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D1277 #14579367
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1277 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);(2,1277)(3,1276)(4,1275)(5,1274)(6,1273)(7,1272)(8,1271)(9,1270)(10,1269)(11,1268)(12,1267)(13,1266)(14,1265)(15,1264)(16,1263)(17,1262)(18,1261)(19,1260)(20,1259)(21,1258)(22,1257)(23,1256)(24,1255)(25,1254)(26,1253)(27,1252)(28,1251)(29,1250)(30,1249)(31,1248)(32,1247)(33,1246)(34,1245)(35,1244)(36,1243)(37,1242)(38,1241)(39,1240)(40,1239)(41,1238)(42,1237)(43,1236)(44,1235)(45,1234)(46,1233)(47,1232)(48,1231)(49,1230)(50,1229)(51,1228)(52,1227)(53,1226)(54,1225)(55,1224)(56,1223)(57,1222)(58,1221)(59,1220)(60,1219)(61,1218)(62,1217)(63,1216)(64,1215)(65,1214)(66,1213)(67,1212)(68,1211)(69,1210)(70,1209)(71,1208)(72,1207)(73,1206)(74,1205)(75,1204)(76,1203)(77,1202)(78,1201)(79,1200)(80,1199)(81,1198)(82,1197)(83,1196)(84,1195)(85,1194)(86,1193)(87,1192)(88,1191)(89,1190)(90,1189)(91,1188)(92,1187)(93,1186)(94,1185)(95,1184)(96,1183)(97,1182)(98,1181)(99,1180)(100,1179)(101,1178)(102,1177)(103,1176)(104,1175)(105,1174)(106,1173)(107,1172)(108,1171)(109,1170)(110,1169)(111,1168)(112,1167)(113,1166)(114,1165)(115,1164)(116,1163)(117,1162)(118,1161)(119,1160)(120,1159)(121,1158)(122,1157)(123,1156)(124,1155)(125,1154)(126,1153)(127,1152)(128,1151)(129,1150)(130,1149)(131,1148)(132,1147)(133,1146)(134,1145)(135,1144)(136,1143)(137,1142)(138,1141)(139,1140)(140,1139)(141,1138)(142,1137)(143,1136)(144,1135)(145,1134)(146,1133)(147,1132)(148,1131)(149,1130)(150,1129)(151,1128)(152,1127)(153,1126)(154,1125)(155,1124)(156,1123)(157,1122)(158,1121)(159,1120)(160,1119)(161,1118)(162,1117)(163,1116)(164,1115)(165,1114)(166,1113)(167,1112)(168,1111)(169,1110)(170,1109)(171,1108)(172,1107)(173,1106)(174,1105)(175,1104)(176,1103)(177,1102)(178,1101)(179,1100)(180,1099)(181,1098)(182,1097)(183,1096)(184,1095)(185,1094)(186,1093)(187,1092)(188,1091)(189,1090)(190,1089)(191,1088)(192,1087)(193,1086)(194,1085)(195,1084)(196,1083)(197,1082)(198,1081)(199,1080)(200,1079)(201,1078)(202,1077)(203,1076)(204,1075)(205,1074)(206,1073)(207,1072)(208,1071)(209,1070)(210,1069)(211,1068)(212,1067)(213,1066)(214,1065)(215,1064)(216,1063)(217,1062)(218,1061)(219,1060)(220,1059)(221,1058)(222,1057)(223,1056)(224,1055)(225,1054)(226,1053)(227,1052)(228,1051)(229,1050)(230,1049)(231,1048)(232,1047)(233,1046)(234,1045)(235,1044)(236,1043)(237,1042)(238,1041)(239,1040)(240,1039)(241,1038)(242,1037)(243,1036)(244,1035)(245,1034)(246,1033)(247,1032)(248,1031)(249,1030)(250,1029)(251,1028)(252,1027)(253,1026)(254,1025)(255,1024)(256,1023)(257,1022)(258,1021)(259,1020)(260,1019)(261,1018)(262,1017)(263,1016)(264,1015)(265,1014)(266,1013)(267,1012)(268,1011)(269,1010)(270,1009)(271,1008)(272,1007)(273,1006)(274,1005)(275,1004)(276,1003)(277,1002)(278,1001)(279,1000)(280,999)(281,998)(282,997)(283,996)(284,995)(285,994)(286,993)(287,992)(288,991)(289,990)(290,989)(291,988)(292,987)(293,986)(294,985)(295,984)(296,983)(297,982)(298,981)(299,980)(300,979)(301,978)(302,977)(303,976)(304,975)(305,974)(306,973)(307,972)(308,971)(309,970)(310,969)(311,968)(312,967)(313,966)(314,965)(315,964)(316,963)(317,962)(318,961)(319,960)(320,959)(321,958)(322,957)(323,956)(324,955)(325,954)(326,953)(327,952)(328,951)(329,950)(330,949)(331,948)(332,947)(333,946)(334,945)(335,944)(336,943)(337,942)(338,941)(339,940)(340,939)(341,938)(342,937)(343,936)(344,935)(345,934)(346,933)(347,932)(348,931)(349,930)(350,929)(351,928)(352,927)(353,926)(354,925)(355,924)(356,923)(357,922)(358,921)(359,920)(360,919)(361,918)(362,917)(363,916)(364,915)(365,914)(366,913)(367,912)(368,911)(369,910)(370,909)(371,908)(372,907)(373,906)(374,905)(375,904)(376,903)(377,902)(378,901)(379,900)(380,899)(381,898)(382,897)(383,896)(384,895)(385,894)(386,893)(387,892)(388,891)(389,890)(390,889)(391,888)(392,887)(393,886)(394,885)(395,884)(396,883)(397,882)(398,881)(399,880)(400,879)(401,878)(402,877)(403,876)(404,875)(405,874)(406,873)(407,872)(408,871)(409,870)(410,869)(411,868)(412,867)(413,866)(414,865)(415,864)(416,863)(417,862)(418,861)(419,860)(420,859)(421,858)(422,857)(423,856)(424,855)(425,854)(426,853)(427,852)(428,851)(429,850)(430,849)(431,848)(432,847)(433,846)(434,845)(435,844)(436,843)(437,842)(438,841)(439,840)(440,839)(441,838)(442,837)(443,836)(444,835)(445,834)(446,833)(447,832)(448,831)(449,830)(450,829)(451,828)(452,827)(453,826)(454,825)(455,824)(456,823)(457,822)(458,821)(459,820)(460,819)(461,818)(462,817)(463,816)(464,815)(465,814)(466,813)(467,812)(468,811)(469,810)(470,809)(471,808)(472,807)(473,806)(474,805)(475,804)(476,803)(477,802)(478,801)(479,800)(480,799)(481,798)(482,797)(483,796)(484,795)(485,794)(486,793)(487,792)(488,791)(489,790)(490,789)(491,788)(492,787)(493,786)(494,785)(495,784)(496,783)(497,782)(498,781)(499,780)(500,779)(501,778)(502,777)(503,776)(504,775)(505,774)(506,773)(507,772)(508,771)(509,770)(510,769)(511,768)(512,767)(513,766)(514,765)(515,764)(516,763)(517,762)(518,761)(519,760)(520,759)(521,758)(522,757)(523,756)(524,755)(525,754)(526,753)(527,752)(528,751)(529,750)(530,749)(531,748)(532,747)(533,746)(534,745)(535,744)(536,743)(537,742)(538,741)(539,740)(540,739)(541,738)(542,737)(543,736)(544,735)(545,734)(546,733)(547,732)(548,731)(549,730)(550,729)(551,728)(552,727)(553,726)(554,725)(555,724)(556,723)(557,722)(558,721)(559,720)(560,719)(561,718)(562,717)(563,716)(564,715)(565,714)(566,713)(567,712)(568,711)(569,710)(570,709)(571,708)(572,707)(573,706)(574,705)(575,704)(576,703)(577,702)(578,701)(579,700)(580,699)(581,698)(582,697)(583,696)(584,695)(585,694)(586,693)(587,692)(588,691)(589,690)(590,689)(591,688)(592,687)(593,686)(594,685)(595,684)(596,683)(597,682)(598,681)(599,680)(600,679)(601,678)(602,677)(603,676)(604,675)(605,674)(606,673)(607,672)(608,671)(609,670)(610,669)(611,668)(612,667)(613,666)(614,665)(615,664)(616,663)(617,662)(618,661)(619,660)(620,659)(621,658)(622,657)(623,656)(624,655)(625,654)(626,653)(627,652)(628,651)(629,650)(630,649)(631,648)(632,647)(633,646)(634,645)(635,644)(636,643)(637,642)(638,641)(639,640)
Polycyclic presentation:
2,1277|b^a=b^1276
Conjugacy classes & character table
640 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2554, 1);
Finite Group Databasebeta