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Dic7818 #72272243
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1314 points:
(1,2,3,4)(5,8,7,6)(9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314);(1,5,3,7)(2,6,4,8)(10,11)(13,1314)(14,1313)(15,1312)(16,1311)(17,1310)(18,1309)(19,1308)(20,1307)(21,1306)(22,1305)(23,1304)(24,1303)(25,1302)(26,1301)(27,1300)(28,1299)(29,1298)(30,1297)(31,1296)(32,1295)(33,1294)(34,1293)(35,1292)(36,1291)(37,1290)(38,1289)(39,1288)(40,1287)(41,1286)(42,1285)(43,1284)(44,1283)(45,1282)(46,1281)(47,1280)(48,1279)(49,1278)(50,1277)(51,1276)(52,1275)(53,1274)(54,1273)(55,1272)(56,1271)(57,1270)(58,1269)(59,1268)(60,1267)(61,1266)(62,1265)(63,1264)(64,1263)(65,1262)(66,1261)(67,1260)(68,1259)(69,1258)(70,1257)(71,1256)(72,1255)(73,1254)(74,1253)(75,1252)(76,1251)(77,1250)(78,1249)(79,1248)(80,1247)(81,1246)(82,1245)(83,1244)(84,1243)(85,1242)(86,1241)(87,1240)(88,1239)(89,1238)(90,1237)(91,1236)(92,1235)(93,1234)(94,1233)(95,1232)(96,1231)(97,1230)(98,1229)(99,1228)(100,1227)(101,1226)(102,1225)(103,1224)(104,1223)(105,1222)(106,1221)(107,1220)(108,1219)(109,1218)(110,1217)(111,1216)(112,1215)(113,1214)(114,1213)(115,1212)(116,1211)(117,1210)(118,1209)(119,1208)(120,1207)(121,1206)(122,1205)(123,1204)(124,1203)(125,1202)(126,1201)(127,1200)(128,1199)(129,1198)(130,1197)(131,1196)(132,1195)(133,1194)(134,1193)(135,1192)(136,1191)(137,1190)(138,1189)(139,1188)(140,1187)(141,1186)(142,1185)(143,1184)(144,1183)(145,1182)(146,1181)(147,1180)(148,1179)(149,1178)(150,1177)(151,1176)(152,1175)(153,1174)(154,1173)(155,1172)(156,1171)(157,1170)(158,1169)(159,1168)(160,1167)(161,1166)(162,1165)(163,1164)(164,1163)(165,1162)(166,1161)(167,1160)(168,1159)(169,1158)(170,1157)(171,1156)(172,1155)(173,1154)(174,1153)(175,1152)(176,1151)(177,1150)(178,1149)(179,1148)(180,1147)(181,1146)(182,1145)(183,1144)(184,1143)(185,1142)(186,1141)(187,1140)(188,1139)(189,1138)(190,1137)(191,1136)(192,1135)(193,1134)(194,1133)(195,1132)(196,1131)(197,1130)(198,1129)(199,1128)(200,1127)(201,1126)(202,1125)(203,1124)(204,1123)(205,1122)(206,1121)(207,1120)(208,1119)(209,1118)(210,1117)(211,1116)(212,1115)(213,1114)(214,1113)(215,1112)(216,1111)(217,1110)(218,1109)(219,1108)(220,1107)(221,1106)(222,1105)(223,1104)(224,1103)(225,1102)(226,1101)(227,1100)(228,1099)(229,1098)(230,1097)(231,1096)(232,1095)(233,1094)(234,1093)(235,1092)(236,1091)(237,1090)(238,1089)(239,1088)(240,1087)(241,1086)(242,1085)(243,1084)(244,1083)(245,1082)(246,1081)(247,1080)(248,1079)(249,1078)(250,1077)(251,1076)(252,1075)(253,1074)(254,1073)(255,1072)(256,1071)(257,1070)(258,1069)(259,1068)(260,1067)(261,1066)(262,1065)(263,1064)(264,1063)(265,1062)(266,1061)(267,1060)(268,1059)(269,1058)(270,1057)(271,1056)(272,1055)(273,1054)(274,1053)(275,1052)(276,1051)(277,1050)(278,1049)(279,1048)(280,1047)(281,1046)(282,1045)(283,1044)(284,1043)(285,1042)(286,1041)(287,1040)(288,1039)(289,1038)(290,1037)(291,1036)(292,1035)(293,1034)(294,1033)(295,1032)(296,1031)(297,1030)(298,1029)(299,1028)(300,1027)(301,1026)(302,1025)(303,1024)(304,1023)(305,1022)(306,1021)(307,1020)(308,1019)(309,1018)(310,1017)(311,1016)(312,1015)(313,1014)(314,1013)(315,1012)(316,1011)(317,1010)(318,1009)(319,1008)(320,1007)(321,1006)(322,1005)(323,1004)(324,1003)(325,1002)(326,1001)(327,1000)(328,999)(329,998)(330,997)(331,996)(332,995)(333,994)(334,993)(335,992)(336,991)(337,990)(338,989)(339,988)(340,987)(341,986)(342,985)(343,984)(344,983)(345,982)(346,981)(347,980)(348,979)(349,978)(350,977)(351,976)(352,975)(353,974)(354,973)(355,972)(356,971)(357,970)(358,969)(359,968)(360,967)(361,966)(362,965)(363,964)(364,963)(365,962)(366,961)(367,960)(368,959)(369,958)(370,957)(371,956)(372,955)(373,954)(374,953)(375,952)(376,951)(377,950)(378,949)(379,948)(380,947)(381,946)(382,945)(383,944)(384,943)(385,942)(386,941)(387,940)(388,939)(389,938)(390,937)(391,936)(392,935)(393,934)(394,933)(395,932)(396,931)(397,930)(398,929)(399,928)(400,927)(401,926)(402,925)(403,924)(404,923)(405,922)(406,921)(407,920)(408,919)(409,918)(410,917)(411,916)(412,915)(413,914)(414,913)(415,912)(416,911)(417,910)(418,909)(419,908)(420,907)(421,906)(422,905)(423,904)(424,903)(425,902)(426,901)(427,900)(428,899)(429,898)(430,897)(431,896)(432,895)(433,894)(434,893)(435,892)(436,891)(437,890)(438,889)(439,888)(440,887)(441,886)(442,885)(443,884)(444,883)(445,882)(446,881)(447,880)(448,879)(449,878)(450,877)(451,876)(452,875)(453,874)(454,873)(455,872)(456,871)(457,870)(458,869)(459,868)(460,867)(461,866)(462,865)(463,864)(464,863)(465,862)(466,861)(467,860)(468,859)(469,858)(470,857)(471,856)(472,855)(473,854)(474,853)(475,852)(476,851)(477,850)(478,849)(479,848)(480,847)(481,846)(482,845)(483,844)(484,843)(485,842)(486,841)(487,840)(488,839)(489,838)(490,837)(491,836)(492,835)(493,834)(494,833)(495,832)(496,831)(497,830)(498,829)(499,828)(500,827)(501,826)(502,825)(503,824)(504,823)(505,822)(506,821)(507,820)(508,819)(509,818)(510,817)(511,816)(512,815)(513,814)(514,813)(515,812)(516,811)(517,810)(518,809)(519,808)(520,807)(521,806)(522,805)(523,804)(524,803)(525,802)(526,801)(527,800)(528,799)(529,798)(530,797)(531,796)(532,795)(533,794)(534,793)(535,792)(536,791)(537,790)(538,789)(539,788)(540,787)(541,786)(542,785)(543,784)(544,783)(545,782)(546,781)(547,780)(548,779)(549,778)(550,777)(551,776)(552,775)(553,774)(554,773)(555,772)(556,771)(557,770)(558,769)(559,768)(560,767)(561,766)(562,765)(563,764)(564,763)(565,762)(566,761)(567,760)(568,759)(569,758)(570,757)(571,756)(572,755)(573,754)(574,753)(575,752)(576,751)(577,750)(578,749)(579,748)(580,747)(581,746)(582,745)(583,744)(584,743)(585,742)(586,741)(587,740)(588,739)(589,738)(590,737)(591,736)(592,735)(593,734)(594,733)(595,732)(596,731)(597,730)(598,729)(599,728)(600,727)(601,726)(602,725)(603,724)(604,723)(605,722)(606,721)(607,720)(608,719)(609,718)(610,717)(611,716)(612,715)(613,714)(614,713)(615,712)(616,711)(617,710)(618,709)(619,708)(620,707)(621,706)(622,705)(623,704)(624,703)(625,702)(626,701)(627,700)(628,699)(629,698)(630,697)(631,696)(632,695)(633,694)(634,693)(635,692)(636,691)(637,690)(638,689)(639,688)(640,687)(641,686)(642,685)(643,684)(644,683)(645,682)(646,681)(647,680)(648,679)(649,678)(650,677)(651,676)(652,675)(653,674)(654,673)(655,672)(656,671)(657,670)(658,669)(659,668)(660,667)(661,666)(662,665)(663,664)
Polycyclic presentation:
2^3,3,1303|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^1302
Conjugacy classes & character table
7821 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 3, 1303]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^1302);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta