412,413,403)(365,416,417,399)(369,420,421,395)(373,424,425,391)(377,428,429,387)(379,432,433,383)(382,437,438,496)(386,441,442,492)(390,445,446,488)(394,449,450,484)(398,453,454,480)(402,457,458,476)(406,461,462,472)(410,465,466,468)(414,469,470,464)(418,473,474,460)(422,477,478,456)(426,481,482,452)(430,485,486,448)(434,489,490,444)(436,493,494,440)(439,498,499,561)(443,502,503,557)(447,506,507,553)(451,510,511,549)(455,514,515,545)(459,518,519,541)(463,522,523,537)(467,526,527,533)(471,530,531,529)(475,534,535,525)(479,538,539,521)(483,542,543,517)(487,546,547,513)(491,550,551,509)(495,554,555,505)(497,558,559,501)(500,563,564,630)(504,567,568,626)(508,571,572,622)(512,575,576,618)(516,579,580,614)(520,583,584,610)(524,587,588,606)(528,591,592,602)(532,595,596,598)(536,599,600,594)(540,603,604,590)(544,607,608,586)(548,611,612,582)(552,615,616,578)(556,619,620,574)(560,623,624,570)(562,627,628,566)(565,632,633,703)(569,636,637,699)(573,640,641,695)(577,644,645,691)(581,648,649,687)(585,652,653,683)(589,656,657,679)(593,660,661,675)(597,664,665,671)(601,668,669,667)(605,672,673,663)(609,676,677,659)(613,680,681,655)(617,684,685,651)(621,688,689,647)(625,692,693,643)(629,696,697,639)(631,700,701,635)(634,705,706,780)(638,709,710,776)(642,713,714,772)(646,717,718,768)(650,721,722,764)(654,725,726,760)(658,729,730,756)(662,733,734,752)(666,737,738,748)(670,741,742,744)(674,745,746,740)(678,749,750,736)(682,753,754,732)(686,757,758,728)(690,761,762,724)(694,765,766,720)(698,769,770,716)(702,773,774,712)(704,777,778,708)(707,782,783,861)(711,786,787,857)(715,790,791,853)(719,794,795,849)(723,798,799,845)(727,802,803,841)(731,806,807,837)(735,810,811,833)(739,814,815,829)(743,818,819,825)(747,822,823,821)(751,826,827,817)(755,830,831,813)(759,834,835,809)(763,838,839,805)(767,842,843,801)(771,846,847,797)(775,850,851,793)(779,854,855,789)(781,858,859,785)(784,863,864,940)(788,867,868,941)(792,871,872,937)(796,875,876,934)(800,879,880,930)(804,883,884,926)(808,887,888,922)(812,891,892,918)(816,895,896,914)(820,899,900,910)(824,903,904,906)(828,907,908,902)(832,911,912,898)(836,915,916,894)(840,919,920,890)(844,923,924,886)(848,927,928,882)(852,931,932,878)(856,865,935,874)(860,938,939,870)(862,942,943,866)(869,944,945,1013)(873,947,948,1014)(877,950,951,1012)(881,954,955,1009)(885,958,959,1005)(889,962,963,1001)(893,966,967,997)(897,970,971,993)(901,974,975,989)(905,978,979,985)(909,982,983,981)(913,986,987,977)(917,990,991,973)(921,994,995,969)(925,998,999,965)(929,1002,1003,961)(933,1006,1007,957)(936,946,1010,953)(949,1015,1016,1080)(952,1018,1019,1081)(956,1021,1022,1079)(960,1025,1026,1076)(964,1029,1030,1072)(968,1033,1034,1068)(972,1037,1038,1064)(976,1041,1042,1060)(980,1045,1046,1056)(984,1049,1050,1052)(988,1053,1054,1048)(992,1057,1058,1044)(996,1061,1062,1040)(1000,1065,1066,1036)(1004,1069,1070,1032)(1008,1073,1074,1028)(1011,1017,1077,1024)(1020,1082,1083,1143)(1023,1085,1086,1144)(1027,1088,1089,1142)(1031,1092,1093,1139)(1035,1096,1097,1135)(1039,1100,1101,1131)(1043,1104,1105,1127)(1047,1108,1109,1123)(1051,1112,1113,1119)(1055,1116,1117,1115)(1059,1120,1121,1111)(1063,1124,1125,1107)(1067,1128,1129,1103)(1071,1132,1133,1099)(1075,1136,1137,1095)(1078,1084,1140,1091)(1087,1145,1146,1202)(1090,1148,1149,1203)(1094,1151,1152,1201)(1098,1155,1156,1198)(1102,1159,1160,1194)(1106,1163,1164,1190)(1110,1167,1168,1186)(1114,1171,1172,1182)(1118,1175,1176,1178)(1122,1179,1180,1174)(1126,1183,1184,1170)(1130,1187,1188,1166)(1134,1191,1192,1162)(1138,1195,1196,1158)(1141,1147,1199,1154)(1150,1204,1205,1257)(1153,1207,1208,1258)(1157,1210,1211,1256)(1161,1214,1215,1253)(1165,1218,1219,1249)(1169,1222,1223,1245)(1173,1226,1227,1241)(1177,1230,1231,1237)(1181,1234,1235,1233)(1185,1238,1239,1229)(1189,1242,1243,1225)(1193,1246,1247,1221)(1197,1250,1251,1217)(1200,1206,1254,1213)(1209,1259,1260,1308)(1212,1262,1263,1309)(1216,1265,1266,1307)(1220,1269,1270,1304)(1224,1273,1274,1300)(1228,1277,1278,1296)(1232,1281,1282,1292)(1236,1285,1286,1288)(1240,1289,1290,1284)(1244,1293,1294,1280)(1248,1297,1298,1276)(1252,1301,1302,1272)(1255,1261,1305,1268)(1264,1310,1311,1355)(1267,1313,1314,1356)(1271,1316,1317,1354)(1275,1320,1321,1351)(1279,1324,1325,1347)(1283,1328,1329,1343)(1287,1332,1333,1339)(1291,1336,1337,1335)(1295,1340,1341,1331)(1299,1344,1345,1327)(1303,1348,1349,1323)(1306,1312,1352,1319)(1315,1357,1358,1398)(1318,1360,1361,1399)(1322,1363,1364,1397)(1326,1367,1368,1394)(1330,1371,1372,1390)(1334,1375,1376,1386)(1338,1379,1380,1382)(1342,1383,1384,1378)(1346,1387,1388,1374)(1350,1391,1392,1370)(1353,1359,1395,1366)(1362,1400,1401,1437)(1365,1403,1404,1438)(1369,1406,1407,1436)(1373,1410,1411,1433)(1377,1414,1415,1429)(1381,1418,1419,1425)(1385,1422,1423,1421)(1389,1426,1427,1417)(1393,1430,1431,1413)(1396,1402,1434,1409)(1405,1439,1440,1472)(1408,1442,1443,1473)(1412,1445,1446,1471)(1416,1449,1450,1468)(1420,1453,1454,1464)(1424,1457,1458,1460)(1428,1461,1462,1456)(1432,1465,1466,1452)(1435,1441,1469,1448)(1444,1474,1475,1503)(1447,1477,1478,1504)(1451,1480,1481,1502)(1455,1484,1485,1499)(1459,1488,1489,1495)(1463,1492,1493,1491)(1467,1496,1497,1487)(1470,1476,1500,1483)(1479,1505,1506,1530)(1482,1508,1509,1531)(1486,1511,1512,1529)(1490,1515,1516,1526)(1494,1519,1520,1522)(1498,1523,1524,1518)(1501,1507,1527,1514)(1510,1532,1533,1553)(1513,1535,1536,1554)(1517,1538,1539,1552)(1521,1542,1543,1549)(1525,1546,1547,1545)(1528,1534,1550,1541)(1537,1555,1556,1572)(1540,1558,1559,1573)(1544,1561,1562,1571)(1548,1565,1566,1568)(1551,1557,1569,1564)(1560,1574,1575,1587)(1563,1577,1578,1588)(1567,1580,1581,1586)(1570,1576,1584,1583)(1579,1589,1590,1598)(1582,1592,1593,1599)(1585,1591,1595,1597)(1594,1600,1601,1605)(1596,1602,1603,1606)(1604,1607,1608,1609);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,565,634,707,784,865,850,769,692,619,550,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,577,646,719,796,877,952,1020,1084,1073,1002,923,838,757,680,607,538,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,589,658,731,808,889,964,1031,1094,1153,1209,1261,1250,1191,1128,1061,990,911,826,745,668,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,670,743,820,901,976,1043,1106,1165,1220,1271,1318,1362,1402,1391,1344,1293,1238,1179,1116,1049,978,899,814,733,656,583,514,449,388,331,278,326,377,430,487,548,613,682,755,832,913,988,1055,1118,1177,1232,1283,1330,1373,1412,1447,1479,1507,1496,1461,1422,1379,1332,1281,1226,1167,1104,1037,966,887,802,721,644,571,502,437,497,560,625,694,767,844,925,1000,1067,1130,1189,1244,1295,1342,1385,1424,1459,1490,1517,1540,1560,1576,1565,1542,1515,1484,1449,1410,1367,1320,1269,1214,1155,1092,1025,954,875,790,709,632,704,779,856,936,1011,1078,1141,1200,1255,1306,1353,1396,1435,1470,1501,1528,1551,1570,1585,1596,1604,1607,1600,1589,1574,1555,1532,1505,1474,1439,1400,1357,1310,1259,1204,1145,1082,1015,944,863,939,859,780,857,937,1012,1079,1142,1201,1256,1307,1354,1397,1436,1471,1502,1529,1552,1571,1586,1597,1590,1578,1562,1543,1520,1493,1462,1427,1388,1345,1298,1247,1192,1133,1070,1003,928,847,770,697,628,561,626,695,768,845,926,1001,1068,1131,1190,1245,1296,1343,1386,1425,1460,1491,1518,1541,1533,1509,1481,1450,1415,1376,1333,1286,1235,1180,1121,1058,991,916,835,758,685,616,551,490,433,378,431,488,549,614,683,756,833,914,989,1056,1119,1178,1233,1284,1331,1374,1413,1448,1440,1404,1364,1321,1274,1223,1168,1109,1046,979,904,823,746,673,604,539,478,421,368,319,274,231,272,317,366,419,476,537,602,671,744,821,902,977,1044,1107,1166,1221,1272,1319,1311,1263,1211,1156,1097,1034,967,892,811,734,661,592,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,590,659,732,809,890,965,1032,1095,1154,1146,1086,1022,955,880,799,722,649,580,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,578,647,720,797,878,953,945,868,787,710,637,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,635,708,785,866,938,854,773,696,623,554,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,573,642,715,792,873,949,1017,1006,927,842,761,684,611,542,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,585,654,727,804,885,960,1027,1090,1150,1206,1195,1132,1065,994,915,830,749,672,599,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,597,666,739,816,897,972,1039,1102,1161,1216,1267,1315,1359,1348,1297,1242,1183,1120,1053,982,903,818,737,660,587,518,453,392,335,282,233,277,324,373,426,483,544,609,678,751,828,909,984,1051,1114,1173,1228,1279,1326,1369,1408,1444,1476,1465,1426,1383,1336,1285,1230,1171,1108,1041,970,891,806,725,648,575,506,441,380,436,495,556,621,690,763,840,921,996,1063,1126,1185,1240,1291,1338,1381,1420,1455,1486,1513,1537,1557,1546,1519,1488,1453,1414,1371,1324,1273,1218,1159,1096,1029,958,879,794,713,636,563,631,702,775,852,933,1008,1075,1138,1197,1252,1303,1350,1393,1432,1467,1498,1525,1548,1567,1582,1594,1602,1592,1577,1558,1535,1508,1477,1442,1403,1360,1313,1262,1207,1148,1085,1018,947,867,782,862,943,861,941,1014,1081,1144,1203,1258,1309,1356,1399,1438,1473,1504,1531,1554,1573,1588,1599,1606,1601,1593,1581,1566,1547,1524,1497,1466,1431,1392,1349,1302,1251,1196,1137,1074,1007,932,851,774,701,630,699,772,849,930,1005,1072,1135,1194,1249,1300,1347,1390,1429,1464,1495,1522,1545,1564,1556,1536,1512,1485,1454,1419,1380,1337,1290,1239,1184,1125,1062,995,920,839,762,689,620,555,494,435,492,553,618,687,760,837,918,993,1060,1123,1182,1237,1288,1335,1378,1417,1452,1483,1475,1443,1407,1368,1325,1278,1227,1172,1113,1050,983,908,827,750,677,608,543,482,425,372,323,276,321,370,423,480,541,606,675,748,825,906,981,1048,1111,1170,1225,1276,1323,1366,1358,1314,1266,1215,1160,1101,1038,971,896,815,738,665,596,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,594,663,736,813,894,969,1036,1099,1158,1213,1205,1149,1089,1026,959,884,803,726,653,584,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,651,724,801,882,957,1024,1016,948,872,791,714,641,572,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,570,639,712,789,870,942,858,777,700,627,558,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,569,638,711,788,869,946,931,846,765,688,615,546,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,581,650,723,800,881,956,1023,1087,1147,1136,1069,998,919,834,753,676,603,534,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,528,593,662,735,812,893,968,1035,1098,1157,1212,1264,1312,1301,1246,1187,1124,1057,986,907,822,741,664,591,522,457,396,339,286,237,192,232,275,320,369,422,479,540,605,674,747,824,905,980,1047,1110,1169,1224,1275,1322,1365,1405,1441,1430,1387,1340,1289,1234,1175,1112,1045,974,895,810,729,652,579,510,445,384,327,379,434,491,552,617,686,759,836,917,992,1059,1122,1181,1236,1287,1334,1377,1416,1451,1482,1510,1534,1523,1492,1457,1418,1375,1328,1277,1222,1163,1100,1033,962,883,798,717,640,567,498,562,629,698,771,848,929,1004,1071,1134,1193,1248,1299,1346,1389,1428,1463,1494,1521,1544,1563,1579,1591,1580,1561,1538,1511,1480,1445,1406,1363,1316,1265,1210,1151,1088,1021,950,871,786,705,781,860,940,1013,1080,1143,1202,1257,1308,1355,1398,1437,1472,1503,1530,1553,1572,1587,1598,1605,1609,1608,1603,1595,1584,1569,1550,1527,1500,1469,1434,1395,1352,1305,1254,1199,1140,1077,1010,935,855,778,703,776,853,934,1009,1076,1139,1198,1253,1304,1351,1394,1433,1468,1499,1526,1549,1568,1583,1575,1559,1539,1516,1489,1458,1423,1384,1341,1294,1243,1188,1129,1066,999,924,843,766,693,624,559,496,557,622,691,764,841,922,997,1064,1127,1186,1241,1292,1339,1382,1421,1456,1487,1514,1506,1478,1446,1411,1372,1329,1282,1231,1176,1117,1054,987,912,831,754,681,612,547,486,429,376,325,374,427,484,545,610,679,752,829,910,985,1052,1115,1174,1229,1280,1327,1370,1409,1401,1361,1317,1270,1219,1164,1105,1042,975,900,819,742,669,600,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,598,667,740,817,898,973,1040,1103,1162,1217,1268,1260,1208,1152,1093,1030,963,888,807,730,657,588,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,586,655,728,805,886,961,1028,1091,1083,1019,951,876,795,718,645,576,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,574,643,716,793,874,864,783,706,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)(1610,1611)
Conjugacy classes & character table
812 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12872, 14);
Finite Group Databasebeta