← Prev (#41001821) Next (#41001823) →
D13437 #41001822
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1502 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);(2,9)(3,8)(4,7)(5,6)(11,1502)(12,1501)(13,1500)(14,1499)(15,1498)(16,1497)(17,1496)(18,1495)(19,1494)(20,1493)(21,1492)(22,1491)(23,1490)(24,1489)(25,1488)(26,1487)(27,1486)(28,1485)(29,1484)(30,1483)(31,1482)(32,1481)(33,1480)(34,1479)(35,1478)(36,1477)(37,1476)(38,1475)(39,1474)(40,1473)(41,1472)(42,1471)(43,1470)(44,1469)(45,1468)(46,1467)(47,1466)(48,1465)(49,1464)(50,1463)(51,1462)(52,1461)(53,1460)(54,1459)(55,1458)(56,1457)(57,1456)(58,1455)(59,1454)(60,1453)(61,1452)(62,1451)(63,1450)(64,1449)(65,1448)(66,1447)(67,1446)(68,1445)(69,1444)(70,1443)(71,1442)(72,1441)(73,1440)(74,1439)(75,1438)(76,1437)(77,1436)(78,1435)(79,1434)(80,1433)(81,1432)(82,1431)(83,1430)(84,1429)(85,1428)(86,1427)(87,1426)(88,1425)(89,1424)(90,1423)(91,1422)(92,1421)(93,1420)(94,1419)(95,1418)(96,1417)(97,1416)(98,1415)(99,1414)(100,1413)(101,1412)(102,1411)(103,1410)(104,1409)(105,1408)(106,1407)(107,1406)(108,1405)(109,1404)(110,1403)(111,1402)(112,1401)(113,1400)(114,1399)(115,1398)(116,1397)(117,1396)(118,1395)(119,1394)(120,1393)(121,1392)(122,1391)(123,1390)(124,1389)(125,1388)(126,1387)(127,1386)(128,1385)(129,1384)(130,1383)(131,1382)(132,1381)(133,1380)(134,1379)(135,1378)(136,1377)(137,1376)(138,1375)(139,1374)(140,1373)(141,1372)(142,1371)(143,1370)(144,1369)(145,1368)(146,1367)(147,1366)(148,1365)(149,1364)(150,1363)(151,1362)(152,1361)(153,1360)(154,1359)(155,1358)(156,1357)(157,1356)(158,1355)(159,1354)(160,1353)(161,1352)(162,1351)(163,1350)(164,1349)(165,1348)(166,1347)(167,1346)(168,1345)(169,1344)(170,1343)(171,1342)(172,1341)(173,1340)(174,1339)(175,1338)(176,1337)(177,1336)(178,1335)(179,1334)(180,1333)(181,1332)(182,1331)(183,1330)(184,1329)(185,1328)(186,1327)(187,1326)(188,1325)(189,1324)(190,1323)(191,1322)(192,1321)(193,1320)(194,1319)(195,1318)(196,1317)(197,1316)(198,1315)(199,1314)(200,1313)(201,1312)(202,1311)(203,1310)(204,1309)(205,1308)(206,1307)(207,1306)(208,1305)(209,1304)(210,1303)(211,1302)(212,1301)(213,1300)(214,1299)(215,1298)(216,1297)(217,1296)(218,1295)(219,1294)(220,1293)(221,1292)(222,1291)(223,1290)(224,1289)(225,1288)(226,1287)(227,1286)(228,1285)(229,1284)(230,1283)(231,1282)(232,1281)(233,1280)(234,1279)(235,1278)(236,1277)(237,1276)(238,1275)(239,1274)(240,1273)(241,1272)(242,1271)(243,1270)(244,1269)(245,1268)(246,1267)(247,1266)(248,1265)(249,1264)(250,1263)(251,1262)(252,1261)(253,1260)(254,1259)(255,1258)(256,1257)(257,1256)(258,1255)(259,1254)(260,1253)(261,1252)(262,1251)(263,1250)(264,1249)(265,1248)(266,1247)(267,1246)(268,1245)(269,1244)(270,1243)(271,1242)(272,1241)(273,1240)(274,1239)(275,1238)(276,1237)(277,1236)(278,1235)(279,1234)(280,1233)(281,1232)(282,1231)(283,1230)(284,1229)(285,1228)(286,1227)(287,1226)(288,1225)(289,1224)(290,1223)(291,1222)(292,1221)(293,1220)(294,1219)(295,1218)(296,1217)(297,1216)(298,1215)(299,1214)(300,1213)(301,1212)(302,1211)(303,1210)(304,1209)(305,1208)(306,1207)(307,1206)(308,1205)(309,1204)(310,1203)(311,1202)(312,1201)(313,1200)(314,1199)(315,1198)(316,1197)(317,1196)(318,1195)(319,1194)(320,1193)(321,1192)(322,1191)(323,1190)(324,1189)(325,1188)(326,1187)(327,1186)(328,1185)(329,1184)(330,1183)(331,1182)(332,1181)(333,1180)(334,1179)(335,1178)(336,1177)(337,1176)(338,1175)(339,1174)(340,1173)(341,1172)(342,1171)(343,1170)(344,1169)(345,1168)(346,1167)(347,1166)(348,1165)(349,1164)(350,1163)(351,1162)(352,1161)(353,1160)(354,1159)(355,1158)(356,1157)(357,1156)(358,1155)(359,1154)(360,1153)(361,1152)(362,1151)(363,1150)(364,1149)(365,1148)(366,1147)(367,1146)(368,1145)(369,1144)(370,1143)(371,1142)(372,1141)(373,1140)(374,1139)(375,1138)(376,1137)(377,1136)(378,1135)(379,1134)(380,1133)(381,1132)(382,1131)(383,1130)(384,1129)(385,1128)(386,1127)(387,1126)(388,1125)(389,1124)(390,1123)(391,1122)(392,1121)(393,1120)(394,1119)(395,1118)(396,1117)(397,1116)(398,1115)(399,1114)(400,1113)(401,1112)(402,1111)(403,1110)(404,1109)(405,1108)(406,1107)(407,1106)(408,1105)(409,1104)(410,1103)(411,1102)(412,1101)(413,1100)(414,1099)(415,1098)(416,1097)(417,1096)(418,1095)(419,1094)(420,1093)(421,1092)(422,1091)(423,1090)(424,1089)(425,1088)(426,1087)(427,1086)(428,1085)(429,1084)(430,1083)(431,1082)(432,1081)(433,1080)(434,1079)(435,1078)(436,1077)(437,1076)(438,1075)(439,1074)(440,1073)(441,1072)(442,1071)(443,1070)(444,1069)(445,1068)(446,1067)(447,1066)(448,1065)(449,1064)(450,1063)(451,1062)(452,1061)(453,1060)(454,1059)(455,1058)(456,1057)(457,1056)(458,1055)(459,1054)(460,1053)(461,1052)(462,1051)(463,1050)(464,1049)(465,1048)(466,1047)(467,1046)(468,1045)(469,1044)(470,1043)(471,1042)(472,1041)(473,1040)(474,1039)(475,1038)(476,1037)(477,1036)(478,1035)(479,1034)(480,1033)(481,1032)(482,1031)(483,1030)(484,1029)(485,1028)(486,1027)(487,1026)(488,1025)(489,1024)(490,1023)(491,1022)(492,1021)(493,1020)(494,1019)(495,1018)(496,1017)(497,1016)(498,1015)(499,1014)(500,1013)(501,1012)(502,1011)(503,1010)(504,1009)(505,1008)(506,1007)(507,1006)(508,1005)(509,1004)(510,1003)(511,1002)(512,1001)(513,1000)(514,999)(515,998)(516,997)(517,996)(518,995)(519,994)(520,993)(521,992)(522,991)(523,990)(524,989)(525,988)(526,987)(527,986)(528,985)(529,984)(530,983)(531,982)(532,981)(533,980)(534,979)(535,978)(536,977)(537,976)(538,975)(539,974)(540,973)(541,972)(542,971)(543,970)(544,969)(545,968)(546,967)(547,966)(548,965)(549,964)(550,963)(551,962)(552,961)(553,960)(554,959)(555,958)(556,957)(557,956)(558,955)(559,954)(560,953)(561,952)(562,951)(563,950)(564,949)(565,948)(566,947)(567,946)(568,945)(569,944)(570,943)(571,942)(572,941)(573,940)(574,939)(575,938)(576,937)(577,936)(578,935)(579,934)(580,933)(581,932)(582,931)(583,930)(584,929)(585,928)(586,927)(587,926)(588,925)(589,924)(590,923)(591,922)(592,921)(593,920)(594,919)(595,918)(596,917)(597,916)(598,915)(599,914)(600,913)(601,912)(602,911)(603,910)(604,909)(605,908)(606,907)(607,906)(608,905)(609,904)(610,903)(611,902)(612,901)(613,900)(614,899)(615,898)(616,897)(617,896)(618,895)(619,894)(620,893)(621,892)(622,891)(623,890)(624,889)(625,888)(626,887)(627,886)(628,885)(629,884)(630,883)(631,882)(632,881)(633,880)(634,879)(635,878)(636,877)(637,876)(638,875)(639,874)(640,873)(641,872)(642,871)(643,870)(644,869)(645,868)(646,867)(647,866)(648,865)(649,864)(650,863)(651,862)(652,861)(653,860)(654,859)(655,858)(656,857)(657,856)(658,855)(659,854)(660,853)(661,852)(662,851)(663,850)(664,849)(665,848)(666,847)(667,846)(668,845)(669,844)(670,843)(671,842)(672,841)(673,840)(674,839)(675,838)(676,837)(677,836)(678,835)(679,834)(680,833)(681,832)(682,831)(683,830)(684,829)(685,828)(686,827)(687,826)(688,825)(689,824)(690,823)(691,822)(692,821)(693,820)(694,819)(695,818)(696,817)(697,816)(698,815)(699,814)(700,813)(701,812)(702,811)(703,810)(704,809)(705,808)(706,807)(707,806)(708,805)(709,804)(710,803)(711,802)(712,801)(713,800)(714,799)(715,798)(716,797)(717,796)(718,795)(719,794)(720,793)(721,792)(722,791)(723,790)(724,789)(725,788)(726,787)(727,786)(728,785)(729,784)(730,783)(731,782)(732,781)(733,780)(734,779)(735,778)(736,777)(737,776)(738,775)(739,774)(740,773)(741,772)(742,771)(743,770)(744,769)(745,768)(746,767)(747,766)(748,765)(749,764)(750,763)(751,762)(752,761)(753,760)(754,759)(755,758)(756,757)
Polycyclic presentation:
2,3,1493,3|b^3=d^2,b^a=b^2d,c^a=c^1492,d^a=d^2
Conjugacy classes & character table
6720 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26874, 4);
Finite Group Databasebeta