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D11979 #72224006
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1340 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340);(2,9)(3,8)(4,7)(5,6)(11,1340)(12,1339)(13,1338)(14,1337)(15,1336)(16,1335)(17,1334)(18,1333)(19,1332)(20,1331)(21,1330)(22,1329)(23,1328)(24,1327)(25,1326)(26,1325)(27,1324)(28,1323)(29,1322)(30,1321)(31,1320)(32,1319)(33,1318)(34,1317)(35,1316)(36,1315)(37,1314)(38,1313)(39,1312)(40,1311)(41,1310)(42,1309)(43,1308)(44,1307)(45,1306)(46,1305)(47,1304)(48,1303)(49,1302)(50,1301)(51,1300)(52,1299)(53,1298)(54,1297)(55,1296)(56,1295)(57,1294)(58,1293)(59,1292)(60,1291)(61,1290)(62,1289)(63,1288)(64,1287)(65,1286)(66,1285)(67,1284)(68,1283)(69,1282)(70,1281)(71,1280)(72,1279)(73,1278)(74,1277)(75,1276)(76,1275)(77,1274)(78,1273)(79,1272)(80,1271)(81,1270)(82,1269)(83,1268)(84,1267)(85,1266)(86,1265)(87,1264)(88,1263)(89,1262)(90,1261)(91,1260)(92,1259)(93,1258)(94,1257)(95,1256)(96,1255)(97,1254)(98,1253)(99,1252)(100,1251)(101,1250)(102,1249)(103,1248)(104,1247)(105,1246)(106,1245)(107,1244)(108,1243)(109,1242)(110,1241)(111,1240)(112,1239)(113,1238)(114,1237)(115,1236)(116,1235)(117,1234)(118,1233)(119,1232)(120,1231)(121,1230)(122,1229)(123,1228)(124,1227)(125,1226)(126,1225)(127,1224)(128,1223)(129,1222)(130,1221)(131,1220)(132,1219)(133,1218)(134,1217)(135,1216)(136,1215)(137,1214)(138,1213)(139,1212)(140,1211)(141,1210)(142,1209)(143,1208)(144,1207)(145,1206)(146,1205)(147,1204)(148,1203)(149,1202)(150,1201)(151,1200)(152,1199)(153,1198)(154,1197)(155,1196)(156,1195)(157,1194)(158,1193)(159,1192)(160,1191)(161,1190)(162,1189)(163,1188)(164,1187)(165,1186)(166,1185)(167,1184)(168,1183)(169,1182)(170,1181)(171,1180)(172,1179)(173,1178)(174,1177)(175,1176)(176,1175)(177,1174)(178,1173)(179,1172)(180,1171)(181,1170)(182,1169)(183,1168)(184,1167)(185,1166)(186,1165)(187,1164)(188,1163)(189,1162)(190,1161)(191,1160)(192,1159)(193,1158)(194,1157)(195,1156)(196,1155)(197,1154)(198,1153)(199,1152)(200,1151)(201,1150)(202,1149)(203,1148)(204,1147)(205,1146)(206,1145)(207,1144)(208,1143)(209,1142)(210,1141)(211,1140)(212,1139)(213,1138)(214,1137)(215,1136)(216,1135)(217,1134)(218,1133)(219,1132)(220,1131)(221,1130)(222,1129)(223,1128)(224,1127)(225,1126)(226,1125)(227,1124)(228,1123)(229,1122)(230,1121)(231,1120)(232,1119)(233,1118)(234,1117)(235,1116)(236,1115)(237,1114)(238,1113)(239,1112)(240,1111)(241,1110)(242,1109)(243,1108)(244,1107)(245,1106)(246,1105)(247,1104)(248,1103)(249,1102)(250,1101)(251,1100)(252,1099)(253,1098)(254,1097)(255,1096)(256,1095)(257,1094)(258,1093)(259,1092)(260,1091)(261,1090)(262,1089)(263,1088)(264,1087)(265,1086)(266,1085)(267,1084)(268,1083)(269,1082)(270,1081)(271,1080)(272,1079)(273,1078)(274,1077)(275,1076)(276,1075)(277,1074)(278,1073)(279,1072)(280,1071)(281,1070)(282,1069)(283,1068)(284,1067)(285,1066)(286,1065)(287,1064)(288,1063)(289,1062)(290,1061)(291,1060)(292,1059)(293,1058)(294,1057)(295,1056)(296,1055)(297,1054)(298,1053)(299,1052)(300,1051)(301,1050)(302,1049)(303,1048)(304,1047)(305,1046)(306,1045)(307,1044)(308,1043)(309,1042)(310,1041)(311,1040)(312,1039)(313,1038)(314,1037)(315,1036)(316,1035)(317,1034)(318,1033)(319,1032)(320,1031)(321,1030)(322,1029)(323,1028)(324,1027)(325,1026)(326,1025)(327,1024)(328,1023)(329,1022)(330,1021)(331,1020)(332,1019)(333,1018)(334,1017)(335,1016)(336,1015)(337,1014)(338,1013)(339,1012)(340,1011)(341,1010)(342,1009)(343,1008)(344,1007)(345,1006)(346,1005)(347,1004)(348,1003)(349,1002)(350,1001)(351,1000)(352,999)(353,998)(354,997)(355,996)(356,995)(357,994)(358,993)(359,992)(360,991)(361,990)(362,989)(363,988)(364,987)(365,986)(366,985)(367,984)(368,983)(369,982)(370,981)(371,980)(372,979)(373,978)(374,977)(375,976)(376,975)(377,974)(378,973)(379,972)(380,971)(381,970)(382,969)(383,968)(384,967)(385,966)(386,965)(387,964)(388,963)(389,962)(390,961)(391,960)(392,959)(393,958)(394,957)(395,956)(396,955)(397,954)(398,953)(399,952)(400,951)(401,950)(402,949)(403,948)(404,947)(405,946)(406,945)(407,944)(408,943)(409,942)(410,941)(411,940)(412,939)(413,938)(414,937)(415,936)(416,935)(417,934)(418,933)(419,932)(420,931)(421,930)(422,929)(423,928)(424,927)(425,926)(426,925)(427,924)(428,923)(429,922)(430,921)(431,920)(432,919)(433,918)(434,917)(435,916)(436,915)(437,914)(438,913)(439,912)(440,911)(441,910)(442,909)(443,908)(444,907)(445,906)(446,905)(447,904)(448,903)(449,902)(450,901)(451,900)(452,899)(453,898)(454,897)(455,896)(456,895)(457,894)(458,893)(459,892)(460,891)(461,890)(462,889)(463,888)(464,887)(465,886)(466,885)(467,884)(468,883)(469,882)(470,881)(471,880)(472,879)(473,878)(474,877)(475,876)(476,875)(477,874)(478,873)(479,872)(480,871)(481,870)(482,869)(483,868)(484,867)(485,866)(486,865)(487,864)(488,863)(489,862)(490,861)(491,860)(492,859)(493,858)(494,857)(495,856)(496,855)(497,854)(498,853)(499,852)(500,851)(501,850)(502,849)(503,848)(504,847)(505,846)(506,845)(507,844)(508,843)(509,842)(510,841)(511,840)(512,839)(513,838)(514,837)(515,836)(516,835)(517,834)(518,833)(519,832)(520,831)(521,830)(522,829)(523,828)(524,827)(525,826)(526,825)(527,824)(528,823)(529,822)(530,821)(531,820)(532,819)(533,818)(534,817)(535,816)(536,815)(537,814)(538,813)(539,812)(540,811)(541,810)(542,809)(543,808)(544,807)(545,806)(546,805)(547,804)(548,803)(549,802)(550,801)(551,800)(552,799)(553,798)(554,797)(555,796)(556,795)(557,794)(558,793)(559,792)(560,791)(561,790)(562,789)(563,788)(564,787)(565,786)(566,785)(567,784)(568,783)(569,782)(570,781)(571,780)(572,779)(573,778)(574,777)(575,776)(576,775)(577,774)(578,773)(579,772)(580,771)(581,770)(582,769)(583,768)(584,767)(585,766)(586,765)(587,764)(588,763)(589,762)(590,761)(591,760)(592,759)(593,758)(594,757)(595,756)(596,755)(597,754)(598,753)(599,752)(600,751)(601,750)(602,749)(603,748)(604,747)(605,746)(606,745)(607,744)(608,743)(609,742)(610,741)(611,740)(612,739)(613,738)(614,737)(615,736)(616,735)(617,734)(618,733)(619,732)(620,731)(621,730)(622,729)(623,728)(624,727)(625,726)(626,725)(627,724)(628,723)(629,722)(630,721)(631,720)(632,719)(633,718)(634,717)(635,716)(636,715)(637,714)(638,713)(639,712)(640,711)(641,710)(642,709)(643,708)(644,707)(645,706)(646,705)(647,704)(648,703)(649,702)(650,701)(651,700)(652,699)(653,698)(654,697)(655,696)(656,695)(657,694)(658,693)(659,692)(660,691)(661,690)(662,689)(663,688)(664,687)(665,686)(666,685)(667,684)(668,683)(669,682)(670,681)(671,680)(672,679)(673,678)(674,677)(675,676)
Polycyclic presentation:
2,3,11,3,11^2|b^3=d,c^11=e,e^11=f,b^a=b^2d^2,c^a=c^10e^10f^10,d^a=d^2,e^a=e^10f^10,f^a=f^10
Conjugacy classes & character table
5991 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", "f");;
gap> coll := SingleCollector(F, [2, 3, 11, 3, 11, 11]);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.5);;
gap> SetPower(coll, 5, F.6);;
gap> SetConjugate(coll, 2, 1, F.2^2*F.4^2);;
gap> SetConjugate(coll, 3, 1, F.3^10*F.5^10*F.6^10);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^10*F.6^10);;
gap> SetConjugate(coll, 6, 1, F.6^10);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta