Finite Group DatabasebetaFinite Group Databasebeta| order | 26032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D13016 |
| Fitting | C8×C1627 ⋊ C2 |
| Sylow | C1627 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D6508 |
| commutator, cosocle | C4×C1627 | C22 |
| Frattini | C4 | C2×D1627 |
| Fitting | C8×C1627 | C2 |
| socle | C2×C1627 | D4 |
| hypercenter | C8 | D1627 |
| hypocenter | C1627 | D8 |
| LCS | G ▷ C4×C1627 ▷ C2×C1627 ▷ C1627 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1635 |
| transitive degree | μt(G) = 13016 |
A minimal faithful permutation representation — 2 generators on 1635 points:
(1,2,3,4,5,6,7,8)(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);(2,8)(3,7)(4,6)(10,1635)(11,1634)(12,1633)(13,1632)(14,1631)(15,1630)(16,1629)(17,1628)(18,1627)(19,1626)(20,1625)(21,1624)(22,1623)(23,1622)(24,1621)(25,1620)(26,1619)(27,1618)(28,1617)(29,1616)(30,1615)(31,1614)(32,1613)(33,1612)(34,1611)(35,1610)(36,1609)(37,1608)(38,1607)(39,1606)(40,1605)(41,1604)(42,1603)(43,1602)(44,1601)(45,1600)(46,1599)(47,1598)(48,1597)(49,1596)(50,1595)(51,1594)(52,1593)(53,1592)(54,1591)(55,1590)(56,1589)(57,1588)(58,1587)(59,1586)(60,1585)(61,1584)(62,1583)(63,1582)(64,1581)(65,1580)(66,1579)(67,1578)(68,1577)(69,1576)(70,1575)(71,1574)(72,1573)(73,1572)(74,1571)(75,1570)(76,1569)(77,1568)(78,1567)(79,1566)(80,1565)(81,1564)(82,1563)(83,1562)(84,1561)(85,1560)(86,1559)(87,1558)(88,1557)(89,1556)(90,1555)(91,1554)(92,1553)(93,1552)(94,1551)(95,1550)(96,1549)(97,1548)(98,1547)(99,1546)(100,1545)(101,1544)(102,1543)(103,1542)(104,1541)(105,1540)(106,1539)(107,1538)(108,1537)(109,1536)(110,1535)(111,1534)(112,1533)(113,1532)(114,1531)(115,1530)(116,1529)(117,1528)(118,1527)(119,1526)(120,1525)(121,1524)(122,1523)(123,1522)(124,1521)(125,1520)(126,1519)(127,1518)(128,1517)(129,1516)(130,1515)(131,1514)(132,1513)(133,1512)(134,1511)(135,1510)(136,1509)(137,1508)(138,1507)(139,1506)(140,1505)(141,1504)(142,1503)(143,1502)(144,1501)(145,1500)(146,1499)(147,1498)(148,1497)(149,1496)(150,1495)(151,1494)(152,1493)(153,1492)(154,1491)(155,1490)(156,1489)(157,1488)(158,1487)(159,1486)(160,1485)(161,1484)(162,1483)(163,1482)(164,1481)(165,1480)(166,1479)(167,1478)(168,1477)(169,1476)(170,1475)(171,1474)(172,1473)(173,1472)(174,1471)(175,1470)(176,1469)(177,1468)(178,1467)(179,1466)(180,1465)(181,1464)(182,1463)(183,1462)(184,1461)(185,1460)(186,1459)(187,1458)(188,1457)(189,1456)(190,1455)(191,1454)(192,1453)(193,1452)(194,1451)(195,1450)(196,1449)(197,1448)(198,1447)(199,1446)(200,1445)(201,1444)(202,1443)(203,1442)(204,1441)(205,1440)(206,1439)(207,1438)(208,1437)(209,1436)(210,1435)(211,1434)(212,1433)(213,1432)(214,1431)(215,1430)(216,1429)(217,1428)(218,1427)(219,1426)(220,1425)(221,1424)(222,1423)(223,1422)(224,1421)(225,1420)(226,1419)(227,1418)(228,1417)(229,1416)(230,1415)(231,1414)(232,1413)(233,1412)(234,1411)(235,1410)(236,1409)(237,1408)(238,1407)(239,1406)(240,1405)(241,1404)(242,1403)(243,1402)(244,1401)(245,1400)(246,1399)(247,1398)(248,1397)(249,1396)(250,1395)(251,1394)(252,1393)(253,1392)(254,1391)(255,1390)(256,1389)(257,1388)(258,1387)(259,1386)(260,1385)(261,1384)(262,1383)(263,1382)(264,1381)(265,1380)(266,1379)(267,1378)(268,1377)(269,1376)(270,1375)(271,1374)(272,1373)(273,1372)(274,1371)(275,1370)(276,1369)(277,1368)(278,1367)(279,1366)(280,1365)(281,1364)(282,1363)(283,1362)(284,1361)(285,1360)(286,1359)(287,1358)(288,1357)(289,1356)(290,1355)(291,1354)(292,1353)(293,1352)(294,1351)(295,1350)(296,1349)(297,1348)(298,1347)(299,1346)(300,1345)(301,1344)(302,1343)(303,1342)(304,1341)(305,1340)(306,1339)(307,1338)(308,1337)(309,1336)(310,1335)(311,1334)(312,1333)(313,1332)(314,1331)(315,1330)(316,1329)(317,1328)(318,1327)(319,1326)(320,1325)(321,1324)(322,1323)(323,1322)(324,1321)(325,1320)(326,1319)(327,1318)(328,1317)(329,1316)(330,1315)(331,1314)(332,1313)(333,1312)(334,1311)(335,1310)(336,1309)(337,1308)(338,1307)(339,1306)(340,1305)(341,1304)(342,1303)(343,1302)(344,1301)(345,1300)(346,1299)(347,1298)(348,1297)(349,1296)(350,1295)(351,1294)(352,1293)(353,1292)(354,1291)(355,1290)(356,1289)(357,1288)(358,1287)(359,1286)(360,1285)(361,1284)(362,1283)(363,1282)(364,1281)(365,1280)(366,1279)(367,1278)(368,1277)(369,1276)(370,1275)(371,1274)(372,1273)(373,1272)(374,1271)(375,1270)(376,1269)(377,1268)(378,1267)(379,1266)(380,1265)(381,1264)(382,1263)(383,1262)(384,1261)(385,1260)(386,1259)(387,1258)(388,1257)(389,1256)(390,1255)(391,1254)(392,1253)(393,1252)(394,1251)(395,1250)(396,1249)(397,1248)(398,1247)(399,1246)(400,1245)(401,1244)(402,1243)(403,1242)(404,1241)(405,1240)(406,1239)(407,1238)(408,1237)(409,1236)(410,1235)(411,1234)(412,1233)(413,1232)(414,1231)(415,1230)(416,1229)(417,1228)(418,1227)(419,1226)(420,1225)(421,1224)(422,1223)(423,1222)(424,1221)(425,1220)(426,1219)(427,1218)(428,1217)(429,1216)(430,1215)(431,1214)(432,1213)(433,1212)(434,1211)(435,1210)(436,1209)(437,1208)(438,1207)(439,1206)(440,1205)(441,1204)(442,1203)(443,1202)(444,1201)(445,1200)(446,1199)(447,1198)(448,1197)(449,1196)(450,1195)(451,1194)(452,1193)(453,1192)(454,1191)(455,1190)(456,1189)(457,1188)(458,1187)(459,1186)(460,1185)(461,1184)(462,1183)(463,1182)(464,1181)(465,1180)(466,1179)(467,1178)(468,1177)(469,1176)(470,1175)(471,1174)(472,1173)(473,1172)(474,1171)(475,1170)(476,1169)(477,1168)(478,1167)(479,1166)(480,1165)(481,1164)(482,1163)(483,1162)(484,1161)(485,1160)(486,1159)(487,1158)(488,1157)(489,1156)(490,1155)(491,1154)(492,1153)(493,1152)(494,1151)(495,1150)(496,1149)(497,1148)(498,1147)(499,1146)(500,1145)(501,1144)(502,1143)(503,1142)(504,1141)(505,1140)(506,1139)(507,1138)(508,1137)(509,1136)(510,1135)(511,1134)(512,1133)(513,1132)(514,1131)(515,1130)(516,1129)(517,1128)(518,1127)(519,1126)(520,1125)(521,1124)(522,1123)(523,1122)(524,1121)(525,1120)(526,1119)(527,1118)(528,1117)(529,1116)(530,1115)(531,1114)(532,1113)(533,1112)(534,1111)(535,1110)(536,1109)(537,1108)(538,1107)(539,1106)(540,1105)(541,1104)(542,1103)(543,1102)(544,1101)(545,1100)(546,1099)(547,1098)(548,1097)(549,1096)(550,1095)(551,1094)(552,1093)(553,1092)(554,1091)(555,1090)(556,1089)(557,1088)(558,1087)(559,1086)(560,1085)(561,1084)(562,1083)(563,1082)(564,1081)(565,1080)(566,1079)(567,1078)(568,1077)(569,1076)(570,1075)(571,1074)(572,1073)(573,1072)(574,1071)(575,1070)(576,1069)(577,1068)(578,1067)(579,1066)(580,1065)(581,1064)(582,1063)(583,1062)(584,1061)(585,1060)(586,1059)(587,1058)(588,1057)(589,1056)(590,1055)(591,1054)(592,1053)(593,1052)(594,1051)(595,1050)(596,1049)(597,1048)(598,1047)(599,1046)(600,1045)(601,1044)(602,1043)(603,1042)(604,1041)(605,1040)(606,1039)(607,1038)(608,1037)(609,1036)(610,1035)(611,1034)(612,1033)(613,1032)(614,1031)(615,1030)(616,1029)(617,1028)(618,1027)(619,1026)(620,1025)(621,1024)(622,1023)(623,1022)(624,1021)(625,1020)(626,1019)(627,1018)(628,1017)(629,1016)(630,1015)(631,1014)(632,1013)(633,1012)(634,1011)(635,1010)(636,1009)(637,1008)(638,1007)(639,1006)(640,1005)(641,1004)(642,1003)(643,1002)(644,1001)(645,1000)(646,999)(647,998)(648,997)(649,996)(650,995)(651,994)(652,993)(653,992)(654,991)(655,990)(656,989)(657,988)(658,987)(659,986)(660,985)(661,984)(662,983)(663,982)(664,981)(665,980)(666,979)(667,978)(668,977)(669,976)(670,975)(671,974)(672,973)(673,972)(674,971)(675,970)(676,969)(677,968)(678,967)(679,966)(680,965)(681,964)(682,963)(683,962)(684,961)(685,960)(686,959)(687,958)(688,957)(689,956)(690,955)(691,954)(692,953)(693,952)(694,951)(695,950)(696,949)(697,948)(698,947)(699,946)(700,945)(701,944)(702,943)(703,942)(704,941)(705,940)(706,939)(707,938)(708,937)(709,936)(710,935)(711,934)(712,933)(713,932)(714,931)(715,930)(716,929)(717,928)(718,927)(719,926)(720,925)(721,924)(722,923)(723,922)(724,921)(725,920)(726,919)(727,918)(728,917)(729,916)(730,915)(731,914)(732,913)(733,912)(734,911)(735,910)(736,909)(737,908)(738,907)(739,906)(740,905)(741,904)(742,903)(743,902)(744,901)(745,900)(746,899)(747,898)(748,897)(749,896)(750,895)(751,894)(752,893)(753,892)(754,891)(755,890)(756,889)(757,888)(758,887)(759,886)(760,885)(761,884)(762,883)(763,882)(764,881)(765,880)(766,879)(767,878)(768,877)(769,876)(770,875)(771,874)(772,873)(773,872)(774,871)(775,870)(776,869)(777,868)(778,867)(779,866)(780,865)(781,864)(782,863)(783,862)(784,861)(785,860)(786,859)(787,858)(788,857)(789,856)(790,855)(791,854)(792,853)(793,852)(794,851)(795,850)(796,849)(797,848)(798,847)(799,846)(800,845)(801,844)(802,843)(803,842)(804,841)(805,840)(806,839)(807,838)(808,837)(809,836)(810,835)(811,834)(812,833)(813,832)(814,831)(815,830)(816,829)(817,828)(818,827)(819,826)(820,825)(821,824)(822,823)Polycyclic presentation:
2^4,1627|c^2=d,b^a=bc,c^a=cd,e^a=e^1626,c^b=cd,e^b=e^16266511 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26032, 26);