Finite Group Databasebeta

?

← Prev (#36346174) Next (#36346176) →

Dic₅₄₆₈ #36346175

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1383 points:

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

Polycyclic presentation:

2^4,1367|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1366,c^b=cd,e^b=e^1366

Conjugacy classes & character table

5471 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21872, 31);