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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1330 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)(593,653,714)(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)(652,654,655)(657,717,775)(660,720,773)(663,723,770)(666,726,767)(669,729,764)(672,732,761)(675,735,758)(678,738,755)(681,741,752)(684,744,749)(687,747,746)(690,750,743)(693,753,740)(696,756,737)(699,759,734)(702,762,731)(705,765,728)(708,768,725)(711,771,722)(713,718,719)(715,776,716)(721,777,832)(724,780,830)(727,783,827)(730,786,824)(733,789,821)(736,792,818)(739,795,815)(742,798,812)(745,801,809)(748,804,806)(751,807,803)(754,810,800)(757,813,797)(760,816,794)(763,819,791)(766,822,788)(769,825,785)(772,828,782)(774,778,779)(781,833,885)(784,836,883)(787,839,880)(790,842,877)(793,845,874)(796,848,871)(799,851,868)(802,854,865)(805,857,862)(808,860,859)(811,863,856)(814,866,853)(817,869,850)(820,872,847)(823,875,844)(826,878,841)(829,881,838)(831,834,835)(837,886,935)(840,889,933)(843,892,930)(846,895,927)(849,898,924)(852,901,921)(855,904,918)(858,907,915)(861,910,912)(864,913,909)(867,916,906)(870,919,903)(873,922,900)(876,925,897)(879,928,894)(882,931,891)(884,887,888)(890,936,982)(893,939,980)(896,942,977)(899,945,974)(902,948,971)(905,951,968)(908,954,965)(911,957,962)(914,960,959)(917,963,956)(920,966,953)(923,969,950)(926,972,947)(929,975,944)(932,978,941)(934,937,938)(940,983,1026)(943,986,1024)(946,989,1021)(949,992,1018)(952,995,1015)(955,998,1012)(958,1001,1009)(961,1004,1006)(964,1007,1003)(967,1010,1000)(970,1013,997)(973,1016,994)(976,1019,991)(979,1022,988)(981,984,985)(987,1027,1067)(990,1030,1065)(993,1033,1062)(996,1036,1059)(999,1039,1056)(1002,1042,1053)(1005,1045,1050)(1008,1048,1047)(1011,1051,1044)(1014,1054,1041)(1017,1057,1038)(1020,1060,1035)(1023,1063,1032)(1025,1028,1029)(1031,1068,1105)(1034,1071,1103)(1037,1074,1100)(1040,1077,1097)(1043,1080,1094)(1046,1083,1091)(1049,1086,1088)(1052,1089,1085)(1055,1092,1082)(1058,1095,1079)(1061,1098,1076)(1064,1101,1073)(1066,1069,1070)(1072,1106,1140)(1075,1109,1138)(1078,1112,1135)(1081,1115,1132)(1084,1118,1129)(1087,1121,1126)(1090,1124,1123)(1093,1127,1120)(1096,1130,1117)(1099,1133,1114)(1102,1136,1111)(1104,1107,1108)(1110,1141,1172)(1113,1144,1170)(1116,1147,1167)(1119,1150,1164)(1122,1153,1161)(1125,1156,1158)(1128,1159,1155)(1131,1162,1152)(1134,1165,1149)(1137,1168,1146)(1139,1142,1143)(1145,1173,1201)(1148,1176,1199)(1151,1179,1196)(1154,1182,1193)(1157,1185,1190)(1160,1188,1187)(1163,1191,1184)(1166,1194,1181)(1169,1197,1178)(1171,1174,1175)(1177,1202,1227)(1180,1205,1225)(1183,1208,1222)(1186,1211,1219)(1189,1214,1216)(1192,1217,1213)(1195,1220,1210)(1198,1223,1207)(1200,1203,1204)(1206,1228,1250)(1209,1231,1248)(1212,1234,1245)(1215,1237,1242)(1218,1240,1239)(1221,1243,1236)(1224,1246,1233)(1226,1229,1230)(1232,1251,1270)(1235,1254,1268)(1238,1257,1265)(1241,1260,1262)(1244,1263,1259)(1247,1266,1256)(1249,1252,1253)(1255,1271,1287)(1258,1274,1285)(1261,1277,1282)(1264,1280,1279)(1267,1283,1276)(1269,1272,1273)(1275,1288,1301)(1278,1291,1299)(1281,1294,1296)(1284,1297,1293)(1286,1289,1290)(1292,1302,1312)(1295,1305,1310)(1298,1308,1307)(1300,1303,1304)(1306,1313,1320)(1309,1316,1318)(1311,1314,1315)(1317,1321,1325)(1319,1322,1323)(1324,1326,1327)(1329,1330);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,590,648,709,770,827,880,930,977,1021,1062,1100,1135,1167,1196,1222,1245,1265,1282,1296,1307,1315,1302,1274,1234,1182,1118,1042,954,854,741,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,727,784,837,887,828,707,585,475,376,422,471,523,578,636,697,758,815,868,918,965,1009,1050,1088,1123,1155,1184,1210,1233,1253,1228,1176,1112,1036,948,848,735,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,739,796,849,899,946,990,1031,1069,1022,928,822,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,746,803,856,906,953,997,1038,1076,1111,1143,1106,1030,942,842,729,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,751,808,861,911,958,1002,1043,1081,1116,1148,1177,1203,1168,1098,1016,922,816,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,734,791,844,894,941,985,936,836,723,598,482,378,426,476,528,583,641,702,763,820,873,923,970,1014,1055,1093,1128,1160,1189,1215,1238,1258,1275,1289,1266,1220,1162,1092,1010,916,810,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,722,779,717,592,652,713,774,831,884,934,981,1025,1066,1104,1139,1171,1200,1226,1249,1269,1286,1300,1311,1319,1324,1326,1316,1294,1260,1214,1156,1086,1004,910,804,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,718,649,532,587,645,706,767,824,877,927,974,1018,1059,1097,1132,1164,1193,1219,1242,1262,1279,1293,1304,1288,1254,1208,1150,1080,998,904,798,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,730,787,840,890,937,881,768,643,527,423,330,373,419,468,520,575,633,694,755,812,865,915,962,1006,1047,1085,1120,1152,1181,1207,1230,1202,1144,1074,992,898,792,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,742,799,852,902,949,993,1034,1072,1107,1063,975,875,762,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,743,800,853,903,950,994,1035,1073,1108,1068,986,892,786,665,543,433,335,249,288,329,372,418,467,519,574,632,693,754,811,864,914,961,1005,1046,1084,1119,1151,1180,1206,1229,1197,1133,1057,969,869,756,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,731,788,841,891,938,886,780,659,537,427,478,531,586,644,705,766,823,876,926,973,1017,1058,1096,1131,1163,1192,1218,1241,1261,1278,1292,1303,1283,1243,1191,1127,1051,963,863,750,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,719,653,715,714,775,832,885,935,982,1026,1067,1105,1140,1172,1201,1227,1250,1270,1287,1301,1312,1320,1325,1327,1321,1305,1277,1237,1185,1121,1045,957,857,744,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,721,778,710,588,477,529,584,642,703,764,821,874,924,971,1015,1056,1094,1129,1161,1190,1216,1239,1259,1276,1290,1271,1231,1179,1115,1039,951,851,738,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,733,790,843,893,940,984,931,825,704,582,472,374,287,327,370,416,465,517,572,630,691,752,809,862,912,959,1003,1044,1082,1117,1149,1178,1204,1173,1109,1033,945,845,732,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,745,802,855,905,952,996,1037,1075,1110,1142,1101,1019,925,819,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,740,797,850,900,947,991,1032,1070,1027,939,839,726,601,485,381,289,331,375,421,470,522,577,635,696,757,814,867,917,964,1008,1049,1087,1122,1154,1183,1209,1232,1252,1223,1165,1095,1013,919,813,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,728,785,838,888,833,720,595,479,533,589,647,708,769,826,879,929,976,1020,1061,1099,1134,1166,1195,1221,1244,1264,1281,1295,1306,1314,1297,1263,1217,1159,1089,1007,913,807,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,716,776,651,712,773,830,883,933,980,1024,1065,1103,1138,1170,1199,1225,1248,1268,1285,1299,1310,1318,1323,1313,1291,1257,1211,1153,1083,1001,907,801,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,724,781,834,771,646,530,425,474,526,581,639,700,761,818,871,921,968,1012,1053,1091,1126,1158,1187,1213,1236,1256,1273,1251,1205,1147,1077,995,901,795,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,736,793,846,896,943,987,1028,978,878,765,640,524,420,328,247,284,324,367,413,462,514,569,627,688,749,806,859,909,956,1000,1041,1079,1114,1146,1175,1141,1071,989,895,789,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,748,805,858,908,955,999,1040,1078,1113,1145,1174,1136,1060,972,872,759,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,737,794,847,897,944,988,1029,983,889,783,662,540,430,332,377,424,473,525,580,638,699,760,817,870,920,967,1011,1052,1090,1125,1157,1186,1212,1235,1255,1272,1246,1194,1130,1054,966,866,753,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,725,782,835,777,656,534,591,650,711,772,829,882,932,979,1023,1064,1102,1137,1169,1198,1224,1247,1267,1284,1298,1309,1317,1322,1308,1280,1240,1188,1124,1048,960,860,747,622,506,402,310,230,162,106,62,30,10)(1328,1329,1330)
Conjugacy classes & character table
1335 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23886, 10);
Finite Group Databasebeta