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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1552 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,917)(788,856,921)(791,859,918)(794,862,915)(797,865,912)(800,868,909)(803,871,906)(806,874,903)(809,877,900)(812,880,897)(815,883,894)(818,886,891)(821,889,888)(824,892,885)(827,895,882)(830,898,879)(833,901,876)(836,904,873)(839,907,870)(842,910,867)(845,913,864)(848,916,861)(851,919,858)(853,922,855)(857,926,984)(860,928,988)(863,931,985)(866,933,983)(869,936,980)(872,939,977)(875,942,974)(878,945,971)(881,948,968)(884,951,965)(887,954,962)(890,957,959)(893,960,956)(896,963,953)(899,966,950)(902,969,947)(905,972,944)(908,975,941)(911,978,938)(914,981,935)(920,986,930)(923,989,927)(924,987,925)(929,993,1047)(932,995,1049)(934,997,1048)(937,999,1046)(940,1002,1043)(943,1005,1040)(946,1008,1037)(949,1011,1034)(952,1014,1031)(955,1017,1028)(958,1020,1025)(961,1023,1022)(964,1026,1019)(967,1029,1016)(970,1032,1013)(973,1035,1010)(976,1038,1007)(979,1041,1004)(982,1044,1001)(990,1050,994)(991,1051,992)(996,1054,1104)(998,1055,1106)(1000,1057,1105)(1003,1059,1103)(1006,1062,1100)(1009,1065,1097)(1012,1068,1094)(1015,1071,1091)(1018,1074,1088)(1021,1077,1085)(1024,1080,1082)(1027,1083,1079)(1030,1086,1076)(1033,1089,1073)(1036,1092,1070)(1039,1095,1067)(1042,1098,1064)(1045,1101,1061)(1052,1107,1053)(1056,1108,1155)(1058,1109,1157)(1060,1111,1156)(1063,1113,1154)(1066,1116,1151)(1069,1119,1148)(1072,1122,1145)(1075,1125,1142)(1078,1128,1139)(1081,1131,1136)(1084,1134,1133)(1087,1137,1130)(1090,1140,1127)(1093,1143,1124)(1096,1146,1121)(1099,1149,1118)(1102,1152,1115)(1110,1158,1202)(1112,1159,1204)(1114,1161,1203)(1117,1163,1201)(1120,1166,1198)(1123,1169,1195)(1126,1172,1192)(1129,1175,1189)(1132,1178,1186)(1135,1181,1183)(1138,1184,1180)(1141,1187,1177)(1144,1190,1174)(1147,1193,1171)(1150,1196,1168)(1153,1199,1165)(1160,1205,1246)(1162,1206,1248)(1164,1208,1247)(1167,1210,1245)(1170,1213,1242)(1173,1216,1239)(1176,1219,1236)(1179,1222,1233)(1182,1225,1230)(1185,1228,1227)(1188,1231,1224)(1191,1234,1221)(1194,1237,1218)(1197,1240,1215)(1200,1243,1212)(1207,1249,1287)(1209,1250,1289)(1211,1252,1288)(1214,1254,1286)(1217,1257,1283)(1220,1260,1280)(1223,1263,1277)(1226,1266,1274)(1229,1269,1271)(1232,1272,1268)(1235,1275,1265)(1238,1278,1262)(1241,1281,1259)(1244,1284,1256)(1251,1290,1325)(1253,1291,1327)(1255,1293,1326)(1258,1295,1324)(1261,1298,1321)(1264,1301,1318)(1267,1304,1315)(1270,1307,1312)(1273,1310,1309)(1276,1313,1306)(1279,1316,1303)(1282,1319,1300)(1285,1322,1297)(1292,1328,1360)(1294,1329,1362)(1296,1331,1361)(1299,1333,1359)(1302,1336,1356)(1305,1339,1353)(1308,1342,1350)(1311,1345,1347)(1314,1348,1344)(1317,1351,1341)(1320,1354,1338)(1323,1357,1335)(1330,1363,1392)(1332,1364,1394)(1334,1366,1393)(1337,1368,1391)(1340,1371,1388)(1343,1374,1385)(1346,1377,1382)(1349,1380,1379)(1352,1383,1376)(1355,1386,1373)(1358,1389,1370)(1365,1395,1421)(1367,1396,1423)(1369,1398,1422)(1372,1400,1420)(1375,1403,1417)(1378,1406,1414)(1381,1409,1411)(1384,1412,1408)(1387,1415,1405)(1390,1418,1402)(1397,1424,1447)(1399,1425,1449)(1401,1427,1448)(1404,1429,1446)(1407,1432,1443)(1410,1435,1440)(1413,1438,1437)(1416,1441,1434)(1419,1444,1431)(1426,1450,1470)(1428,1451,1472)(1430,1453,1471)(1433,1455,1469)(1436,1458,1466)(1439,1461,1463)(1442,1464,1460)(1445,1467,1457)(1452,1473,1490)(1454,1474,1492)(1456,1476,1491)(1459,1478,1489)(1462,1481,1486)(1465,1484,1483)(1468,1487,1480)(1475,1493,1507)(1477,1494,1509)(1479,1496,1508)(1482,1498,1506)(1485,1501,1503)(1488,1504,1500)(1495,1510,1521)(1497,1511,1523)(1499,1513,1522)(1502,1515,1520)(1505,1518,1517)(1512,1524,1532)(1514,1525,1534)(1516,1527,1533)(1519,1529,1531)(1526,1535,1540)(1528,1536,1542)(1530,1538,1541)(1537,1543,1546)(1539,1544,1547)(1545,1548,1549)(1551,1552);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,718,785,844,710,588,477,529,584,642,703,767,834,903,971,1034,1091,1142,1189,1233,1274,1312,1347,1379,1408,1434,1457,1450,1396,1331,1254,1166,1065,942,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,887,955,1018,1075,1126,1173,1217,1258,1296,1332,1365,1389,1319,1237,1143,1032,898,759,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,870,938,1001,993,856,717,783,851,920,987,852,921,988,1049,1106,1157,1204,1248,1289,1327,1362,1394,1423,1449,1472,1492,1509,1523,1534,1542,1547,1543,1525,1496,1455,1403,1339,1263,1175,1074,951,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,869,937,1000,1058,1110,1152,1041,907,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,819,888,956,1019,1076,1127,1174,1218,1259,1297,1290,1206,1111,999,865,726,598,482,378,426,476,528,583,641,702,766,833,902,970,1033,1090,1141,1188,1232,1273,1311,1346,1378,1407,1433,1456,1477,1495,1504,1464,1412,1348,1272,1184,1083,960,820,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,719,786,855,925,916,777,649,532,587,645,706,770,837,906,974,1037,1094,1145,1192,1236,1277,1315,1350,1382,1411,1437,1460,1480,1473,1425,1366,1295,1213,1119,1008,874,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,884,952,1015,1072,1123,1170,1214,1255,1294,1330,1357,1281,1193,1092,969,829,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,873,941,1004,1061,1054,928,787,653,716,781,848,917,984,1047,1104,1155,1202,1246,1287,1325,1360,1392,1421,1447,1470,1490,1507,1521,1532,1540,1546,1549,1548,1536,1513,1478,1432,1374,1304,1222,1128,1017,883,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,866,934,998,1056,1101,978,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,891,959,1022,1079,1130,1177,1221,1262,1300,1335,1328,1250,1161,1059,936,796,662,540,430,332,377,424,473,525,580,638,699,763,830,899,967,1030,1087,1138,1185,1229,1270,1308,1343,1375,1404,1430,1454,1475,1487,1441,1383,1313,1231,1137,1026,892,753,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,858,927,992,986,847,713,590,648,709,773,840,909,977,1040,1097,1148,1195,1239,1280,1318,1353,1385,1414,1440,1463,1483,1500,1493,1451,1398,1333,1257,1169,1068,945,805,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,812,881,949,1012,1069,1120,1167,1211,1253,1292,1322,1240,1146,1035,901,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,876,944,1007,1064,1115,1108,995,859,720,592,652,714,778,845,914,982,1045,1102,1153,1200,1244,1285,1323,1358,1390,1419,1445,1468,1488,1505,1519,1530,1539,1545,1544,1527,1498,1458,1406,1342,1266,1178,1077,954,814,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,863,932,996,1044,910,771,643,527,423,330,373,419,468,520,575,633,694,758,825,894,962,1025,1082,1133,1180,1224,1265,1303,1338,1370,1363,1291,1208,1113,1002,868,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,896,964,1027,1084,1135,1182,1226,1267,1305,1340,1372,1401,1428,1452,1467,1415,1351,1275,1187,1086,963,823,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,861,930,994,1053,1050,919,780,651,712,776,843,912,980,1043,1100,1151,1198,1242,1283,1321,1356,1388,1417,1443,1466,1486,1503,1517,1510,1474,1427,1368,1298,1216,1122,1011,877,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,878,946,1009,1066,1117,1164,1209,1251,1284,1196,1095,972,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,879,947,1010,1067,1118,1165,1158,1055,931,790,656,534,591,650,711,775,842,911,979,1042,1099,1150,1197,1241,1282,1320,1355,1387,1416,1442,1465,1485,1502,1516,1528,1537,1538,1515,1481,1435,1377,1307,1225,1131,1020,886,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,860,929,981,841,707,585,475,376,422,471,523,578,636,697,761,828,897,965,1028,1085,1136,1183,1227,1268,1306,1341,1373,1402,1395,1329,1252,1163,1062,939,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,893,961,1024,1081,1132,1179,1223,1264,1302,1337,1369,1399,1426,1444,1386,1316,1234,1140,1029,895,756,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,864,854,924,991,1052,1107,989,850,715,779,846,915,983,1046,1103,1154,1201,1245,1286,1324,1359,1391,1420,1446,1469,1489,1506,1520,1531,1524,1494,1453,1400,1336,1260,1172,1071,948,808,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,875,943,1006,1063,1114,1162,1207,1243,1149,1038,904,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,813,882,950,1013,1070,1121,1168,1212,1205,1109,997,862,723,595,479,533,589,647,708,772,839,908,976,1039,1096,1147,1194,1238,1279,1317,1352,1384,1413,1439,1462,1482,1499,1514,1526,1529,1501,1461,1409,1345,1269,1181,1080,957,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,857,913,774,646,530,425,474,526,581,639,700,764,831,900,968,1031,1088,1139,1186,1230,1271,1309,1344,1376,1405,1431,1424,1364,1293,1210,1116,1005,871,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,890,958,1021,1078,1129,1176,1220,1261,1299,1334,1367,1397,1418,1354,1278,1190,1089,966,826,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,867,935,926,784,853,923,990,1051,922,782,849,918,985,1048,1105,1156,1203,1247,1288,1326,1361,1393,1422,1448,1471,1491,1508,1522,1533,1541,1535,1511,1476,1429,1371,1301,1219,1125,1014,880,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,872,940,1003,1060,1112,1160,1199,1098,975,835,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,749,816,885,953,1016,1073,1124,1171,1215,1256,1249,1159,1057,933,793,659,537,427,478,531,586,644,705,769,836,905,973,1036,1093,1144,1191,1235,1276,1314,1349,1381,1410,1436,1459,1479,1497,1512,1518,1484,1438,1380,1310,1228,1134,1023,889,750,622,506,402,310,230,162,106,62,30,10)(1550,1551,1552)
Conjugacy classes & character table
1557 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27882, 12);
Finite Group Databasebeta