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D1289 #14579486
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1289 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);(2,1289)(3,1288)(4,1287)(5,1286)(6,1285)(7,1284)(8,1283)(9,1282)(10,1281)(11,1280)(12,1279)(13,1278)(14,1277)(15,1276)(16,1275)(17,1274)(18,1273)(19,1272)(20,1271)(21,1270)(22,1269)(23,1268)(24,1267)(25,1266)(26,1265)(27,1264)(28,1263)(29,1262)(30,1261)(31,1260)(32,1259)(33,1258)(34,1257)(35,1256)(36,1255)(37,1254)(38,1253)(39,1252)(40,1251)(41,1250)(42,1249)(43,1248)(44,1247)(45,1246)(46,1245)(47,1244)(48,1243)(49,1242)(50,1241)(51,1240)(52,1239)(53,1238)(54,1237)(55,1236)(56,1235)(57,1234)(58,1233)(59,1232)(60,1231)(61,1230)(62,1229)(63,1228)(64,1227)(65,1226)(66,1225)(67,1224)(68,1223)(69,1222)(70,1221)(71,1220)(72,1219)(73,1218)(74,1217)(75,1216)(76,1215)(77,1214)(78,1213)(79,1212)(80,1211)(81,1210)(82,1209)(83,1208)(84,1207)(85,1206)(86,1205)(87,1204)(88,1203)(89,1202)(90,1201)(91,1200)(92,1199)(93,1198)(94,1197)(95,1196)(96,1195)(97,1194)(98,1193)(99,1192)(100,1191)(101,1190)(102,1189)(103,1188)(104,1187)(105,1186)(106,1185)(107,1184)(108,1183)(109,1182)(110,1181)(111,1180)(112,1179)(113,1178)(114,1177)(115,1176)(116,1175)(117,1174)(118,1173)(119,1172)(120,1171)(121,1170)(122,1169)(123,1168)(124,1167)(125,1166)(126,1165)(127,1164)(128,1163)(129,1162)(130,1161)(131,1160)(132,1159)(133,1158)(134,1157)(135,1156)(136,1155)(137,1154)(138,1153)(139,1152)(140,1151)(141,1150)(142,1149)(143,1148)(144,1147)(145,1146)(146,1145)(147,1144)(148,1143)(149,1142)(150,1141)(151,1140)(152,1139)(153,1138)(154,1137)(155,1136)(156,1135)(157,1134)(158,1133)(159,1132)(160,1131)(161,1130)(162,1129)(163,1128)(164,1127)(165,1126)(166,1125)(167,1124)(168,1123)(169,1122)(170,1121)(171,1120)(172,1119)(173,1118)(174,1117)(175,1116)(176,1115)(177,1114)(178,1113)(179,1112)(180,1111)(181,1110)(182,1109)(183,1108)(184,1107)(185,1106)(186,1105)(187,1104)(188,1103)(189,1102)(190,1101)(191,1100)(192,1099)(193,1098)(194,1097)(195,1096)(196,1095)(197,1094)(198,1093)(199,1092)(200,1091)(201,1090)(202,1089)(203,1088)(204,1087)(205,1086)(206,1085)(207,1084)(208,1083)(209,1082)(210,1081)(211,1080)(212,1079)(213,1078)(214,1077)(215,1076)(216,1075)(217,1074)(218,1073)(219,1072)(220,1071)(221,1070)(222,1069)(223,1068)(224,1067)(225,1066)(226,1065)(227,1064)(228,1063)(229,1062)(230,1061)(231,1060)(232,1059)(233,1058)(234,1057)(235,1056)(236,1055)(237,1054)(238,1053)(239,1052)(240,1051)(241,1050)(242,1049)(243,1048)(244,1047)(245,1046)(246,1045)(247,1044)(248,1043)(249,1042)(250,1041)(251,1040)(252,1039)(253,1038)(254,1037)(255,1036)(256,1035)(257,1034)(258,1033)(259,1032)(260,1031)(261,1030)(262,1029)(263,1028)(264,1027)(265,1026)(266,1025)(267,1024)(268,1023)(269,1022)(270,1021)(271,1020)(272,1019)(273,1018)(274,1017)(275,1016)(276,1015)(277,1014)(278,1013)(279,1012)(280,1011)(281,1010)(282,1009)(283,1008)(284,1007)(285,1006)(286,1005)(287,1004)(288,1003)(289,1002)(290,1001)(291,1000)(292,999)(293,998)(294,997)(295,996)(296,995)(297,994)(298,993)(299,992)(300,991)(301,990)(302,989)(303,988)(304,987)(305,986)(306,985)(307,984)(308,983)(309,982)(310,981)(311,980)(312,979)(313,978)(314,977)(315,976)(316,975)(317,974)(318,973)(319,972)(320,971)(321,970)(322,969)(323,968)(324,967)(325,966)(326,965)(327,964)(328,963)(329,962)(330,961)(331,960)(332,959)(333,958)(334,957)(335,956)(336,955)(337,954)(338,953)(339,952)(340,951)(341,950)(342,949)(343,948)(344,947)(345,946)(346,945)(347,944)(348,943)(349,942)(350,941)(351,940)(352,939)(353,938)(354,937)(355,936)(356,935)(357,934)(358,933)(359,932)(360,931)(361,930)(362,929)(363,928)(364,927)(365,926)(366,925)(367,924)(368,923)(369,922)(370,921)(371,920)(372,919)(373,918)(374,917)(375,916)(376,915)(377,914)(378,913)(379,912)(380,911)(381,910)(382,909)(383,908)(384,907)(385,906)(386,905)(387,904)(388,903)(389,902)(390,901)(391,900)(392,899)(393,898)(394,897)(395,896)(396,895)(397,894)(398,893)(399,892)(400,891)(401,890)(402,889)(403,888)(404,887)(405,886)(406,885)(407,884)(408,883)(409,882)(410,881)(411,880)(412,879)(413,878)(414,877)(415,876)(416,875)(417,874)(418,873)(419,872)(420,871)(421,870)(422,869)(423,868)(424,867)(425,866)(426,865)(427,864)(428,863)(429,862)(430,861)(431,860)(432,859)(433,858)(434,857)(435,856)(436,855)(437,854)(438,853)(439,852)(440,851)(441,850)(442,849)(443,848)(444,847)(445,846)(446,845)(447,844)(448,843)(449,842)(450,841)(451,840)(452,839)(453,838)(454,837)(455,836)(456,835)(457,834)(458,833)(459,832)(460,831)(461,830)(462,829)(463,828)(464,827)(465,826)(466,825)(467,824)(468,823)(469,822)(470,821)(471,820)(472,819)(473,818)(474,817)(475,816)(476,815)(477,814)(478,813)(479,812)(480,811)(481,810)(482,809)(483,808)(484,807)(485,806)(486,805)(487,804)(488,803)(489,802)(490,801)(491,800)(492,799)(493,798)(494,797)(495,796)(496,795)(497,794)(498,793)(499,792)(500,791)(501,790)(502,789)(503,788)(504,787)(505,786)(506,785)(507,784)(508,783)(509,782)(510,781)(511,780)(512,779)(513,778)(514,777)(515,776)(516,775)(517,774)(518,773)(519,772)(520,771)(521,770)(522,769)(523,768)(524,767)(525,766)(526,765)(527,764)(528,763)(529,762)(530,761)(531,760)(532,759)(533,758)(534,757)(535,756)(536,755)(537,754)(538,753)(539,752)(540,751)(541,750)(542,749)(543,748)(544,747)(545,746)(546,745)(547,744)(548,743)(549,742)(550,741)(551,740)(552,739)(553,738)(554,737)(555,736)(556,735)(557,734)(558,733)(559,732)(560,731)(561,730)(562,729)(563,728)(564,727)(565,726)(566,725)(567,724)(568,723)(569,722)(570,721)(571,720)(572,719)(573,718)(574,717)(575,716)(576,715)(577,714)(578,713)(579,712)(580,711)(581,710)(582,709)(583,708)(584,707)(585,706)(586,705)(587,704)(588,703)(589,702)(590,701)(591,700)(592,699)(593,698)(594,697)(595,696)(596,695)(597,694)(598,693)(599,692)(600,691)(601,690)(602,689)(603,688)(604,687)(605,686)(606,685)(607,684)(608,683)(609,682)(610,681)(611,680)(612,679)(613,678)(614,677)(615,676)(616,675)(617,674)(618,673)(619,672)(620,671)(621,670)(622,669)(623,668)(624,667)(625,666)(626,665)(627,664)(628,663)(629,662)(630,661)(631,660)(632,659)(633,658)(634,657)(635,656)(636,655)(637,654)(638,653)(639,652)(640,651)(641,650)(642,649)(643,648)(644,647)(645,646)
Polycyclic presentation:
2,1289|b^a=b^1288
Conjugacy classes & character table
646 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2578, 1);
Finite Group Databasebeta