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D10328 #35207696
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1299 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);(2,8)(3,7)(4,6)(10,1299)(11,1298)(12,1297)(13,1296)(14,1295)(15,1294)(16,1293)(17,1292)(18,1291)(19,1290)(20,1289)(21,1288)(22,1287)(23,1286)(24,1285)(25,1284)(26,1283)(27,1282)(28,1281)(29,1280)(30,1279)(31,1278)(32,1277)(33,1276)(34,1275)(35,1274)(36,1273)(37,1272)(38,1271)(39,1270)(40,1269)(41,1268)(42,1267)(43,1266)(44,1265)(45,1264)(46,1263)(47,1262)(48,1261)(49,1260)(50,1259)(51,1258)(52,1257)(53,1256)(54,1255)(55,1254)(56,1253)(57,1252)(58,1251)(59,1250)(60,1249)(61,1248)(62,1247)(63,1246)(64,1245)(65,1244)(66,1243)(67,1242)(68,1241)(69,1240)(70,1239)(71,1238)(72,1237)(73,1236)(74,1235)(75,1234)(76,1233)(77,1232)(78,1231)(79,1230)(80,1229)(81,1228)(82,1227)(83,1226)(84,1225)(85,1224)(86,1223)(87,1222)(88,1221)(89,1220)(90,1219)(91,1218)(92,1217)(93,1216)(94,1215)(95,1214)(96,1213)(97,1212)(98,1211)(99,1210)(100,1209)(101,1208)(102,1207)(103,1206)(104,1205)(105,1204)(106,1203)(107,1202)(108,1201)(109,1200)(110,1199)(111,1198)(112,1197)(113,1196)(114,1195)(115,1194)(116,1193)(117,1192)(118,1191)(119,1190)(120,1189)(121,1188)(122,1187)(123,1186)(124,1185)(125,1184)(126,1183)(127,1182)(128,1181)(129,1180)(130,1179)(131,1178)(132,1177)(133,1176)(134,1175)(135,1174)(136,1173)(137,1172)(138,1171)(139,1170)(140,1169)(141,1168)(142,1167)(143,1166)(144,1165)(145,1164)(146,1163)(147,1162)(148,1161)(149,1160)(150,1159)(151,1158)(152,1157)(153,1156)(154,1155)(155,1154)(156,1153)(157,1152)(158,1151)(159,1150)(160,1149)(161,1148)(162,1147)(163,1146)(164,1145)(165,1144)(166,1143)(167,1142)(168,1141)(169,1140)(170,1139)(171,1138)(172,1137)(173,1136)(174,1135)(175,1134)(176,1133)(177,1132)(178,1131)(179,1130)(180,1129)(181,1128)(182,1127)(183,1126)(184,1125)(185,1124)(186,1123)(187,1122)(188,1121)(189,1120)(190,1119)(191,1118)(192,1117)(193,1116)(194,1115)(195,1114)(196,1113)(197,1112)(198,1111)(199,1110)(200,1109)(201,1108)(202,1107)(203,1106)(204,1105)(205,1104)(206,1103)(207,1102)(208,1101)(209,1100)(210,1099)(211,1098)(212,1097)(213,1096)(214,1095)(215,1094)(216,1093)(217,1092)(218,1091)(219,1090)(220,1089)(221,1088)(222,1087)(223,1086)(224,1085)(225,1084)(226,1083)(227,1082)(228,1081)(229,1080)(230,1079)(231,1078)(232,1077)(233,1076)(234,1075)(235,1074)(236,1073)(237,1072)(238,1071)(239,1070)(240,1069)(241,1068)(242,1067)(243,1066)(244,1065)(245,1064)(246,1063)(247,1062)(248,1061)(249,1060)(250,1059)(251,1058)(252,1057)(253,1056)(254,1055)(255,1054)(256,1053)(257,1052)(258,1051)(259,1050)(260,1049)(261,1048)(262,1047)(263,1046)(264,1045)(265,1044)(266,1043)(267,1042)(268,1041)(269,1040)(270,1039)(271,1038)(272,1037)(273,1036)(274,1035)(275,1034)(276,1033)(277,1032)(278,1031)(279,1030)(280,1029)(281,1028)(282,1027)(283,1026)(284,1025)(285,1024)(286,1023)(287,1022)(288,1021)(289,1020)(290,1019)(291,1018)(292,1017)(293,1016)(294,1015)(295,1014)(296,1013)(297,1012)(298,1011)(299,1010)(300,1009)(301,1008)(302,1007)(303,1006)(304,1005)(305,1004)(306,1003)(307,1002)(308,1001)(309,1000)(310,999)(311,998)(312,997)(313,996)(314,995)(315,994)(316,993)(317,992)(318,991)(319,990)(320,989)(321,988)(322,987)(323,986)(324,985)(325,984)(326,983)(327,982)(328,981)(329,980)(330,979)(331,978)(332,977)(333,976)(334,975)(335,974)(336,973)(337,972)(338,971)(339,970)(340,969)(341,968)(342,967)(343,966)(344,965)(345,964)(346,963)(347,962)(348,961)(349,960)(350,959)(351,958)(352,957)(353,956)(354,955)(355,954)(356,953)(357,952)(358,951)(359,950)(360,949)(361,948)(362,947)(363,946)(364,945)(365,944)(366,943)(367,942)(368,941)(369,940)(370,939)(371,938)(372,937)(373,936)(374,935)(375,934)(376,933)(377,932)(378,931)(379,930)(380,929)(381,928)(382,927)(383,926)(384,925)(385,924)(386,923)(387,922)(388,921)(389,920)(390,919)(391,918)(392,917)(393,916)(394,915)(395,914)(396,913)(397,912)(398,911)(399,910)(400,909)(401,908)(402,907)(403,906)(404,905)(405,904)(406,903)(407,902)(408,901)(409,900)(410,899)(411,898)(412,897)(413,896)(414,895)(415,894)(416,893)(417,892)(418,891)(419,890)(420,889)(421,888)(422,887)(423,886)(424,885)(425,884)(426,883)(427,882)(428,881)(429,880)(430,879)(431,878)(432,877)(433,876)(434,875)(435,874)(436,873)(437,872)(438,871)(439,870)(440,869)(441,868)(442,867)(443,866)(444,865)(445,864)(446,863)(447,862)(448,861)(449,860)(450,859)(451,858)(452,857)(453,856)(454,855)(455,854)(456,853)(457,852)(458,851)(459,850)(460,849)(461,848)(462,847)(463,846)(464,845)(465,844)(466,843)(467,842)(468,841)(469,840)(470,839)(471,838)(472,837)(473,836)(474,835)(475,834)(476,833)(477,832)(478,831)(479,830)(480,829)(481,828)(482,827)(483,826)(484,825)(485,824)(486,823)(487,822)(488,821)(489,820)(490,819)(491,818)(492,817)(493,816)(494,815)(495,814)(496,813)(497,812)(498,811)(499,810)(500,809)(501,808)(502,807)(503,806)(504,805)(505,804)(506,803)(507,802)(508,801)(509,800)(510,799)(511,798)(512,797)(513,796)(514,795)(515,794)(516,793)(517,792)(518,791)(519,790)(520,789)(521,788)(522,787)(523,786)(524,785)(525,784)(526,783)(527,782)(528,781)(529,780)(530,779)(531,778)(532,777)(533,776)(534,775)(535,774)(536,773)(537,772)(538,771)(539,770)(540,769)(541,768)(542,767)(543,766)(544,765)(545,764)(546,763)(547,762)(548,761)(549,760)(550,759)(551,758)(552,757)(553,756)(554,755)(555,754)(556,753)(557,752)(558,751)(559,750)(560,749)(561,748)(562,747)(563,746)(564,745)(565,744)(566,743)(567,742)(568,741)(569,740)(570,739)(571,738)(572,737)(573,736)(574,735)(575,734)(576,733)(577,732)(578,731)(579,730)(580,729)(581,728)(582,727)(583,726)(584,725)(585,724)(586,723)(587,722)(588,721)(589,720)(590,719)(591,718)(592,717)(593,716)(594,715)(595,714)(596,713)(597,712)(598,711)(599,710)(600,709)(601,708)(602,707)(603,706)(604,705)(605,704)(606,703)(607,702)(608,701)(609,700)(610,699)(611,698)(612,697)(613,696)(614,695)(615,694)(616,693)(617,692)(618,691)(619,690)(620,689)(621,688)(622,687)(623,686)(624,685)(625,684)(626,683)(627,682)(628,681)(629,680)(630,679)(631,678)(632,677)(633,676)(634,675)(635,674)(636,673)(637,672)(638,671)(639,670)(640,669)(641,668)(642,667)(643,666)(644,665)(645,664)(646,663)(647,662)(648,661)(649,660)(650,659)(651,658)(652,657)(653,656)(654,655)
Polycyclic presentation:
2^4,1291|c^2=d,b^a=bc,c^a=cd,e^a=e^1290,c^b=cd,e^b=e^1290
Conjugacy classes & character table
5167 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20656, 26);
Finite Group Databasebeta