← Prev (#30680954) Next (#30680956) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1404 points:
(1,2)(3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404);(4,5)(7,1404)(8,1403)(9,1402)(10,1401)(11,1400)(12,1399)(13,1398)(14,1397)(15,1396)(16,1395)(17,1394)(18,1393)(19,1392)(20,1391)(21,1390)(22,1389)(23,1388)(24,1387)(25,1386)(26,1385)(27,1384)(28,1383)(29,1382)(30,1381)(31,1380)(32,1379)(33,1378)(34,1377)(35,1376)(36,1375)(37,1374)(38,1373)(39,1372)(40,1371)(41,1370)(42,1369)(43,1368)(44,1367)(45,1366)(46,1365)(47,1364)(48,1363)(49,1362)(50,1361)(51,1360)(52,1359)(53,1358)(54,1357)(55,1356)(56,1355)(57,1354)(58,1353)(59,1352)(60,1351)(61,1350)(62,1349)(63,1348)(64,1347)(65,1346)(66,1345)(67,1344)(68,1343)(69,1342)(70,1341)(71,1340)(72,1339)(73,1338)(74,1337)(75,1336)(76,1335)(77,1334)(78,1333)(79,1332)(80,1331)(81,1330)(82,1329)(83,1328)(84,1327)(85,1326)(86,1325)(87,1324)(88,1323)(89,1322)(90,1321)(91,1320)(92,1319)(93,1318)(94,1317)(95,1316)(96,1315)(97,1314)(98,1313)(99,1312)(100,1311)(101,1310)(102,1309)(103,1308)(104,1307)(105,1306)(106,1305)(107,1304)(108,1303)(109,1302)(110,1301)(111,1300)(112,1299)(113,1298)(114,1297)(115,1296)(116,1295)(117,1294)(118,1293)(119,1292)(120,1291)(121,1290)(122,1289)(123,1288)(124,1287)(125,1286)(126,1285)(127,1284)(128,1283)(129,1282)(130,1281)(131,1280)(132,1279)(133,1278)(134,1277)(135,1276)(136,1275)(137,1274)(138,1273)(139,1272)(140,1271)(141,1270)(142,1269)(143,1268)(144,1267)(145,1266)(146,1265)(147,1264)(148,1263)(149,1262)(150,1261)(151,1260)(152,1259)(153,1258)(154,1257)(155,1256)(156,1255)(157,1254)(158,1253)(159,1252)(160,1251)(161,1250)(162,1249)(163,1248)(164,1247)(165,1246)(166,1245)(167,1244)(168,1243)(169,1242)(170,1241)(171,1240)(172,1239)(173,1238)(174,1237)(175,1236)(176,1235)(177,1234)(178,1233)(179,1232)(180,1231)(181,1230)(182,1229)(183,1228)(184,1227)(185,1226)(186,1225)(187,1224)(188,1223)(189,1222)(190,1221)(191,1220)(192,1219)(193,1218)(194,1217)(195,1216)(196,1215)(197,1214)(198,1213)(199,1212)(200,1211)(201,1210)(202,1209)(203,1208)(204,1207)(205,1206)(206,1205)(207,1204)(208,1203)(209,1202)(210,1201)(211,1200)(212,1199)(213,1198)(214,1197)(215,1196)(216,1195)(217,1194)(218,1193)(219,1192)(220,1191)(221,1190)(222,1189)(223,1188)(224,1187)(225,1186)(226,1185)(227,1184)(228,1183)(229,1182)(230,1181)(231,1180)(232,1179)(233,1178)(234,1177)(235,1176)(236,1175)(237,1174)(238,1173)(239,1172)(240,1171)(241,1170)(242,1169)(243,1168)(244,1167)(245,1166)(246,1165)(247,1164)(248,1163)(249,1162)(250,1161)(251,1160)(252,1159)(253,1158)(254,1157)(255,1156)(256,1155)(257,1154)(258,1153)(259,1152)(260,1151)(261,1150)(262,1149)(263,1148)(264,1147)(265,1146)(266,1145)(267,1144)(268,1143)(269,1142)(270,1141)(271,1140)(272,1139)(273,1138)(274,1137)(275,1136)(276,1135)(277,1134)(278,1133)(279,1132)(280,1131)(281,1130)(282,1129)(283,1128)(284,1127)(285,1126)(286,1125)(287,1124)(288,1123)(289,1122)(290,1121)(291,1120)(292,1119)(293,1118)(294,1117)(295,1116)(296,1115)(297,1114)(298,1113)(299,1112)(300,1111)(301,1110)(302,1109)(303,1108)(304,1107)(305,1106)(306,1105)(307,1104)(308,1103)(309,1102)(310,1101)(311,1100)(312,1099)(313,1098)(314,1097)(315,1096)(316,1095)(317,1094)(318,1093)(319,1092)(320,1091)(321,1090)(322,1089)(323,1088)(324,1087)(325,1086)(326,1085)(327,1084)(328,1083)(329,1082)(330,1081)(331,1080)(332,1079)(333,1078)(334,1077)(335,1076)(336,1075)(337,1074)(338,1073)(339,1072)(340,1071)(341,1070)(342,1069)(343,1068)(344,1067)(345,1066)(346,1065)(347,1064)(348,1063)(349,1062)(350,1061)(351,1060)(352,1059)(353,1058)(354,1057)(355,1056)(356,1055)(357,1054)(358,1053)(359,1052)(360,1051)(361,1050)(362,1049)(363,1048)(364,1047)(365,1046)(366,1045)(367,1044)(368,1043)(369,1042)(370,1041)(371,1040)(372,1039)(373,1038)(374,1037)(375,1036)(376,1035)(377,1034)(378,1033)(379,1032)(380,1031)(381,1030)(382,1029)(383,1028)(384,1027)(385,1026)(386,1025)(387,1024)(388,1023)(389,1022)(390,1021)(391,1020)(392,1019)(393,1018)(394,1017)(395,1016)(396,1015)(397,1014)(398,1013)(399,1012)(400,1011)(401,1010)(402,1009)(403,1008)(404,1007)(405,1006)(406,1005)(407,1004)(408,1003)(409,1002)(410,1001)(411,1000)(412,999)(413,998)(414,997)(415,996)(416,995)(417,994)(418,993)(419,992)(420,991)(421,990)(422,989)(423,988)(424,987)(425,986)(426,985)(427,984)(428,983)(429,982)(430,981)(431,980)(432,979)(433,978)(434,977)(435,976)(436,975)(437,974)(438,973)(439,972)(440,971)(441,970)(442,969)(443,968)(444,967)(445,966)(446,965)(447,964)(448,963)(449,962)(450,961)(451,960)(452,959)(453,958)(454,957)(455,956)(456,955)(457,954)(458,953)(459,952)(460,951)(461,950)(462,949)(463,948)(464,947)(465,946)(466,945)(467,944)(468,943)(469,942)(470,941)(471,940)(472,939)(473,938)(474,937)(475,936)(476,935)(477,934)(478,933)(479,932)(480,931)(481,930)(482,929)(483,928)(484,927)(485,926)(486,925)(487,924)(488,923)(489,922)(490,921)(491,920)(492,919)(493,918)(494,917)(495,916)(496,915)(497,914)(498,913)(499,912)(500,911)(501,910)(502,909)(503,908)(504,907)(505,906)(506,905)(507,904)(508,903)(509,902)(510,901)(511,900)(512,899)(513,898)(514,897)(515,896)(516,895)(517,894)(518,893)(519,892)(520,891)(521,890)(522,889)(523,888)(524,887)(525,886)(526,885)(527,884)(528,883)(529,882)(530,881)(531,880)(532,879)(533,878)(534,877)(535,876)(536,875)(537,874)(538,873)(539,872)(540,871)(541,870)(542,869)(543,868)(544,867)(545,866)(546,865)(547,864)(548,863)(549,862)(550,861)(551,860)(552,859)(553,858)(554,857)(555,856)(556,855)(557,854)(558,853)(559,852)(560,851)(561,850)(562,849)(563,848)(564,847)(565,846)(566,845)(567,844)(568,843)(569,842)(570,841)(571,840)(572,839)(573,838)(574,837)(575,836)(576,835)(577,834)(578,833)(579,832)(580,831)(581,830)(582,829)(583,828)(584,827)(585,826)(586,825)(587,824)(588,823)(589,822)(590,821)(591,820)(592,819)(593,818)(594,817)(595,816)(596,815)(597,814)(598,813)(599,812)(600,811)(601,810)(602,809)(603,808)(604,807)(605,806)(606,805)(607,804)(608,803)(609,802)(610,801)(611,800)(612,799)(613,798)(614,797)(615,796)(616,795)(617,794)(618,793)(619,792)(620,791)(621,790)(622,789)(623,788)(624,787)(625,786)(626,785)(627,784)(628,783)(629,782)(630,781)(631,780)(632,779)(633,778)(634,777)(635,776)(636,775)(637,774)(638,773)(639,772)(640,771)(641,770)(642,769)(643,768)(644,767)(645,766)(646,765)(647,764)(648,763)(649,762)(650,761)(651,760)(652,759)(653,758)(654,757)(655,756)(656,755)(657,754)(658,753)(659,752)(660,751)(661,750)(662,749)(663,748)(664,747)(665,746)(666,745)(667,744)(668,743)(669,742)(670,741)(671,740)(672,739)(673,738)(674,737)(675,736)(676,735)(677,734)(678,733)(679,732)(680,731)(681,730)(682,729)(683,728)(684,727)(685,726)(686,725)(687,724)(688,723)(689,722)(690,721)(691,720)(692,719)(693,718)(694,717)(695,716)(696,715)(697,714)(698,713)(699,712)(700,711)(701,710)(702,709)(703,708)(704,707)(705,706)
Conjugacy classes & character table
4200 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16788, 13);
Finite Group Databasebeta