Finite Group Databasebeta

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Dic₅₄₉₂ #36347014

• 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 1389 points:

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

Polycyclic presentation:

2^4,1373|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1372,c^b=cd,e^b=e^1372

Conjugacy classes & character table

5495 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21968, 31);