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Dic2746 #24926899
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1381 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381);(1,5,3,7)(2,6,4,8)(10,1381)(11,1380)(12,1379)(13,1378)(14,1377)(15,1376)(16,1375)(17,1374)(18,1373)(19,1372)(20,1371)(21,1370)(22,1369)(23,1368)(24,1367)(25,1366)(26,1365)(27,1364)(28,1363)(29,1362)(30,1361)(31,1360)(32,1359)(33,1358)(34,1357)(35,1356)(36,1355)(37,1354)(38,1353)(39,1352)(40,1351)(41,1350)(42,1349)(43,1348)(44,1347)(45,1346)(46,1345)(47,1344)(48,1343)(49,1342)(50,1341)(51,1340)(52,1339)(53,1338)(54,1337)(55,1336)(56,1335)(57,1334)(58,1333)(59,1332)(60,1331)(61,1330)(62,1329)(63,1328)(64,1327)(65,1326)(66,1325)(67,1324)(68,1323)(69,1322)(70,1321)(71,1320)(72,1319)(73,1318)(74,1317)(75,1316)(76,1315)(77,1314)(78,1313)(79,1312)(80,1311)(81,1310)(82,1309)(83,1308)(84,1307)(85,1306)(86,1305)(87,1304)(88,1303)(89,1302)(90,1301)(91,1300)(92,1299)(93,1298)(94,1297)(95,1296)(96,1295)(97,1294)(98,1293)(99,1292)(100,1291)(101,1290)(102,1289)(103,1288)(104,1287)(105,1286)(106,1285)(107,1284)(108,1283)(109,1282)(110,1281)(111,1280)(112,1279)(113,1278)(114,1277)(115,1276)(116,1275)(117,1274)(118,1273)(119,1272)(120,1271)(121,1270)(122,1269)(123,1268)(124,1267)(125,1266)(126,1265)(127,1264)(128,1263)(129,1262)(130,1261)(131,1260)(132,1259)(133,1258)(134,1257)(135,1256)(136,1255)(137,1254)(138,1253)(139,1252)(140,1251)(141,1250)(142,1249)(143,1248)(144,1247)(145,1246)(146,1245)(147,1244)(148,1243)(149,1242)(150,1241)(151,1240)(152,1239)(153,1238)(154,1237)(155,1236)(156,1235)(157,1234)(158,1233)(159,1232)(160,1231)(161,1230)(162,1229)(163,1228)(164,1227)(165,1226)(166,1225)(167,1224)(168,1223)(169,1222)(170,1221)(171,1220)(172,1219)(173,1218)(174,1217)(175,1216)(176,1215)(177,1214)(178,1213)(179,1212)(180,1211)(181,1210)(182,1209)(183,1208)(184,1207)(185,1206)(186,1205)(187,1204)(188,1203)(189,1202)(190,1201)(191,1200)(192,1199)(193,1198)(194,1197)(195,1196)(196,1195)(197,1194)(198,1193)(199,1192)(200,1191)(201,1190)(202,1189)(203,1188)(204,1187)(205,1186)(206,1185)(207,1184)(208,1183)(209,1182)(210,1181)(211,1180)(212,1179)(213,1178)(214,1177)(215,1176)(216,1175)(217,1174)(218,1173)(219,1172)(220,1171)(221,1170)(222,1169)(223,1168)(224,1167)(225,1166)(226,1165)(227,1164)(228,1163)(229,1162)(230,1161)(231,1160)(232,1159)(233,1158)(234,1157)(235,1156)(236,1155)(237,1154)(238,1153)(239,1152)(240,1151)(241,1150)(242,1149)(243,1148)(244,1147)(245,1146)(246,1145)(247,1144)(248,1143)(249,1142)(250,1141)(251,1140)(252,1139)(253,1138)(254,1137)(255,1136)(256,1135)(257,1134)(258,1133)(259,1132)(260,1131)(261,1130)(262,1129)(263,1128)(264,1127)(265,1126)(266,1125)(267,1124)(268,1123)(269,1122)(270,1121)(271,1120)(272,1119)(273,1118)(274,1117)(275,1116)(276,1115)(277,1114)(278,1113)(279,1112)(280,1111)(281,1110)(282,1109)(283,1108)(284,1107)(285,1106)(286,1105)(287,1104)(288,1103)(289,1102)(290,1101)(291,1100)(292,1099)(293,1098)(294,1097)(295,1096)(296,1095)(297,1094)(298,1093)(299,1092)(300,1091)(301,1090)(302,1089)(303,1088)(304,1087)(305,1086)(306,1085)(307,1084)(308,1083)(309,1082)(310,1081)(311,1080)(312,1079)(313,1078)(314,1077)(315,1076)(316,1075)(317,1074)(318,1073)(319,1072)(320,1071)(321,1070)(322,1069)(323,1068)(324,1067)(325,1066)(326,1065)(327,1064)(328,1063)(329,1062)(330,1061)(331,1060)(332,1059)(333,1058)(334,1057)(335,1056)(336,1055)(337,1054)(338,1053)(339,1052)(340,1051)(341,1050)(342,1049)(343,1048)(344,1047)(345,1046)(346,1045)(347,1044)(348,1043)(349,1042)(350,1041)(351,1040)(352,1039)(353,1038)(354,1037)(355,1036)(356,1035)(357,1034)(358,1033)(359,1032)(360,1031)(361,1030)(362,1029)(363,1028)(364,1027)(365,1026)(366,1025)(367,1024)(368,1023)(369,1022)(370,1021)(371,1020)(372,1019)(373,1018)(374,1017)(375,1016)(376,1015)(377,1014)(378,1013)(379,1012)(380,1011)(381,1010)(382,1009)(383,1008)(384,1007)(385,1006)(386,1005)(387,1004)(388,1003)(389,1002)(390,1001)(391,1000)(392,999)(393,998)(394,997)(395,996)(396,995)(397,994)(398,993)(399,992)(400,991)(401,990)(402,989)(403,988)(404,987)(405,986)(406,985)(407,984)(408,983)(409,982)(410,981)(411,980)(412,979)(413,978)(414,977)(415,976)(416,975)(417,974)(418,973)(419,972)(420,971)(421,970)(422,969)(423,968)(424,967)(425,966)(426,965)(427,964)(428,963)(429,962)(430,961)(431,960)(432,959)(433,958)(434,957)(435,956)(436,955)(437,954)(438,953)(439,952)(440,951)(441,950)(442,949)(443,948)(444,947)(445,946)(446,945)(447,944)(448,943)(449,942)(450,941)(451,940)(452,939)(453,938)(454,937)(455,936)(456,935)(457,934)(458,933)(459,932)(460,931)(461,930)(462,929)(463,928)(464,927)(465,926)(466,925)(467,924)(468,923)(469,922)(470,921)(471,920)(472,919)(473,918)(474,917)(475,916)(476,915)(477,914)(478,913)(479,912)(480,911)(481,910)(482,909)(483,908)(484,907)(485,906)(486,905)(487,904)(488,903)(489,902)(490,901)(491,900)(492,899)(493,898)(494,897)(495,896)(496,895)(497,894)(498,893)(499,892)(500,891)(501,890)(502,889)(503,888)(504,887)(505,886)(506,885)(507,884)(508,883)(509,882)(510,881)(511,880)(512,879)(513,878)(514,877)(515,876)(516,875)(517,874)(518,873)(519,872)(520,871)(521,870)(522,869)(523,868)(524,867)(525,866)(526,865)(527,864)(528,863)(529,862)(530,861)(531,860)(532,859)(533,858)(534,857)(535,856)(536,855)(537,854)(538,853)(539,852)(540,851)(541,850)(542,849)(543,848)(544,847)(545,846)(546,845)(547,844)(548,843)(549,842)(550,841)(551,840)(552,839)(553,838)(554,837)(555,836)(556,835)(557,834)(558,833)(559,832)(560,831)(561,830)(562,829)(563,828)(564,827)(565,826)(566,825)(567,824)(568,823)(569,822)(570,821)(571,820)(572,819)(573,818)(574,817)(575,816)(576,815)(577,814)(578,813)(579,812)(580,811)(581,810)(582,809)(583,808)(584,807)(585,806)(586,805)(587,804)(588,803)(589,802)(590,801)(591,800)(592,799)(593,798)(594,797)(595,796)(596,795)(597,794)(598,793)(599,792)(600,791)(601,790)(602,789)(603,788)(604,787)(605,786)(606,785)(607,784)(608,783)(609,782)(610,781)(611,780)(612,779)(613,778)(614,777)(615,776)(616,775)(617,774)(618,773)(619,772)(620,771)(621,770)(622,769)(623,768)(624,767)(625,766)(626,765)(627,764)(628,763)(629,762)(630,761)(631,760)(632,759)(633,758)(634,757)(635,756)(636,755)(637,754)(638,753)(639,752)(640,751)(641,750)(642,749)(643,748)(644,747)(645,746)(646,745)(647,744)(648,743)(649,742)(650,741)(651,740)(652,739)(653,738)(654,737)(655,736)(656,735)(657,734)(658,733)(659,732)(660,731)(661,730)(662,729)(663,728)(664,727)(665,726)(666,725)(667,724)(668,723)(669,722)(670,721)(671,720)(672,719)(673,718)(674,717)(675,716)(676,715)(677,714)(678,713)(679,712)(680,711)(681,710)(682,709)(683,708)(684,707)(685,706)(686,705)(687,704)(688,703)(689,702)(690,701)(691,700)(692,699)(693,698)(694,697)(695,696)
Polycyclic presentation:
2^3,1373|a^2=c,b^2=c,b^a=bc,d^b=d^1372
Conjugacy classes & character table
2749 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10984, 11);
Finite Group Databasebeta