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D6445 #27166286
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1294 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);(2,5)(3,4)(7,1294)(8,1293)(9,1292)(10,1291)(11,1290)(12,1289)(13,1288)(14,1287)(15,1286)(16,1285)(17,1284)(18,1283)(19,1282)(20,1281)(21,1280)(22,1279)(23,1278)(24,1277)(25,1276)(26,1275)(27,1274)(28,1273)(29,1272)(30,1271)(31,1270)(32,1269)(33,1268)(34,1267)(35,1266)(36,1265)(37,1264)(38,1263)(39,1262)(40,1261)(41,1260)(42,1259)(43,1258)(44,1257)(45,1256)(46,1255)(47,1254)(48,1253)(49,1252)(50,1251)(51,1250)(52,1249)(53,1248)(54,1247)(55,1246)(56,1245)(57,1244)(58,1243)(59,1242)(60,1241)(61,1240)(62,1239)(63,1238)(64,1237)(65,1236)(66,1235)(67,1234)(68,1233)(69,1232)(70,1231)(71,1230)(72,1229)(73,1228)(74,1227)(75,1226)(76,1225)(77,1224)(78,1223)(79,1222)(80,1221)(81,1220)(82,1219)(83,1218)(84,1217)(85,1216)(86,1215)(87,1214)(88,1213)(89,1212)(90,1211)(91,1210)(92,1209)(93,1208)(94,1207)(95,1206)(96,1205)(97,1204)(98,1203)(99,1202)(100,1201)(101,1200)(102,1199)(103,1198)(104,1197)(105,1196)(106,1195)(107,1194)(108,1193)(109,1192)(110,1191)(111,1190)(112,1189)(113,1188)(114,1187)(115,1186)(116,1185)(117,1184)(118,1183)(119,1182)(120,1181)(121,1180)(122,1179)(123,1178)(124,1177)(125,1176)(126,1175)(127,1174)(128,1173)(129,1172)(130,1171)(131,1170)(132,1169)(133,1168)(134,1167)(135,1166)(136,1165)(137,1164)(138,1163)(139,1162)(140,1161)(141,1160)(142,1159)(143,1158)(144,1157)(145,1156)(146,1155)(147,1154)(148,1153)(149,1152)(150,1151)(151,1150)(152,1149)(153,1148)(154,1147)(155,1146)(156,1145)(157,1144)(158,1143)(159,1142)(160,1141)(161,1140)(162,1139)(163,1138)(164,1137)(165,1136)(166,1135)(167,1134)(168,1133)(169,1132)(170,1131)(171,1130)(172,1129)(173,1128)(174,1127)(175,1126)(176,1125)(177,1124)(178,1123)(179,1122)(180,1121)(181,1120)(182,1119)(183,1118)(184,1117)(185,1116)(186,1115)(187,1114)(188,1113)(189,1112)(190,1111)(191,1110)(192,1109)(193,1108)(194,1107)(195,1106)(196,1105)(197,1104)(198,1103)(199,1102)(200,1101)(201,1100)(202,1099)(203,1098)(204,1097)(205,1096)(206,1095)(207,1094)(208,1093)(209,1092)(210,1091)(211,1090)(212,1089)(213,1088)(214,1087)(215,1086)(216,1085)(217,1084)(218,1083)(219,1082)(220,1081)(221,1080)(222,1079)(223,1078)(224,1077)(225,1076)(226,1075)(227,1074)(228,1073)(229,1072)(230,1071)(231,1070)(232,1069)(233,1068)(234,1067)(235,1066)(236,1065)(237,1064)(238,1063)(239,1062)(240,1061)(241,1060)(242,1059)(243,1058)(244,1057)(245,1056)(246,1055)(247,1054)(248,1053)(249,1052)(250,1051)(251,1050)(252,1049)(253,1048)(254,1047)(255,1046)(256,1045)(257,1044)(258,1043)(259,1042)(260,1041)(261,1040)(262,1039)(263,1038)(264,1037)(265,1036)(266,1035)(267,1034)(268,1033)(269,1032)(270,1031)(271,1030)(272,1029)(273,1028)(274,1027)(275,1026)(276,1025)(277,1024)(278,1023)(279,1022)(280,1021)(281,1020)(282,1019)(283,1018)(284,1017)(285,1016)(286,1015)(287,1014)(288,1013)(289,1012)(290,1011)(291,1010)(292,1009)(293,1008)(294,1007)(295,1006)(296,1005)(297,1004)(298,1003)(299,1002)(300,1001)(301,1000)(302,999)(303,998)(304,997)(305,996)(306,995)(307,994)(308,993)(309,992)(310,991)(311,990)(312,989)(313,988)(314,987)(315,986)(316,985)(317,984)(318,983)(319,982)(320,981)(321,980)(322,979)(323,978)(324,977)(325,976)(326,975)(327,974)(328,973)(329,972)(330,971)(331,970)(332,969)(333,968)(334,967)(335,966)(336,965)(337,964)(338,963)(339,962)(340,961)(341,960)(342,959)(343,958)(344,957)(345,956)(346,955)(347,954)(348,953)(349,952)(350,951)(351,950)(352,949)(353,948)(354,947)(355,946)(356,945)(357,944)(358,943)(359,942)(360,941)(361,940)(362,939)(363,938)(364,937)(365,936)(366,935)(367,934)(368,933)(369,932)(370,931)(371,930)(372,929)(373,928)(374,927)(375,926)(376,925)(377,924)(378,923)(379,922)(380,921)(381,920)(382,919)(383,918)(384,917)(385,916)(386,915)(387,914)(388,913)(389,912)(390,911)(391,910)(392,909)(393,908)(394,907)(395,906)(396,905)(397,904)(398,903)(399,902)(400,901)(401,900)(402,899)(403,898)(404,897)(405,896)(406,895)(407,894)(408,893)(409,892)(410,891)(411,890)(412,889)(413,888)(414,887)(415,886)(416,885)(417,884)(418,883)(419,882)(420,881)(421,880)(422,879)(423,878)(424,877)(425,876)(426,875)(427,874)(428,873)(429,872)(430,871)(431,870)(432,869)(433,868)(434,867)(435,866)(436,865)(437,864)(438,863)(439,862)(440,861)(441,860)(442,859)(443,858)(444,857)(445,856)(446,855)(447,854)(448,853)(449,852)(450,851)(451,850)(452,849)(453,848)(454,847)(455,846)(456,845)(457,844)(458,843)(459,842)(460,841)(461,840)(462,839)(463,838)(464,837)(465,836)(466,835)(467,834)(468,833)(469,832)(470,831)(471,830)(472,829)(473,828)(474,827)(475,826)(476,825)(477,824)(478,823)(479,822)(480,821)(481,820)(482,819)(483,818)(484,817)(485,816)(486,815)(487,814)(488,813)(489,812)(490,811)(491,810)(492,809)(493,808)(494,807)(495,806)(496,805)(497,804)(498,803)(499,802)(500,801)(501,800)(502,799)(503,798)(504,797)(505,796)(506,795)(507,794)(508,793)(509,792)(510,791)(511,790)(512,789)(513,788)(514,787)(515,786)(516,785)(517,784)(518,783)(519,782)(520,781)(521,780)(522,779)(523,778)(524,777)(525,776)(526,775)(527,774)(528,773)(529,772)(530,771)(531,770)(532,769)(533,768)(534,767)(535,766)(536,765)(537,764)(538,763)(539,762)(540,761)(541,760)(542,759)(543,758)(544,757)(545,756)(546,755)(547,754)(548,753)(549,752)(550,751)(551,750)(552,749)(553,748)(554,747)(555,746)(556,745)(557,744)(558,743)(559,742)(560,741)(561,740)(562,739)(563,738)(564,737)(565,736)(566,735)(567,734)(568,733)(569,732)(570,731)(571,730)(572,729)(573,728)(574,727)(575,726)(576,725)(577,724)(578,723)(579,722)(580,721)(581,720)(582,719)(583,718)(584,717)(585,716)(586,715)(587,714)(588,713)(589,712)(590,711)(591,710)(592,709)(593,708)(594,707)(595,706)(596,705)(597,704)(598,703)(599,702)(600,701)(601,700)(602,699)(603,698)(604,697)(605,696)(606,695)(607,694)(608,693)(609,692)(610,691)(611,690)(612,689)(613,688)(614,687)(615,686)(616,685)(617,684)(618,683)(619,682)(620,681)(621,680)(622,679)(623,678)(624,677)(625,676)(626,675)(627,674)(628,673)(629,672)(630,671)(631,670)(632,669)(633,668)(634,667)(635,666)(636,665)(637,664)(638,663)(639,662)(640,661)(641,660)(642,659)(643,658)(644,657)(645,656)(646,655)(647,654)(648,653)(649,652)(650,651)
Polycyclic presentation:
2,5,1289|b^a=b^4,c^a=c^1288
Conjugacy classes & character table
3224 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12890, 3);
Finite Group Databasebeta