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D2153 #16864418
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 2153 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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609)(547,1608)(548,1607)(549,1606)(550,1605)(551,1604)(552,1603)(553,1602)(554,1601)(555,1600)(556,1599)(557,1598)(558,1597)(559,1596)(560,1595)(561,1594)(562,1593)(563,1592)(564,1591)(565,1590)(566,1589)(567,1588)(568,1587)(569,1586)(570,1585)(571,1584)(572,1583)(573,1582)(574,1581)(575,1580)(576,1579)(577,1578)(578,1577)(579,1576)(580,1575)(581,1574)(582,1573)(583,1572)(584,1571)(585,1570)(586,1569)(587,1568)(588,1567)(589,1566)(590,1565)(591,1564)(592,1563)(593,1562)(594,1561)(595,1560)(596,1559)(597,1558)(598,1557)(599,1556)(600,1555)(601,1554)(602,1553)(603,1552)(604,1551)(605,1550)(606,1549)(607,1548)(608,1547)(609,1546)(610,1545)(611,1544)(612,1543)(613,1542)(614,1541)(615,1540)(616,1539)(617,1538)(618,1537)(619,1536)(620,1535)(621,1534)(622,1533)(623,1532)(624,1531)(625,1530)(626,1529)(627,1528)(628,1527)(629,1526)(630,1525)(631,1524)(632,1523)(633,1522)(634,1521)(635,1520)(636,1519)(637,1518)(638,1517)(639,1516)(640,1515)(641,1514)(642,1513)(643,1512)(644,1511)(645,1510)(646,1509)(647,1508)(648,1507)(649,1506)(650,1505)(651,1504)(652,1503)(653,1502)(654,1501)(655,1500)(656,1499)(657,1498)(658,1497)(659,1496)(660,1495)(661,1494)(662,1493)(663,1492)(664,1491)(665,1490)(666,1489)(667,1488)(668,1487)(669,1486)(670,1485)(671,1484)(672,1483)(673,1482)(674,1481)(675,1480)(676,1479)(677,1478)(678,1477)(679,1476)(680,1475)(681,1474)(682,1473)(683,1472)(684,1471)(685,1470)(686,1469)(687,1468)(688,1467)(689,1466)(690,1465)(691,1464)(692,1463)(693,1462)(694,1461)(695,1460)(696,1459)(697,1458)(698,1457)(699,1456)(700,1455)(701,1454)(702,1453)(703,1452)(704,1451)(705,1450)(706,1449)(707,1448)(708,1447)(709,1446)(710,1445)(711,1444)(712,1443)(713,1442)(714,1441)(715,1440)(716,1439)(717,1438)(718,1437)(719,1436)(720,1435)(721,1434)(722,1433)(723,1432)(724,1431)(725,1430)(726,1429)(727,1428)(728,1427)(729,1426)(730,1425)(731,1424)(732,1423)(733,1422)(734,1421)(735,1420)(736,1419)(737,1418)(738,1417)(739,1416)(740,1415)(741,1414)(742,1413)(743,1412)(744,1411)(745,1410)(746,1409)(747,1408)(748,1407)(749,1406)(750,1405)(751,1404)(752,1403)(753,1402)(754,1401)(755,1400)(756,1399)(757,1398)(758,1397)(759,1396)(760,1395)(761,1394)(762,1393)(763,1392)(764,1391)(765,1390)(766,1389)(767,1388)(768,1387)(769,1386)(770,1385)(771,1384)(772,1383)(773,1382)(774,1381)(775,1380)(776,1379)(777,1378)(778,1377)(779,1376)(780,1375)(781,1374)(782,1373)(783,1372)(784,1371)(785,1370)(786,1369)(787,1368)(788,1367)(789,1366)(790,1365)(791,1364)(792,1363)(793,1362)(794,1361)(795,1360)(796,1359)(797,1358)(798,1357)(799,1356)(800,1355)(801,1354)(802,1353)(803,1352)(804,1351)(805,1350)(806,1349)(807,1348)(808,1347)(809,1346)(810,1345)(811,1344)(812,1343)(813,1342)(814,1341)(815,1340)(816,1339)(817,1338)(818,1337)(819,1336)(820,1335)(821,1334)(822,1333)(823,1332)(824,1331)(825,1330)(826,1329)(827,1328)(828,1327)(829,1326)(830,1325)(831,1324)(832,1323)(833,1322)(834,1321)(835,1320)(836,1319)(837,1318)(838,1317)(839,1316)(840,1315)(841,1314)(842,1313)(843,1312)(844,1311)(845,1310)(846,1309)(847,1308)(848,1307)(849,1306)(850,1305)(851,1304)(852,1303)(853,1302)(854,1301)(855,1300)(856,1299)(857,1298)(858,1297)(859,1296)(860,1295)(861,1294)(862,1293)(863,1292)(864,1291)(865,1290)(866,1289)(867,1288)(868,1287)(869,1286)(870,1285)(871,1284)(872,1283)(873,1282)(874,1281)(875,1280)(876,1279)(877,1278)(878,1277)(879,1276)(880,1275)(881,1274)(882,1273)(883,1272)(884,1271)(885,1270)(886,1269)(887,1268)(888,1267)(889,1266)(890,1265)(891,1264)(892,1263)(893,1262)(894,1261)(895,1260)(896,1259)(897,1258)(898,1257)(899,1256)(900,1255)(901,1254)(902,1253)(903,1252)(904,1251)(905,1250)(906,1249)(907,1248)(908,1247)(909,1246)(910,1245)(911,1244)(912,1243)(913,1242)(914,1241)(915,1240)(916,1239)(917,1238)(918,1237)(919,1236)(920,1235)(921,1234)(922,1233)(923,1232)(924,1231)(925,1230)(926,1229)(927,1228)(928,1227)(929,1226)(930,1225)(931,1224)(932,1223)(933,1222)(934,1221)(935,1220)(936,1219)(937,1218)(938,1217)(939,1216)(940,1215)(941,1214)(942,1213)(943,1212)(944,1211)(945,1210)(946,1209)(947,1208)(948,1207)(949,1206)(950,1205)(951,1204)(952,1203)(953,1202)(954,1201)(955,1200)(956,1199)(957,1198)(958,1197)(959,1196)(960,1195)(961,1194)(962,1193)(963,1192)(964,1191)(965,1190)(966,1189)(967,1188)(968,1187)(969,1186)(970,1185)(971,1184)(972,1183)(973,1182)(974,1181)(975,1180)(976,1179)(977,1178)(978,1177)(979,1176)(980,1175)(981,1174)(982,1173)(983,1172)(984,1171)(985,1170)(986,1169)(987,1168)(988,1167)(989,1166)(990,1165)(991,1164)(992,1163)(993,1162)(994,1161)(995,1160)(996,1159)(997,1158)(998,1157)(999,1156)(1000,1155)(1001,1154)(1002,1153)(1003,1152)(1004,1151)(1005,1150)(1006,1149)(1007,1148)(1008,1147)(1009,1146)(1010,1145)(1011,1144)(1012,1143)(1013,1142)(1014,1141)(1015,1140)(1016,1139)(1017,1138)(1018,1137)(1019,1136)(1020,1135)(1021,1134)(1022,1133)(1023,1132)(1024,1131)(1025,1130)(1026,1129)(1027,1128)(1028,1127)(1029,1126)(1030,1125)(1031,1124)(1032,1123)(1033,1122)(1034,1121)(1035,1120)(1036,1119)(1037,1118)(1038,1117)(1039,1116)(1040,1115)(1041,1114)(1042,1113)(1043,1112)(1044,1111)(1045,1110)(1046,1109)(1047,1108)(1048,1107)(1049,1106)(1050,1105)(1051,1104)(1052,1103)(1053,1102)(1054,1101)(1055,1100)(1056,1099)(1057,1098)(1058,1097)(1059,1096)(1060,1095)(1061,1094)(1062,1093)(1063,1092)(1064,1091)(1065,1090)(1066,1089)(1067,1088)(1068,1087)(1069,1086)(1070,1085)(1071,1084)(1072,1083)(1073,1082)(1074,1081)(1075,1080)(1076,1079)(1077,1078)
Polycyclic presentation:
2,2153|b^a=b^2152
Conjugacy classes & character table
1078 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4306, 1);
Finite Group Databasebeta