Finite Group Databasebeta

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Dic₆₅₀₈ #39907414

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1643 points:

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

Polycyclic presentation:

2^4,1627|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1626,c^b=cd,e^b=e^1626

Conjugacy classes & character table

6511 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26032, 31);