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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1326 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);(4,5)(7,1326)(8,1325)(9,1324)(10,1323)(11,1322)(12,1321)(13,1320)(14,1319)(15,1318)(16,1317)(17,1316)(18,1315)(19,1314)(20,1313)(21,1312)(22,1311)(23,1310)(24,1309)(25,1308)(26,1307)(27,1306)(28,1305)(29,1304)(30,1303)(31,1302)(32,1301)(33,1300)(34,1299)(35,1298)(36,1297)(37,1296)(38,1295)(39,1294)(40,1293)(41,1292)(42,1291)(43,1290)(44,1289)(45,1288)(46,1287)(47,1286)(48,1285)(49,1284)(50,1283)(51,1282)(52,1281)(53,1280)(54,1279)(55,1278)(56,1277)(57,1276)(58,1275)(59,1274)(60,1273)(61,1272)(62,1271)(63,1270)(64,1269)(65,1268)(66,1267)(67,1266)(68,1265)(69,1264)(70,1263)(71,1262)(72,1261)(73,1260)(74,1259)(75,1258)(76,1257)(77,1256)(78,1255)(79,1254)(80,1253)(81,1252)(82,1251)(83,1250)(84,1249)(85,1248)(86,1247)(87,1246)(88,1245)(89,1244)(90,1243)(91,1242)(92,1241)(93,1240)(94,1239)(95,1238)(96,1237)(97,1236)(98,1235)(99,1234)(100,1233)(101,1232)(102,1231)(103,1230)(104,1229)(105,1228)(106,1227)(107,1226)(108,1225)(109,1224)(110,1223)(111,1222)(112,1221)(113,1220)(114,1219)(115,1218)(116,1217)(117,1216)(118,1215)(119,1214)(120,1213)(121,1212)(122,1211)(123,1210)(124,1209)(125,1208)(126,1207)(127,1206)(128,1205)(129,1204)(130,1203)(131,1202)(132,1201)(133,1200)(134,1199)(135,1198)(136,1197)(137,1196)(138,1195)(139,1194)(140,1193)(141,1192)(142,1191)(143,1190)(144,1189)(145,1188)(146,1187)(147,1186)(148,1185)(149,1184)(150,1183)(151,1182)(152,1181)(153,1180)(154,1179)(155,1178)(156,1177)(157,1176)(158,1175)(159,1174)(160,1173)(161,1172)(162,1171)(163,1170)(164,1169)(165,1168)(166,1167)(167,1166)(168,1165)(169,1164)(170,1163)(171,1162)(172,1161)(173,1160)(174,1159)(175,1158)(176,1157)(177,1156)(178,1155)(179,1154)(180,1153)(181,1152)(182,1151)(183,1150)(184,1149)(185,1148)(186,1147)(187,1146)(188,1145)(189,1144)(190,1143)(191,1142)(192,1141)(193,1140)(194,1139)(195,1138)(196,1137)(197,1136)(198,1135)(199,1134)(200,1133)(201,1132)(202,1131)(203,1130)(204,1129)(205,1128)(206,1127)(207,1126)(208,1125)(209,1124)(210,1123)(211,1122)(212,1121)(213,1120)(214,1119)(215,1118)(216,1117)(217,1116)(218,1115)(219,1114)(220,1113)(221,1112)(222,1111)(223,1110)(224,1109)(225,1108)(226,1107)(227,1106)(228,1105)(229,1104)(230,1103)(231,1102)(232,1101)(233,1100)(234,1099)(235,1098)(236,1097)(237,1096)(238,1095)(239,1094)(240,1093)(241,1092)(242,1091)(243,1090)(244,1089)(245,1088)(246,1087)(247,1086)(248,1085)(249,1084)(250,1083)(251,1082)(252,1081)(253,1080)(254,1079)(255,1078)(256,1077)(257,1076)(258,1075)(259,1074)(260,1073)(261,1072)(262,1071)(263,1070)(264,1069)(265,1068)(266,1067)(267,1066)(268,1065)(269,1064)(270,1063)(271,1062)(272,1061)(273,1060)(274,1059)(275,1058)(276,1057)(277,1056)(278,1055)(279,1054)(280,1053)(281,1052)(282,1051)(283,1050)(284,1049)(285,1048)(286,1047)(287,1046)(288,1045)(289,1044)(290,1043)(291,1042)(292,1041)(293,1040)(294,1039)(295,1038)(296,1037)(297,1036)(298,1035)(299,1034)(300,1033)(301,1032)(302,1031)(303,1030)(304,1029)(305,1028)(306,1027)(307,1026)(308,1025)(309,1024)(310,1023)(311,1022)(312,1021)(313,1020)(314,1019)(315,1018)(316,1017)(317,1016)(318,1015)(319,1014)(320,1013)(321,1012)(322,1011)(323,1010)(324,1009)(325,1008)(326,1007)(327,1006)(328,1005)(329,1004)(330,1003)(331,1002)(332,1001)(333,1000)(334,999)(335,998)(336,997)(337,996)(338,995)(339,994)(340,993)(341,992)(342,991)(343,990)(344,989)(345,988)(346,987)(347,986)(348,985)(349,984)(350,983)(351,982)(352,981)(353,980)(354,979)(355,978)(356,977)(357,976)(358,975)(359,974)(360,973)(361,972)(362,971)(363,970)(364,969)(365,968)(366,967)(367,966)(368,965)(369,964)(370,963)(371,962)(372,961)(373,960)(374,959)(375,958)(376,957)(377,956)(378,955)(379,954)(380,953)(381,952)(382,951)(383,950)(384,949)(385,948)(386,947)(387,946)(388,945)(389,944)(390,943)(391,942)(392,941)(393,940)(394,939)(395,938)(396,937)(397,936)(398,935)(399,934)(400,933)(401,932)(402,931)(403,930)(404,929)(405,928)(406,927)(407,926)(408,925)(409,924)(410,923)(411,922)(412,921)(413,920)(414,919)(415,918)(416,917)(417,916)(418,915)(419,914)(420,913)(421,912)(422,911)(423,910)(424,909)(425,908)(426,907)(427,906)(428,905)(429,904)(430,903)(431,902)(432,901)(433,900)(434,899)(435,898)(436,897)(437,896)(438,895)(439,894)(440,893)(441,892)(442,891)(443,890)(444,889)(445,888)(446,887)(447,886)(448,885)(449,884)(450,883)(451,882)(452,881)(453,880)(454,879)(455,878)(456,877)(457,876)(458,875)(459,874)(460,873)(461,872)(462,871)(463,870)(464,869)(465,868)(466,867)(467,866)(468,865)(469,864)(470,863)(471,862)(472,861)(473,860)(474,859)(475,858)(476,857)(477,856)(478,855)(479,854)(480,853)(481,852)(482,851)(483,850)(484,849)(485,848)(486,847)(487,846)(488,845)(489,844)(490,843)(491,842)(492,841)(493,840)(494,839)(495,838)(496,837)(497,836)(498,835)(499,834)(500,833)(501,832)(502,831)(503,830)(504,829)(505,828)(506,827)(507,826)(508,825)(509,824)(510,823)(511,822)(512,821)(513,820)(514,819)(515,818)(516,817)(517,816)(518,815)(519,814)(520,813)(521,812)(522,811)(523,810)(524,809)(525,808)(526,807)(527,806)(528,805)(529,804)(530,803)(531,802)(532,801)(533,800)(534,799)(535,798)(536,797)(537,796)(538,795)(539,794)(540,793)(541,792)(542,791)(543,790)(544,789)(545,788)(546,787)(547,786)(548,785)(549,784)(550,783)(551,782)(552,781)(553,780)(554,779)(555,778)(556,777)(557,776)(558,775)(559,774)(560,773)(561,772)(562,771)(563,770)(564,769)(565,768)(566,767)(567,766)(568,765)(569,764)(570,763)(571,762)(572,761)(573,760)(574,759)(575,758)(576,757)(577,756)(578,755)(579,754)(580,753)(581,752)(582,751)(583,750)(584,749)(585,748)(586,747)(587,746)(588,745)(589,744)(590,743)(591,742)(592,741)(593,740)(594,739)(595,738)(596,737)(597,736)(598,735)(599,734)(600,733)(601,732)(602,731)(603,730)(604,729)(605,728)(606,727)(607,726)(608,725)(609,724)(610,723)(611,722)(612,721)(613,720)(614,719)(615,718)(616,717)(617,716)(618,715)(619,714)(620,713)(621,712)(622,711)(623,710)(624,709)(625,708)(626,707)(627,706)(628,705)(629,704)(630,703)(631,702)(632,701)(633,700)(634,699)(635,698)(636,697)(637,696)(638,695)(639,694)(640,693)(641,692)(642,691)(643,690)(644,689)(645,688)(646,687)(647,686)(648,685)(649,684)(650,683)(651,682)(652,681)(653,680)(654,679)(655,678)(656,677)(657,676)(658,675)(659,674)(660,673)(661,672)(662,671)(663,670)(664,669)(665,668)(666,667)
Conjugacy classes & character table
3966 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15852, 16);
Finite Group Databasebeta