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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1402 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,781)(657,720,778)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,718,722)(716,779,719)(721,784,844)(724,787,842)(727,790,840)(730,793,837)(733,796,834)(736,799,831)(739,802,828)(742,805,825)(745,808,822)(748,811,819)(751,814,816)(754,817,813)(757,820,810)(760,823,807)(763,826,804)(766,829,801)(769,832,798)(772,835,795)(775,838,792)(777,785,789)(780,843,786)(782,845,783)(788,848,903)(791,850,902)(794,853,900)(797,856,897)(800,859,894)(803,862,891)(806,865,888)(809,868,885)(812,871,882)(815,874,879)(818,877,876)(821,880,873)(824,883,870)(827,886,867)(830,889,864)(833,892,861)(836,895,858)(839,898,855)(841,849,852)(846,904,847)(851,905,957)(854,907,956)(857,910,954)(860,913,951)(863,916,948)(866,919,945)(869,922,942)(872,925,939)(875,928,936)(878,931,933)(881,934,930)(884,937,927)(887,940,924)(890,943,921)(893,946,918)(896,949,915)(899,952,912)(901,906,909)(908,958,1007)(911,960,1006)(914,963,1004)(917,966,1001)(920,969,998)(923,972,995)(926,975,992)(929,978,989)(932,981,986)(935,984,983)(938,987,980)(941,990,977)(944,993,974)(947,996,971)(950,999,968)(953,1002,965)(955,959,962)(961,1008,1054)(964,1010,1053)(967,1013,1051)(970,1016,1048)(973,1019,1045)(976,1022,1042)(979,1025,1039)(982,1028,1036)(985,1031,1033)(988,1034,1030)(991,1037,1027)(994,1040,1024)(997,1043,1021)(1000,1046,1018)(1003,1049,1015)(1005,1009,1012)(1011,1055,1098)(1014,1057,1097)(1017,1060,1095)(1020,1063,1092)(1023,1066,1089)(1026,1069,1086)(1029,1072,1083)(1032,1075,1080)(1035,1078,1077)(1038,1081,1074)(1041,1084,1071)(1044,1087,1068)(1047,1090,1065)(1050,1093,1062)(1052,1056,1059)(1058,1099,1139)(1061,1101,1138)(1064,1104,1136)(1067,1107,1133)(1070,1110,1130)(1073,1113,1127)(1076,1116,1124)(1079,1119,1121)(1082,1122,1118)(1085,1125,1115)(1088,1128,1112)(1091,1131,1109)(1094,1134,1106)(1096,1100,1103)(1102,1140,1177)(1105,1142,1176)(1108,1145,1174)(1111,1148,1171)(1114,1151,1168)(1117,1154,1165)(1120,1157,1162)(1123,1160,1159)(1126,1163,1156)(1129,1166,1153)(1132,1169,1150)(1135,1172,1147)(1137,1141,1144)(1143,1178,1212)(1146,1180,1211)(1149,1183,1209)(1152,1186,1206)(1155,1189,1203)(1158,1192,1200)(1161,1195,1197)(1164,1198,1194)(1167,1201,1191)(1170,1204,1188)(1173,1207,1185)(1175,1179,1182)(1181,1213,1244)(1184,1215,1243)(1187,1218,1241)(1190,1221,1238)(1193,1224,1235)(1196,1227,1232)(1199,1230,1229)(1202,1233,1226)(1205,1236,1223)(1208,1239,1220)(1210,1214,1217)(1216,1245,1273)(1219,1247,1272)(1222,1250,1270)(1225,1253,1267)(1228,1256,1264)(1231,1259,1261)(1234,1262,1258)(1237,1265,1255)(1240,1268,1252)(1242,1246,1249)(1248,1274,1299)(1251,1276,1298)(1254,1279,1296)(1257,1282,1293)(1260,1285,1290)(1263,1288,1287)(1266,1291,1284)(1269,1294,1281)(1271,1275,1278)(1277,1300,1322)(1280,1302,1321)(1283,1305,1319)(1286,1308,1316)(1289,1311,1313)(1292,1314,1310)(1295,1317,1307)(1297,1301,1304)(1303,1323,1342)(1306,1325,1341)(1309,1328,1339)(1312,1331,1336)(1315,1334,1333)(1318,1337,1330)(1320,1324,1327)(1326,1343,1359)(1329,1345,1358)(1332,1348,1356)(1335,1351,1353)(1338,1354,1350)(1340,1344,1347)(1346,1360,1373)(1349,1362,1372)(1352,1365,1370)(1355,1368,1367)(1357,1361,1364)(1363,1374,1384)(1366,1376,1383)(1369,1379,1381)(1371,1375,1378)(1377,1385,1392)(1380,1387,1391)(1382,1386,1389)(1388,1393,1397)(1390,1394,1396)(1395,1398,1399)(1401,1402);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,718,649,532,587,645,706,770,834,894,948,998,1045,1089,1130,1168,1203,1235,1264,1290,1313,1333,1350,1364,1343,1302,1250,1186,1110,1022,922,805,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,803,863,917,967,1014,1058,1100,1049,949,832,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,749,813,873,927,977,1024,1068,1109,1147,1182,1140,1057,963,856,729,601,485,381,289,331,375,421,470,522,577,635,696,760,824,884,938,988,1035,1079,1120,1158,1193,1225,1254,1280,1303,1324,1294,1236,1166,1084,990,883,756,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,792,852,784,653,716,780,781,844,903,957,1007,1054,1098,1139,1177,1212,1244,1273,1299,1322,1342,1359,1373,1384,1392,1397,1399,1393,1376,1348,1308,1256,1192,1116,1028,928,811,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,791,851,906,838,707,585,475,376,422,471,523,578,636,697,761,825,885,939,989,1036,1080,1121,1159,1194,1226,1255,1281,1304,1274,1215,1145,1063,969,862,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,812,872,926,976,1023,1067,1108,1146,1181,1214,1172,1090,996,889,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,804,864,918,968,1015,1059,1008,907,790,659,537,427,478,531,586,644,705,769,833,893,947,997,1044,1088,1129,1167,1202,1234,1263,1289,1312,1332,1349,1363,1375,1354,1314,1262,1198,1122,1034,934,817,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,719,783,843,713,590,648,709,773,837,897,951,1001,1048,1092,1133,1171,1206,1238,1267,1293,1316,1336,1353,1367,1378,1360,1325,1279,1221,1151,1069,975,868,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,800,860,914,964,1011,1056,1002,895,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,816,876,930,980,1027,1071,1112,1150,1185,1217,1178,1101,1013,913,796,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,821,881,935,985,1032,1076,1117,1155,1190,1222,1251,1277,1301,1268,1204,1128,1040,940,823,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,795,855,909,848,720,592,652,714,777,841,901,955,1005,1052,1096,1137,1175,1210,1242,1271,1297,1320,1340,1357,1371,1382,1390,1395,1398,1387,1365,1331,1285,1227,1157,1075,981,874,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,788,849,774,646,530,425,474,526,581,639,700,764,828,888,942,992,1039,1083,1124,1162,1197,1229,1258,1284,1307,1327,1300,1247,1183,1107,1019,919,802,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,809,869,923,973,1020,1064,1105,1143,1179,1134,1046,946,829,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,807,867,921,971,1018,1062,1103,1055,960,853,726,598,482,378,426,476,528,583,641,702,766,830,890,944,994,1041,1085,1126,1164,1199,1231,1260,1286,1309,1329,1346,1361,1337,1291,1233,1163,1081,987,880,753,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,786,847,904,779,651,712,776,840,900,954,1004,1051,1095,1136,1174,1209,1241,1270,1296,1319,1339,1356,1370,1381,1389,1374,1345,1305,1253,1189,1113,1025,925,808,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,797,857,911,961,1009,952,835,704,582,472,374,287,327,370,416,465,517,572,630,691,755,819,879,933,983,1030,1074,1115,1153,1188,1220,1249,1213,1142,1060,966,859,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,818,878,932,982,1029,1073,1114,1152,1187,1219,1248,1275,1239,1169,1087,993,886,759,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,798,858,912,962,905,787,656,534,591,650,711,775,839,899,953,1003,1050,1094,1135,1173,1208,1240,1269,1295,1318,1338,1355,1369,1380,1388,1394,1379,1351,1311,1259,1195,1119,1031,931,814,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,785,710,588,477,529,584,642,703,767,831,891,945,995,1042,1086,1127,1165,1200,1232,1261,1287,1310,1330,1347,1323,1276,1218,1148,1066,972,865,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,806,866,920,970,1017,1061,1102,1141,1093,999,892,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,810,870,924,974,1021,1065,1106,1144,1099,1010,910,793,662,540,430,332,377,424,473,525,580,638,699,763,827,887,941,991,1038,1082,1123,1161,1196,1228,1257,1283,1306,1326,1344,1317,1265,1201,1125,1037,937,820,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,789,717,782,846,845,715,778,842,902,956,1006,1053,1097,1138,1176,1211,1243,1272,1298,1321,1341,1358,1372,1383,1391,1396,1385,1362,1328,1282,1224,1154,1072,978,871,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,794,854,908,959,898,771,643,527,423,330,373,419,468,520,575,633,694,758,822,882,936,986,1033,1077,1118,1156,1191,1223,1252,1278,1245,1180,1104,1016,916,799,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,815,875,929,979,1026,1070,1111,1149,1184,1216,1246,1207,1131,1043,943,826,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,801,861,915,965,1012,958,850,723,595,479,533,589,647,708,772,836,896,950,1000,1047,1091,1132,1170,1205,1237,1266,1292,1315,1335,1352,1366,1377,1386,1368,1334,1288,1230,1160,1078,984,877,750,622,506,402,310,230,162,106,62,30,10)(1400,1401,1402)
Conjugacy classes & character table
1407 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25182, 10);
Finite Group Databasebeta