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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1284 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);(4,7)(5,6)(9,1284)(10,1283)(11,1282)(12,1281)(13,1280)(14,1279)(15,1278)(16,1277)(17,1276)(18,1275)(19,1274)(20,1273)(21,1272)(22,1271)(23,1270)(24,1269)(25,1268)(26,1267)(27,1266)(28,1265)(29,1264)(30,1263)(31,1262)(32,1261)(33,1260)(34,1259)(35,1258)(36,1257)(37,1256)(38,1255)(39,1254)(40,1253)(41,1252)(42,1251)(43,1250)(44,1249)(45,1248)(46,1247)(47,1246)(48,1245)(49,1244)(50,1243)(51,1242)(52,1241)(53,1240)(54,1239)(55,1238)(56,1237)(57,1236)(58,1235)(59,1234)(60,1233)(61,1232)(62,1231)(63,1230)(64,1229)(65,1228)(66,1227)(67,1226)(68,1225)(69,1224)(70,1223)(71,1222)(72,1221)(73,1220)(74,1219)(75,1218)(76,1217)(77,1216)(78,1215)(79,1214)(80,1213)(81,1212)(82,1211)(83,1210)(84,1209)(85,1208)(86,1207)(87,1206)(88,1205)(89,1204)(90,1203)(91,1202)(92,1201)(93,1200)(94,1199)(95,1198)(96,1197)(97,1196)(98,1195)(99,1194)(100,1193)(101,1192)(102,1191)(103,1190)(104,1189)(105,1188)(106,1187)(107,1186)(108,1185)(109,1184)(110,1183)(111,1182)(112,1181)(113,1180)(114,1179)(115,1178)(116,1177)(117,1176)(118,1175)(119,1174)(120,1173)(121,1172)(122,1171)(123,1170)(124,1169)(125,1168)(126,1167)(127,1166)(128,1165)(129,1164)(130,1163)(131,1162)(132,1161)(133,1160)(134,1159)(135,1158)(136,1157)(137,1156)(138,1155)(139,1154)(140,1153)(141,1152)(142,1151)(143,1150)(144,1149)(145,1148)(146,1147)(147,1146)(148,1145)(149,1144)(150,1143)(151,1142)(152,1141)(153,1140)(154,1139)(155,1138)(156,1137)(157,1136)(158,1135)(159,1134)(160,1133)(161,1132)(162,1131)(163,1130)(164,1129)(165,1128)(166,1127)(167,1126)(168,1125)(169,1124)(170,1123)(171,1122)(172,1121)(173,1120)(174,1119)(175,1118)(176,1117)(177,1116)(178,1115)(179,1114)(180,1113)(181,1112)(182,1111)(183,1110)(184,1109)(185,1108)(186,1107)(187,1106)(188,1105)(189,1104)(190,1103)(191,1102)(192,1101)(193,1100)(194,1099)(195,1098)(196,1097)(197,1096)(198,1095)(199,1094)(200,1093)(201,1092)(202,1091)(203,1090)(204,1089)(205,1088)(206,1087)(207,1086)(208,1085)(209,1084)(210,1083)(211,1082)(212,1081)(213,1080)(214,1079)(215,1078)(216,1077)(217,1076)(218,1075)(219,1074)(220,1073)(221,1072)(222,1071)(223,1070)(224,1069)(225,1068)(226,1067)(227,1066)(228,1065)(229,1064)(230,1063)(231,1062)(232,1061)(233,1060)(234,1059)(235,1058)(236,1057)(237,1056)(238,1055)(239,1054)(240,1053)(241,1052)(242,1051)(243,1050)(244,1049)(245,1048)(246,1047)(247,1046)(248,1045)(249,1044)(250,1043)(251,1042)(252,1041)(253,1040)(254,1039)(255,1038)(256,1037)(257,1036)(258,1035)(259,1034)(260,1033)(261,1032)(262,1031)(263,1030)(264,1029)(265,1028)(266,1027)(267,1026)(268,1025)(269,1024)(270,1023)(271,1022)(272,1021)(273,1020)(274,1019)(275,1018)(276,1017)(277,1016)(278,1015)(279,1014)(280,1013)(281,1012)(282,1011)(283,1010)(284,1009)(285,1008)(286,1007)(287,1006)(288,1005)(289,1004)(290,1003)(291,1002)(292,1001)(293,1000)(294,999)(295,998)(296,997)(297,996)(298,995)(299,994)(300,993)(301,992)(302,991)(303,990)(304,989)(305,988)(306,987)(307,986)(308,985)(309,984)(310,983)(311,982)(312,981)(313,980)(314,979)(315,978)(316,977)(317,976)(318,975)(319,974)(320,973)(321,972)(322,971)(323,970)(324,969)(325,968)(326,967)(327,966)(328,965)(329,964)(330,963)(331,962)(332,961)(333,960)(334,959)(335,958)(336,957)(337,956)(338,955)(339,954)(340,953)(341,952)(342,951)(343,950)(344,949)(345,948)(346,947)(347,946)(348,945)(349,944)(350,943)(351,942)(352,941)(353,940)(354,939)(355,938)(356,937)(357,936)(358,935)(359,934)(360,933)(361,932)(362,931)(363,930)(364,929)(365,928)(366,927)(367,926)(368,925)(369,924)(370,923)(371,922)(372,921)(373,920)(374,919)(375,918)(376,917)(377,916)(378,915)(379,914)(380,913)(381,912)(382,911)(383,910)(384,909)(385,908)(386,907)(387,906)(388,905)(389,904)(390,903)(391,902)(392,901)(393,900)(394,899)(395,898)(396,897)(397,896)(398,895)(399,894)(400,893)(401,892)(402,891)(403,890)(404,889)(405,888)(406,887)(407,886)(408,885)(409,884)(410,883)(411,882)(412,881)(413,880)(414,879)(415,878)(416,877)(417,876)(418,875)(419,874)(420,873)(421,872)(422,871)(423,870)(424,869)(425,868)(426,867)(427,866)(428,865)(429,864)(430,863)(431,862)(432,861)(433,860)(434,859)(435,858)(436,857)(437,856)(438,855)(439,854)(440,853)(441,852)(442,851)(443,850)(444,849)(445,848)(446,847)(447,846)(448,845)(449,844)(450,843)(451,842)(452,841)(453,840)(454,839)(455,838)(456,837)(457,836)(458,835)(459,834)(460,833)(461,832)(462,831)(463,830)(464,829)(465,828)(466,827)(467,826)(468,825)(469,824)(470,823)(471,822)(472,821)(473,820)(474,819)(475,818)(476,817)(477,816)(478,815)(479,814)(480,813)(481,812)(482,811)(483,810)(484,809)(485,808)(486,807)(487,806)(488,805)(489,804)(490,803)(491,802)(492,801)(493,800)(494,799)(495,798)(496,797)(497,796)(498,795)(499,794)(500,793)(501,792)(502,791)(503,790)(504,789)(505,788)(506,787)(507,786)(508,785)(509,784)(510,783)(511,782)(512,781)(513,780)(514,779)(515,778)(516,777)(517,776)(518,775)(519,774)(520,773)(521,772)(522,771)(523,770)(524,769)(525,768)(526,767)(527,766)(528,765)(529,764)(530,763)(531,762)(532,761)(533,760)(534,759)(535,758)(536,757)(537,756)(538,755)(539,754)(540,753)(541,752)(542,751)(543,750)(544,749)(545,748)(546,747)(547,746)(548,745)(549,744)(550,743)(551,742)(552,741)(553,740)(554,739)(555,738)(556,737)(557,736)(558,735)(559,734)(560,733)(561,732)(562,731)(563,730)(564,729)(565,728)(566,727)(567,726)(568,725)(569,724)(570,723)(571,722)(572,721)(573,720)(574,719)(575,718)(576,717)(577,716)(578,715)(579,714)(580,713)(581,712)(582,711)(583,710)(584,709)(585,708)(586,707)(587,706)(588,705)(589,704)(590,703)(591,702)(592,701)(593,700)(594,699)(595,698)(596,697)(597,696)(598,695)(599,694)(600,693)(601,692)(602,691)(603,690)(604,689)(605,688)(606,687)(607,686)(608,685)(609,684)(610,683)(611,682)(612,681)(613,680)(614,679)(615,678)(616,677)(617,676)(618,675)(619,674)(620,673)(621,672)(622,671)(623,670)(624,669)(625,668)(626,667)(627,666)(628,665)(629,664)(630,663)(631,662)(632,661)(633,660)(634,659)(635,658)(636,657)(637,656)(638,655)(639,654)(640,653)(641,652)(642,651)(643,650)(644,649)(645,648)(646,647)
Conjugacy classes & character table
6388 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25540, 15);
Finite Group Databasebeta