← Prev (#26045111) Next (#26045113) →
D5932 #26045112
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1487 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);(2,4)(6,1487)(7,1486)(8,1485)(9,1484)(10,1483)(11,1482)(12,1481)(13,1480)(14,1479)(15,1478)(16,1477)(17,1476)(18,1475)(19,1474)(20,1473)(21,1472)(22,1471)(23,1470)(24,1469)(25,1468)(26,1467)(27,1466)(28,1465)(29,1464)(30,1463)(31,1462)(32,1461)(33,1460)(34,1459)(35,1458)(36,1457)(37,1456)(38,1455)(39,1454)(40,1453)(41,1452)(42,1451)(43,1450)(44,1449)(45,1448)(46,1447)(47,1446)(48,1445)(49,1444)(50,1443)(51,1442)(52,1441)(53,1440)(54,1439)(55,1438)(56,1437)(57,1436)(58,1435)(59,1434)(60,1433)(61,1432)(62,1431)(63,1430)(64,1429)(65,1428)(66,1427)(67,1426)(68,1425)(69,1424)(70,1423)(71,1422)(72,1421)(73,1420)(74,1419)(75,1418)(76,1417)(77,1416)(78,1415)(79,1414)(80,1413)(81,1412)(82,1411)(83,1410)(84,1409)(85,1408)(86,1407)(87,1406)(88,1405)(89,1404)(90,1403)(91,1402)(92,1401)(93,1400)(94,1399)(95,1398)(96,1397)(97,1396)(98,1395)(99,1394)(100,1393)(101,1392)(102,1391)(103,1390)(104,1389)(105,1388)(106,1387)(107,1386)(108,1385)(109,1384)(110,1383)(111,1382)(112,1381)(113,1380)(114,1379)(115,1378)(116,1377)(117,1376)(118,1375)(119,1374)(120,1373)(121,1372)(122,1371)(123,1370)(124,1369)(125,1368)(126,1367)(127,1366)(128,1365)(129,1364)(130,1363)(131,1362)(132,1361)(133,1360)(134,1359)(135,1358)(136,1357)(137,1356)(138,1355)(139,1354)(140,1353)(141,1352)(142,1351)(143,1350)(144,1349)(145,1348)(146,1347)(147,1346)(148,1345)(149,1344)(150,1343)(151,1342)(152,1341)(153,1340)(154,1339)(155,1338)(156,1337)(157,1336)(158,1335)(159,1334)(160,1333)(161,1332)(162,1331)(163,1330)(164,1329)(165,1328)(166,1327)(167,1326)(168,1325)(169,1324)(170,1323)(171,1322)(172,1321)(173,1320)(174,1319)(175,1318)(176,1317)(177,1316)(178,1315)(179,1314)(180,1313)(181,1312)(182,1311)(183,1310)(184,1309)(185,1308)(186,1307)(187,1306)(188,1305)(189,1304)(190,1303)(191,1302)(192,1301)(193,1300)(194,1299)(195,1298)(196,1297)(197,1296)(198,1295)(199,1294)(200,1293)(201,1292)(202,1291)(203,1290)(204,1289)(205,1288)(206,1287)(207,1286)(208,1285)(209,1284)(210,1283)(211,1282)(212,1281)(213,1280)(214,1279)(215,1278)(216,1277)(217,1276)(218,1275)(219,1274)(220,1273)(221,1272)(222,1271)(223,1270)(224,1269)(225,1268)(226,1267)(227,1266)(228,1265)(229,1264)(230,1263)(231,1262)(232,1261)(233,1260)(234,1259)(235,1258)(236,1257)(237,1256)(238,1255)(239,1254)(240,1253)(241,1252)(242,1251)(243,1250)(244,1249)(245,1248)(246,1247)(247,1246)(248,1245)(249,1244)(250,1243)(251,1242)(252,1241)(253,1240)(254,1239)(255,1238)(256,1237)(257,1236)(258,1235)(259,1234)(260,1233)(261,1232)(262,1231)(263,1230)(264,1229)(265,1228)(266,1227)(267,1226)(268,1225)(269,1224)(270,1223)(271,1222)(272,1221)(273,1220)(274,1219)(275,1218)(276,1217)(277,1216)(278,1215)(279,1214)(280,1213)(281,1212)(282,1211)(283,1210)(284,1209)(285,1208)(286,1207)(287,1206)(288,1205)(289,1204)(290,1203)(291,1202)(292,1201)(293,1200)(294,1199)(295,1198)(296,1197)(297,1196)(298,1195)(299,1194)(300,1193)(301,1192)(302,1191)(303,1190)(304,1189)(305,1188)(306,1187)(307,1186)(308,1185)(309,1184)(310,1183)(311,1182)(312,1181)(313,1180)(314,1179)(315,1178)(316,1177)(317,1176)(318,1175)(319,1174)(320,1173)(321,1172)(322,1171)(323,1170)(324,1169)(325,1168)(326,1167)(327,1166)(328,1165)(329,1164)(330,1163)(331,1162)(332,1161)(333,1160)(334,1159)(335,1158)(336,1157)(337,1156)(338,1155)(339,1154)(340,1153)(341,1152)(342,1151)(343,1150)(344,1149)(345,1148)(346,1147)(347,1146)(348,1145)(349,1144)(350,1143)(351,1142)(352,1141)(353,1140)(354,1139)(355,1138)(356,1137)(357,1136)(358,1135)(359,1134)(360,1133)(361,1132)(362,1131)(363,1130)(364,1129)(365,1128)(366,1127)(367,1126)(368,1125)(369,1124)(370,1123)(371,1122)(372,1121)(373,1120)(374,1119)(375,1118)(376,1117)(377,1116)(378,1115)(379,1114)(380,1113)(381,1112)(382,1111)(383,1110)(384,1109)(385,1108)(386,1107)(387,1106)(388,1105)(389,1104)(390,1103)(391,1102)(392,1101)(393,1100)(394,1099)(395,1098)(396,1097)(397,1096)(398,1095)(399,1094)(400,1093)(401,1092)(402,1091)(403,1090)(404,1089)(405,1088)(406,1087)(407,1086)(408,1085)(409,1084)(410,1083)(411,1082)(412,1081)(413,1080)(414,1079)(415,1078)(416,1077)(417,1076)(418,1075)(419,1074)(420,1073)(421,1072)(422,1071)(423,1070)(424,1069)(425,1068)(426,1067)(427,1066)(428,1065)(429,1064)(430,1063)(431,1062)(432,1061)(433,1060)(434,1059)(435,1058)(436,1057)(437,1056)(438,1055)(439,1054)(440,1053)(441,1052)(442,1051)(443,1050)(444,1049)(445,1048)(446,1047)(447,1046)(448,1045)(449,1044)(450,1043)(451,1042)(452,1041)(453,1040)(454,1039)(455,1038)(456,1037)(457,1036)(458,1035)(459,1034)(460,1033)(461,1032)(462,1031)(463,1030)(464,1029)(465,1028)(466,1027)(467,1026)(468,1025)(469,1024)(470,1023)(471,1022)(472,1021)(473,1020)(474,1019)(475,1018)(476,1017)(477,1016)(478,1015)(479,1014)(480,1013)(481,1012)(482,1011)(483,1010)(484,1009)(485,1008)(486,1007)(487,1006)(488,1005)(489,1004)(490,1003)(491,1002)(492,1001)(493,1000)(494,999)(495,998)(496,997)(497,996)(498,995)(499,994)(500,993)(501,992)(502,991)(503,990)(504,989)(505,988)(506,987)(507,986)(508,985)(509,984)(510,983)(511,982)(512,981)(513,980)(514,979)(515,978)(516,977)(517,976)(518,975)(519,974)(520,973)(521,972)(522,971)(523,970)(524,969)(525,968)(526,967)(527,966)(528,965)(529,964)(530,963)(531,962)(532,961)(533,960)(534,959)(535,958)(536,957)(537,956)(538,955)(539,954)(540,953)(541,952)(542,951)(543,950)(544,949)(545,948)(546,947)(547,946)(548,945)(549,944)(550,943)(551,942)(552,941)(553,940)(554,939)(555,938)(556,937)(557,936)(558,935)(559,934)(560,933)(561,932)(562,931)(563,930)(564,929)(565,928)(566,927)(567,926)(568,925)(569,924)(570,923)(571,922)(572,921)(573,920)(574,919)(575,918)(576,917)(577,916)(578,915)(579,914)(580,913)(581,912)(582,911)(583,910)(584,909)(585,908)(586,907)(587,906)(588,905)(589,904)(590,903)(591,902)(592,901)(593,900)(594,899)(595,898)(596,897)(597,896)(598,895)(599,894)(600,893)(601,892)(602,891)(603,890)(604,889)(605,888)(606,887)(607,886)(608,885)(609,884)(610,883)(611,882)(612,881)(613,880)(614,879)(615,878)(616,877)(617,876)(618,875)(619,874)(620,873)(621,872)(622,871)(623,870)(624,869)(625,868)(626,867)(627,866)(628,865)(629,864)(630,863)(631,862)(632,861)(633,860)(634,859)(635,858)(636,857)(637,856)(638,855)(639,854)(640,853)(641,852)(642,851)(643,850)(644,849)(645,848)(646,847)(647,846)(648,845)(649,844)(650,843)(651,842)(652,841)(653,840)(654,839)(655,838)(656,837)(657,836)(658,835)(659,834)(660,833)(661,832)(662,831)(663,830)(664,829)(665,828)(666,827)(667,826)(668,825)(669,824)(670,823)(671,822)(672,821)(673,820)(674,819)(675,818)(676,817)(677,816)(678,815)(679,814)(680,813)(681,812)(682,811)(683,810)(684,809)(685,808)(686,807)(687,806)(688,805)(689,804)(690,803)(691,802)(692,801)(693,800)(694,799)(695,798)(696,797)(697,796)(698,795)(699,794)(700,793)(701,792)(702,791)(703,790)(704,789)(705,788)(706,787)(707,786)(708,785)(709,784)(710,783)(711,782)(712,781)(713,780)(714,779)(715,778)(716,777)(717,776)(718,775)(719,774)(720,773)(721,772)(722,771)(723,770)(724,769)(725,768)(726,767)(727,766)(728,765)(729,764)(730,763)(731,762)(732,761)(733,760)(734,759)(735,758)(736,757)(737,756)(738,755)(739,754)(740,753)(741,752)(742,751)(743,750)(744,749)(745,748)(746,747)
Polycyclic presentation:
2^3,1483|b^a=bc,d^a=d^1482,d^b=d^1482
Conjugacy classes & character table
2969 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11864, 10);
Finite Group Databasebeta