Finite Group DatabasebetaFinite Group Databasebeta| order | 29286 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D1627⋊C3) |
| unambiguous semidirect product | (C1627⋊C3)⋊D3 |
| unambiguous semidirect product | D4881⋊C3 |
| Fitting, socle, derived | C3×C1627 ⋊ C2×C3 |
| Hall | C3×C1627⋊C3 ⋊ C2 |
| Sylow | C1627 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C1627 | C2×C3 |
| LCS | G ▷ C3×C1627 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1630 |
| transitive degree | μt(G) = 4881 |
A minimal faithful permutation representation — 2 generators on 1630 points:
(2,3)(5,9,10,6,7,11)(8,17,18,12,13,27)(14,30,31,20,21,44)(15,29,25,23,19,16)(22,49,50,33,34,67)(24,47,48,36,32,41)(26,28,46,38,39,42)(35,72,73,52,53,96)(37,70,71,55,51,64)(40,45,69,57,58,65)(43,85,83,61,62,60)(54,101,102,75,76,131)(56,99,100,78,74,93)(59,68,98,80,81,94)(63,114,115,86,87,89)(66,120,112,90,91,84)(77,136,137,104,105,172)(79,134,135,107,103,128)(82,97,133,109,110,129)(88,149,150,116,117,124)(92,156,154,121,122,119)(95,161,147,125,126,113)(106,177,178,139,140,219)(108,175,176,142,138,169)(111,132,174,144,145,170)(118,190,191,151,152,165)(123,197,198,157,158,160)(127,203,195,162,163,155)(130,208,188,166,167,148)(141,224,225,180,181,272)(143,222,223,183,179,216)(146,173,221,185,186,217)(153,237,238,192,193,212)(159,244,245,199,200,207)(164,251,249,204,205,202)(168,256,242,209,210,196)(171,261,235,213,214,189)(182,277,278,227,228,331)(184,275,276,230,226,269)(187,220,274,232,233,270)(194,290,291,239,240,265)(201,297,298,246,247,260)(206,304,305,252,253,255)(211,310,302,257,258,250)(215,315,295,262,263,243)(218,320,288,266,267,236)(229,336,337,280,281,396)(231,334,335,283,279,328)(234,273,333,285,286,329)(241,349,350,292,293,324)(248,356,357,299,300,319)(254,363,364,306,307,314)(259,370,368,311,312,309)(264,375,361,316,317,303)(268,380,354,321,322,296)(271,385,347,325,326,289)(282,401,402,339,340,467)(284,399,400,342,338,393)(287,332,398,344,345,394)(294,414,415,351,352,389)(301,421,422,358,359,384)(308,428,429,365,366,379)(313,435,436,371,372,374)(318,441,433,376,377,369)(323,446,426,381,382,362)(327,451,419,386,387,355)(330,456,412,390,391,348)(341,472,473,404,405,544)(343,470,471,407,403,464)(346,397,469,409,410,465)(353,485,486,416,417,460)(360,492,493,423,424,455)(367,499,500,430,431,450)(373,506,507,437,438,445)(378,513,511,442,443,440)(383,518,504,447,448,434)(388,523,497,452,453,427)(392,528,490,457,458,420)(395,533,483,461,462,413)(406,549,550,475,476,627)(408,547,548,478,474,541)(411,468,546,480,481,542)(418,562,563,487,488,537)(425,569,570,494,495,532)(432,576,577,501,502,527)(439,583,584,508,509,522)(444,590,591,514,515,517)(449,596,588,519,520,512)(454,601,581,524,525,505)(459,606,574,529,530,498)(463,611,567,534,535,491)(466,616,560,538,539,484)(477,632,633,552,553,716)(479,630,631,555,551,624)(482,545,629,557,558,625)(489,645,646,564,565,620)(496,652,653,571,572,615)(503,659,660,578,579,610)(510,666,667,585,586,605)(516,673,674,592,593,600)(521,680,678,597,598,595)(526,685,671,602,603,589)(531,690,664,607,608,582)(536,695,657,612,613,575)(540,700,650,617,618,568)(543,705,643,621,622,561)(554,721,722,635,636,811)(556,719,720,638,634,713)(559,628,718,640,641,714)(566,734,735,647,648,709)(573,741,742,654,655,704)(580,748,749,661,662,699)(587,755,756,668,669,694)(594,762,763,675,676,689)(599,769,770,681,682,684)(604,775,767,686,687,679)(609,780,760,691,692,672)(614,785,753,696,697,665)(619,790,746,701,702,658)(623,795,739,706,707,651)(626,800,732,710,711,644)(637,816,817,724,725,912)(639,814,815,727,723,808)(642,717,813,729,730,809)(649,829,830,736,737,804)(656,836,837,743,744,799)(663,843,844,750,751,794)(670,850,851,757,758,789)(677,857,858,764,765,784)(683,864,865,771,772,779)(688,871,869,776,777,774)(693,876,862,781,782,768)(698,881,855,786,787,761)(703,886,848,791,792,754)(708,891,841,796,797,747)(712,896,834,801,802,740)(715,901,827,805,806,733)(726,917,918,819,820,1019)(728,915,916,822,818,909)(731,812,914,824,825,910)(738,930,931,831,832,905)(745,937,938,838,839,900)(752,944,945,845,846,895)(759,951,952,852,853,890)(766,958,959,859,860,885)(773,965,966,866,867,880)(778,972,973,872,873,875)(783,978,970,877,878,870)(788,983,963,882,883,863)(793,988,956,887,888,856)(798,993,949,892,893,849)(803,998,942,897,898,842)(807,1003,935,902,903,835)(810,1008,928,906,907,828)(821,1024,1025,920,921,1132)(823,1022,1023,923,919,1016)(826,913,1021,925,926,1017)(833,1037,1038,932,933,1012)(840,1044,1045,939,940,1007)(847,1051,1052,946,947,1002)(854,1058,1059,953,954,997)(861,1065,1066,960,961,992)(868,1072,1073,967,968,987)(874,1079,1080,974,975,982)(879,1086,1084,979,980,977)(884,1091,1077,984,985,971)(889,1096,1070,989,990,964)(894,1101,1063,994,995,957)(899,1106,1056,999,1000,950)(904,1111,1049,1004,1005,943)(908,1116,1042,1009,1010,936)(911,1121,1035,1013,1014,929)(922,1137,1138,1027,1028,1251)(924,1135,1136,1030,1026,1129)(927,1020,1134,1032,1033,1130)(934,1150,1151,1039,1040,1125)(941,1157,1158,1046,1047,1120)(948,1164,1165,1053,1054,1115)(955,1171,1172,1060,1061,1110)(962,1178,1179,1067,1068,1105)(969,1185,1186,1074,1075,1100)(976,1192,1193,1081,1082,1095)(981,1199,1200,1087,1088,1090)(986,1205,1197,1092,1093,1085)(991,1210,1190,1097,1098,1078)(996,1215,1183,1102,1103,1071)(1001,1220,1176,1107,1108,1064)(1006,1225,1169,1112,1113,1057)(1011,1230,1162,1117,1118,1050)(1015,1235,1155,1122,1123,1043)(1018,1240,1148,1126,1127,1036)(1029,1256,1257,1140,1141,1367)(1031,1254,1255,1143,1139,1248)(1034,1133,1253,1145,1146,1249)(1041,1267,1268,1152,1153,1244)(1048,1274,1275,1159,1160,1239)(1055,1280,1281,1166,1167,1234)(1062,1285,1286,1173,1174,1229)(1069,1290,1291,1180,1181,1224)(1076,1295,1296,1187,1188,1219)(1083,1302,1303,1194,1195,1214)(1089,1309,1310,1201,1202,1209)(1094,1316,1314,1206,1207,1204)(1099,1321,1307,1211,1212,1198)(1104,1326,1300,1216,1217,1191)(1109,1331,1293,1221,1222,1184)(1114,1336,1288,1226,1227,1177)(1119,1341,1283,1231,1232,1170)(1124,1346,1278,1236,1237,1163)(1128,1351,1272,1241,1242,1156)(1131,1356,1265,1245,1246,1149)(1142,1292,1340,1182,1259,1391)(1144,1370,1371,1260,1258,1364)(1147,1252,1369,1262,1263,1365)(1154,1376,1377,1269,1270,1360)(1161,1381,1382,1276,1277,1355)(1168,1378,1385,1271,1282,1350)(1175,1372,1388,1261,1287,1345)(1189,1394,1395,1297,1298,1335)(1196,1398,1399,1304,1305,1330)(1203,1405,1406,1311,1312,1325)(1208,1412,1413,1317,1318,1320)(1213,1418,1410,1322,1323,1315)(1218,1423,1403,1327,1328,1308)(1223,1428,1396,1332,1333,1301)(1228,1433,1392,1337,1338,1294)(1233,1438,1389,1342,1343,1289)(1238,1442,1386,1347,1348,1284)(1243,1446,1383,1352,1353,1279)(1247,1450,1379,1357,1358,1273)(1250,1454,1374,1361,1362,1266)(1264,1368,1437,1299,1373,1461)(1306,1474,1475,1400,1401,1432)(1313,1478,1479,1407,1408,1427)(1319,1482,1483,1414,1415,1422)(1324,1489,1487,1419,1420,1417)(1329,1494,1480,1424,1425,1411)(1334,1499,1476,1429,1430,1404)(1339,1504,1472,1434,1435,1397)(1344,1509,1470,1439,1440,1393)(1349,1513,1468,1443,1444,1390)(1354,1517,1466,1447,1448,1387)(1359,1521,1464,1451,1452,1384)(1363,1525,1462,1455,1456,1380)(1366,1508,1402,1458,1459,1375)(1409,1529,1530,1463,1460,1503)(1416,1543,1544,1484,1485,1498)(1421,1547,1548,1490,1491,1493)(1426,1550,1545,1495,1496,1488)(1431,1555,1541,1500,1501,1481)(1436,1560,1539,1505,1506,1477)(1441,1564,1537,1510,1511,1473)(1445,1568,1535,1514,1515,1471)(1449,1572,1533,1518,1519,1469)(1453,1576,1531,1522,1523,1467)(1457,1559,1486,1526,1527,1465)(1492,1580,1581,1532,1528,1554)(1497,1594,1592,1551,1552,1549)(1502,1596,1590,1556,1557,1546)(1507,1597,1588,1561,1562,1542)(1512,1601,1586,1565,1566,1540)(1516,1605,1584,1569,1570,1538)(1520,1609,1582,1573,1574,1536)(1524,1595,1553,1577,1578,1534)(1558,1613,1614,1583,1579,1593)(1563,1622,1619,1598,1599,1591)(1567,1623,1617,1602,1603,1589)(1571,1624,1615,1606,1607,1587)(1575,1621,1600,1610,1611,1585)(1604,1628,1629,1616,1612,1620)(1608,1630,1627,1625,1626,1618);(1,2,3)(4,5,8,14,22,35,54,77,106,141,182,229,282,341,406,477,554,637,726,821,922,1029,1142,1180,1067,960,859,764,675,592,514,442,376,316,262,213,145,76,103,117,122,126,129,131,169,212,260,314,374,440,512,589,672,761,856,957,1064,1177,1289,1390,1469,1534,1551,1495,1424,1327,1216,1102,994,892,796,706,621,481,340,403,417,424,431,438,443,448,453,458,462,465,467,541,620,704,794,890,992,1100,1214,1325,1422,1493,1549,1593,1621,1624,1623,1622,1613,1577,1522,1451,1357,1245,1033,820,919,933,940,947,954,961,968,975,980,985,990,995,1000,1005,1010,1014,1017,1019,1129,1244,1355,1377,1255,1025,1134,1240,1235,1230,1225,1220,1215,1210,1205,1199,1192,1185,1178,1171,1164,1157,1150,1135,1024,1133,1250,1363,1457,1528,1552,1557,1562,1566,1570,1574,1578,1581,1544,1479,1399,1296,1179,1059,945,837,735,631,473,546,616,611,606,601,596,590,583,576,569,562,547,472,545,626,712,803,899,1001,1109,1223,1334,1431,1502,1558,1582,1535,1470,1392,1293,1183,1070,963,862,767,678,591,507,429,357,291,223,137,174,208,203,197,190,175,136,173,218,268,323,383,449,521,599,683,773,868,969,1076,1189,1299,1262,1145,1032,925,824,729,640,557,480,409,344,285,232,185,144,109,80,57,38,25,10,9,15,24,37,56,79,108,143,184,231,284,343,408,479,556,639,728,823,924,1031,1144,1261,1173,1060,953,852,757,668,585,508,437,371,311,257,209,166,110,53,74,87,91,94,96,128,165,207,255,309,369,434,505,582,665,754,849,950,1057,1170,1284,1387,1467,1532,1490,1419,1322,1211,1097,989,887,791,701,617,538,410,281,338,352,359,366,372,377,382,387,391,394,396,464,537,615,699,789,885,987,1095,1209,1320,1417,1488,1546,1591,1620,1630,1628,1610,1573,1518,1447,1352,1241,1126,926,725,818,832,839,846,853,860,867,873,878,883,888,893,898,903,907,910,912,1016,1125,1239,1350,1371,1138,1253,1356,1351,1346,1341,1336,1331,1326,1321,1316,1309,1302,1295,1290,1285,1280,1274,1267,1254,1137,1252,1366,1460,1485,1491,1496,1501,1506,1511,1515,1519,1523,1527,1530,1475,1395,1291,1172,1052,938,830,720,550,629,705,700,695,690,685,680,673,666,659,652,645,630,549,628,715,807,904,1006,1114,1228,1339,1436,1507,1563,1600,1584,1537,1472,1396,1300,1190,1077,970,869,770,674,584,500,422,350,276,178,221,261,256,251,244,237,222,177,220,271,327,388,454,526,604,688,778,874,976,1083,1196,1306,1402,1374,1265,1148,1035,928,827,732,643,560,483,412,347,288,235,188,147,112,83,48,18,29,17,28,43,63,88,118,153,194,241,294,353,418,489,566,649,738,833,934,1041,1154,1271,1166,1053,946,845,750,661,578,501,430,365,306,252,204,162,125,81,34,51,62,65,67,93,124,160,202,250,303,362,427,498,575,658,747,842,943,1050,1163,1279,1384,1465,1484,1414,1317,1206,1092,984,882,786,696,612,534,461,345,228,279,293,300,307,312,317,322,326,329,331,393,460,532,610,694,784,880,982,1090,1204,1315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presentation:
2,3^2,1627|c^a=c^2,d^a=d^1626,d^b=d^1362822 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29286, 9);