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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1332 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);(4,5)(7,1332)(8,1331)(9,1330)(10,1329)(11,1328)(12,1327)(13,1326)(14,1325)(15,1324)(16,1323)(17,1322)(18,1321)(19,1320)(20,1319)(21,1318)(22,1317)(23,1316)(24,1315)(25,1314)(26,1313)(27,1312)(28,1311)(29,1310)(30,1309)(31,1308)(32,1307)(33,1306)(34,1305)(35,1304)(36,1303)(37,1302)(38,1301)(39,1300)(40,1299)(41,1298)(42,1297)(43,1296)(44,1295)(45,1294)(46,1293)(47,1292)(48,1291)(49,1290)(50,1289)(51,1288)(52,1287)(53,1286)(54,1285)(55,1284)(56,1283)(57,1282)(58,1281)(59,1280)(60,1279)(61,1278)(62,1277)(63,1276)(64,1275)(65,1274)(66,1273)(67,1272)(68,1271)(69,1270)(70,1269)(71,1268)(72,1267)(73,1266)(74,1265)(75,1264)(76,1263)(77,1262)(78,1261)(79,1260)(80,1259)(81,1258)(82,1257)(83,1256)(84,1255)(85,1254)(86,1253)(87,1252)(88,1251)(89,1250)(90,1249)(91,1248)(92,1247)(93,1246)(94,1245)(95,1244)(96,1243)(97,1242)(98,1241)(99,1240)(100,1239)(101,1238)(102,1237)(103,1236)(104,1235)(105,1234)(106,1233)(107,1232)(108,1231)(109,1230)(110,1229)(111,1228)(112,1227)(113,1226)(114,1225)(115,1224)(116,1223)(117,1222)(118,1221)(119,1220)(120,1219)(121,1218)(122,1217)(123,1216)(124,1215)(125,1214)(126,1213)(127,1212)(128,1211)(129,1210)(130,1209)(131,1208)(132,1207)(133,1206)(134,1205)(135,1204)(136,1203)(137,1202)(138,1201)(139,1200)(140,1199)(141,1198)(142,1197)(143,1196)(144,1195)(145,1194)(146,1193)(147,1192)(148,1191)(149,1190)(150,1189)(151,1188)(152,1187)(153,1186)(154,1185)(155,1184)(156,1183)(157,1182)(158,1181)(159,1180)(160,1179)(161,1178)(162,1177)(163,1176)(164,1175)(165,1174)(166,1173)(167,1172)(168,1171)(169,1170)(170,1169)(171,1168)(172,1167)(173,1166)(174,1165)(175,1164)(176,1163)(177,1162)(178,1161)(179,1160)(180,1159)(181,1158)(182,1157)(183,1156)(184,1155)(185,1154)(186,1153)(187,1152)(188,1151)(189,1150)(190,1149)(191,1148)(192,1147)(193,1146)(194,1145)(195,1144)(196,1143)(197,1142)(198,1141)(199,1140)(200,1139)(201,1138)(202,1137)(203,1136)(204,1135)(205,1134)(206,1133)(207,1132)(208,1131)(209,1130)(210,1129)(211,1128)(212,1127)(213,1126)(214,1125)(215,1124)(216,1123)(217,1122)(218,1121)(219,1120)(220,1119)(221,1118)(222,1117)(223,1116)(224,1115)(225,1114)(226,1113)(227,1112)(228,1111)(229,1110)(230,1109)(231,1108)(232,1107)(233,1106)(234,1105)(235,1104)(236,1103)(237,1102)(238,1101)(239,1100)(240,1099)(241,1098)(242,1097)(243,1096)(244,1095)(245,1094)(246,1093)(247,1092)(248,1091)(249,1090)(250,1089)(251,1088)(252,1087)(253,1086)(254,1085)(255,1084)(256,1083)(257,1082)(258,1081)(259,1080)(260,1079)(261,1078)(262,1077)(263,1076)(264,1075)(265,1074)(266,1073)(267,1072)(268,1071)(269,1070)(270,1069)(271,1068)(272,1067)(273,1066)(274,1065)(275,1064)(276,1063)(277,1062)(278,1061)(279,1060)(280,1059)(281,1058)(282,1057)(283,1056)(284,1055)(285,1054)(286,1053)(287,1052)(288,1051)(289,1050)(290,1049)(291,1048)(292,1047)(293,1046)(294,1045)(295,1044)(296,1043)(297,1042)(298,1041)(299,1040)(300,1039)(301,1038)(302,1037)(303,1036)(304,1035)(305,1034)(306,1033)(307,1032)(308,1031)(309,1030)(310,1029)(311,1028)(312,1027)(313,1026)(314,1025)(315,1024)(316,1023)(317,1022)(318,1021)(319,1020)(320,1019)(321,1018)(322,1017)(323,1016)(324,1015)(325,1014)(326,1013)(327,1012)(328,1011)(329,1010)(330,1009)(331,1008)(332,1007)(333,1006)(334,1005)(335,1004)(336,1003)(337,1002)(338,1001)(339,1000)(340,999)(341,998)(342,997)(343,996)(344,995)(345,994)(346,993)(347,992)(348,991)(349,990)(350,989)(351,988)(352,987)(353,986)(354,985)(355,984)(356,983)(357,982)(358,981)(359,980)(360,979)(361,978)(362,977)(363,976)(364,975)(365,974)(366,973)(367,972)(368,971)(369,970)(370,969)(371,968)(372,967)(373,966)(374,965)(375,964)(376,963)(377,962)(378,961)(379,960)(380,959)(381,958)(382,957)(383,956)(384,955)(385,954)(386,953)(387,952)(388,951)(389,950)(390,949)(391,948)(392,947)(393,946)(394,945)(395,944)(396,943)(397,942)(398,941)(399,940)(400,939)(401,938)(402,937)(403,936)(404,935)(405,934)(406,933)(407,932)(408,931)(409,930)(410,929)(411,928)(412,927)(413,926)(414,925)(415,924)(416,923)(417,922)(418,921)(419,920)(420,919)(421,918)(422,917)(423,916)(424,915)(425,914)(426,913)(427,912)(428,911)(429,910)(430,909)(431,908)(432,907)(433,906)(434,905)(435,904)(436,903)(437,902)(438,901)(439,900)(440,899)(441,898)(442,897)(443,896)(444,895)(445,894)(446,893)(447,892)(448,891)(449,890)(450,889)(451,888)(452,887)(453,886)(454,885)(455,884)(456,883)(457,882)(458,881)(459,880)(460,879)(461,878)(462,877)(463,876)(464,875)(465,874)(466,873)(467,872)(468,871)(469,870)(470,869)(471,868)(472,867)(473,866)(474,865)(475,864)(476,863)(477,862)(478,861)(479,860)(480,859)(481,858)(482,857)(483,856)(484,855)(485,854)(486,853)(487,852)(488,851)(489,850)(490,849)(491,848)(492,847)(493,846)(494,845)(495,844)(496,843)(497,842)(498,841)(499,840)(500,839)(501,838)(502,837)(503,836)(504,835)(505,834)(506,833)(507,832)(508,831)(509,830)(510,829)(511,828)(512,827)(513,826)(514,825)(515,824)(516,823)(517,822)(518,821)(519,820)(520,819)(521,818)(522,817)(523,816)(524,815)(525,814)(526,813)(527,812)(528,811)(529,810)(530,809)(531,808)(532,807)(533,806)(534,805)(535,804)(536,803)(537,802)(538,801)(539,800)(540,799)(541,798)(542,797)(543,796)(544,795)(545,794)(546,793)(547,792)(548,791)(549,790)(550,789)(551,788)(552,787)(553,786)(554,785)(555,784)(556,783)(557,782)(558,781)(559,780)(560,779)(561,778)(562,777)(563,776)(564,775)(565,774)(566,773)(567,772)(568,771)(569,770)(570,769)(571,768)(572,767)(573,766)(574,765)(575,764)(576,763)(577,762)(578,761)(579,760)(580,759)(581,758)(582,757)(583,756)(584,755)(585,754)(586,753)(587,752)(588,751)(589,750)(590,749)(591,748)(592,747)(593,746)(594,745)(595,744)(596,743)(597,742)(598,741)(599,740)(600,739)(601,738)(602,737)(603,736)(604,735)(605,734)(606,733)(607,732)(608,731)(609,730)(610,729)(611,728)(612,727)(613,726)(614,725)(615,724)(616,723)(617,722)(618,721)(619,720)(620,719)(621,718)(622,717)(623,716)(624,715)(625,714)(626,713)(627,712)(628,711)(629,710)(630,709)(631,708)(632,707)(633,706)(634,705)(635,704)(636,703)(637,702)(638,701)(639,700)(640,699)(641,698)(642,697)(643,696)(644,695)(645,694)(646,693)(647,692)(648,691)(649,690)(650,689)(651,688)(652,687)(653,686)(654,685)(655,684)(656,683)(657,682)(658,681)(659,680)(660,679)(661,678)(662,677)(663,676)(664,675)(665,674)(666,673)(667,672)(668,671)(669,670)
Conjugacy classes & character table
3984 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15924, 13);
Finite Group Databasebeta