Finite Group Databasebeta

?

← Prev (#27190057) Next (#27190059) →

#27190058

• metacyclic
• supersolvable
• metabelian
• solvable
• monolithic
• monomial
• stem
• Frobenius

Aliases

No aliases for this group.

Splittings

Subgroups

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1459 points:

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

Polycyclic presentation:

3^2,1459|a^3=b,c^a=c^1187,c^b=c^339

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13131, 3);