← Prev (#35209603) Next (#35209605) →
D10408 #35209604
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1309 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);(2,8)(3,7)(4,6)(10,1309)(11,1308)(12,1307)(13,1306)(14,1305)(15,1304)(16,1303)(17,1302)(18,1301)(19,1300)(20,1299)(21,1298)(22,1297)(23,1296)(24,1295)(25,1294)(26,1293)(27,1292)(28,1291)(29,1290)(30,1289)(31,1288)(32,1287)(33,1286)(34,1285)(35,1284)(36,1283)(37,1282)(38,1281)(39,1280)(40,1279)(41,1278)(42,1277)(43,1276)(44,1275)(45,1274)(46,1273)(47,1272)(48,1271)(49,1270)(50,1269)(51,1268)(52,1267)(53,1266)(54,1265)(55,1264)(56,1263)(57,1262)(58,1261)(59,1260)(60,1259)(61,1258)(62,1257)(63,1256)(64,1255)(65,1254)(66,1253)(67,1252)(68,1251)(69,1250)(70,1249)(71,1248)(72,1247)(73,1246)(74,1245)(75,1244)(76,1243)(77,1242)(78,1241)(79,1240)(80,1239)(81,1238)(82,1237)(83,1236)(84,1235)(85,1234)(86,1233)(87,1232)(88,1231)(89,1230)(90,1229)(91,1228)(92,1227)(93,1226)(94,1225)(95,1224)(96,1223)(97,1222)(98,1221)(99,1220)(100,1219)(101,1218)(102,1217)(103,1216)(104,1215)(105,1214)(106,1213)(107,1212)(108,1211)(109,1210)(110,1209)(111,1208)(112,1207)(113,1206)(114,1205)(115,1204)(116,1203)(117,1202)(118,1201)(119,1200)(120,1199)(121,1198)(122,1197)(123,1196)(124,1195)(125,1194)(126,1193)(127,1192)(128,1191)(129,1190)(130,1189)(131,1188)(132,1187)(133,1186)(134,1185)(135,1184)(136,1183)(137,1182)(138,1181)(139,1180)(140,1179)(141,1178)(142,1177)(143,1176)(144,1175)(145,1174)(146,1173)(147,1172)(148,1171)(149,1170)(150,1169)(151,1168)(152,1167)(153,1166)(154,1165)(155,1164)(156,1163)(157,1162)(158,1161)(159,1160)(160,1159)(161,1158)(162,1157)(163,1156)(164,1155)(165,1154)(166,1153)(167,1152)(168,1151)(169,1150)(170,1149)(171,1148)(172,1147)(173,1146)(174,1145)(175,1144)(176,1143)(177,1142)(178,1141)(179,1140)(180,1139)(181,1138)(182,1137)(183,1136)(184,1135)(185,1134)(186,1133)(187,1132)(188,1131)(189,1130)(190,1129)(191,1128)(192,1127)(193,1126)(194,1125)(195,1124)(196,1123)(197,1122)(198,1121)(199,1120)(200,1119)(201,1118)(202,1117)(203,1116)(204,1115)(205,1114)(206,1113)(207,1112)(208,1111)(209,1110)(210,1109)(211,1108)(212,1107)(213,1106)(214,1105)(215,1104)(216,1103)(217,1102)(218,1101)(219,1100)(220,1099)(221,1098)(222,1097)(223,1096)(224,1095)(225,1094)(226,1093)(227,1092)(228,1091)(229,1090)(230,1089)(231,1088)(232,1087)(233,1086)(234,1085)(235,1084)(236,1083)(237,1082)(238,1081)(239,1080)(240,1079)(241,1078)(242,1077)(243,1076)(244,1075)(245,1074)(246,1073)(247,1072)(248,1071)(249,1070)(250,1069)(251,1068)(252,1067)(253,1066)(254,1065)(255,1064)(256,1063)(257,1062)(258,1061)(259,1060)(260,1059)(261,1058)(262,1057)(263,1056)(264,1055)(265,1054)(266,1053)(267,1052)(268,1051)(269,1050)(270,1049)(271,1048)(272,1047)(273,1046)(274,1045)(275,1044)(276,1043)(277,1042)(278,1041)(279,1040)(280,1039)(281,1038)(282,1037)(283,1036)(284,1035)(285,1034)(286,1033)(287,1032)(288,1031)(289,1030)(290,1029)(291,1028)(292,1027)(293,1026)(294,1025)(295,1024)(296,1023)(297,1022)(298,1021)(299,1020)(300,1019)(301,1018)(302,1017)(303,1016)(304,1015)(305,1014)(306,1013)(307,1012)(308,1011)(309,1010)(310,1009)(311,1008)(312,1007)(313,1006)(314,1005)(315,1004)(316,1003)(317,1002)(318,1001)(319,1000)(320,999)(321,998)(322,997)(323,996)(324,995)(325,994)(326,993)(327,992)(328,991)(329,990)(330,989)(331,988)(332,987)(333,986)(334,985)(335,984)(336,983)(337,982)(338,981)(339,980)(340,979)(341,978)(342,977)(343,976)(344,975)(345,974)(346,973)(347,972)(348,971)(349,970)(350,969)(351,968)(352,967)(353,966)(354,965)(355,964)(356,963)(357,962)(358,961)(359,960)(360,959)(361,958)(362,957)(363,956)(364,955)(365,954)(366,953)(367,952)(368,951)(369,950)(370,949)(371,948)(372,947)(373,946)(374,945)(375,944)(376,943)(377,942)(378,941)(379,940)(380,939)(381,938)(382,937)(383,936)(384,935)(385,934)(386,933)(387,932)(388,931)(389,930)(390,929)(391,928)(392,927)(393,926)(394,925)(395,924)(396,923)(397,922)(398,921)(399,920)(400,919)(401,918)(402,917)(403,916)(404,915)(405,914)(406,913)(407,912)(408,911)(409,910)(410,909)(411,908)(412,907)(413,906)(414,905)(415,904)(416,903)(417,902)(418,901)(419,900)(420,899)(421,898)(422,897)(423,896)(424,895)(425,894)(426,893)(427,892)(428,891)(429,890)(430,889)(431,888)(432,887)(433,886)(434,885)(435,884)(436,883)(437,882)(438,881)(439,880)(440,879)(441,878)(442,877)(443,876)(444,875)(445,874)(446,873)(447,872)(448,871)(449,870)(450,869)(451,868)(452,867)(453,866)(454,865)(455,864)(456,863)(457,862)(458,861)(459,860)(460,859)(461,858)(462,857)(463,856)(464,855)(465,854)(466,853)(467,852)(468,851)(469,850)(470,849)(471,848)(472,847)(473,846)(474,845)(475,844)(476,843)(477,842)(478,841)(479,840)(480,839)(481,838)(482,837)(483,836)(484,835)(485,834)(486,833)(487,832)(488,831)(489,830)(490,829)(491,828)(492,827)(493,826)(494,825)(495,824)(496,823)(497,822)(498,821)(499,820)(500,819)(501,818)(502,817)(503,816)(504,815)(505,814)(506,813)(507,812)(508,811)(509,810)(510,809)(511,808)(512,807)(513,806)(514,805)(515,804)(516,803)(517,802)(518,801)(519,800)(520,799)(521,798)(522,797)(523,796)(524,795)(525,794)(526,793)(527,792)(528,791)(529,790)(530,789)(531,788)(532,787)(533,786)(534,785)(535,784)(536,783)(537,782)(538,781)(539,780)(540,779)(541,778)(542,777)(543,776)(544,775)(545,774)(546,773)(547,772)(548,771)(549,770)(550,769)(551,768)(552,767)(553,766)(554,765)(555,764)(556,763)(557,762)(558,761)(559,760)(560,759)(561,758)(562,757)(563,756)(564,755)(565,754)(566,753)(567,752)(568,751)(569,750)(570,749)(571,748)(572,747)(573,746)(574,745)(575,744)(576,743)(577,742)(578,741)(579,740)(580,739)(581,738)(582,737)(583,736)(584,735)(585,734)(586,733)(587,732)(588,731)(589,730)(590,729)(591,728)(592,727)(593,726)(594,725)(595,724)(596,723)(597,722)(598,721)(599,720)(600,719)(601,718)(602,717)(603,716)(604,715)(605,714)(606,713)(607,712)(608,711)(609,710)(610,709)(611,708)(612,707)(613,706)(614,705)(615,704)(616,703)(617,702)(618,701)(619,700)(620,699)(621,698)(622,697)(623,696)(624,695)(625,694)(626,693)(627,692)(628,691)(629,690)(630,689)(631,688)(632,687)(633,686)(634,685)(635,684)(636,683)(637,682)(638,681)(639,680)(640,679)(641,678)(642,677)(643,676)(644,675)(645,674)(646,673)(647,672)(648,671)(649,670)(650,669)(651,668)(652,667)(653,666)(654,665)(655,664)(656,663)(657,662)(658,661)(659,660)
Polycyclic presentation:
2^4,1301|c^2=d,b^a=bc,c^a=cd,e^a=e^1300,c^b=cd,e^b=e^1300
Conjugacy classes & character table
5207 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20816, 26);
Finite Group Databasebeta