Finite Group Databasebeta

?

← Prev (#44536027) Next (#44536029) →

D₁₅₆₉₇ #44536028

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

Aliases

Splittings

Subgroups

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1438 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336,1337,1338,1339,1340,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352,1353,1354,1355,1356,1357,1358,1359,1360,1361,1362,1363,1364,1365,1366,1367,1368,1369,1370,1371,1372,1373,1374,1375,1376,1377,1378,1379,1380,1381,1382,1383,1384,1385,1386,1387,1388,1389,1390,1391,1392,1393,1394,1395,1396,1397,1398,1399,1400,1401,1402,1403,1404,1405,1406,1407,1408,1409,1410,1411,1412,1413,1414,1415,1416,1417,1418,1419,1420,1421,1422,1423,1424,1425,1426,1427,1428,1429,1430,1431,1432,1433,1434,1435,1436,1437,1438);(2,11)(3,10)(4,9)(5,8)(6,7)(13,1438)(14,1437)(15,1436)(16,1435)(17,1434)(18,1433)(19,1432)(20,1431)(21,1430)(22,1429)(23,1428)(24,1427)(25,1426)(26,1425)(27,1424)(28,1423)(29,1422)(30,1421)(31,1420)(32,1419)(33,1418)(34,1417)(35,1416)(36,1415)(37,1414)(38,1413)(39,1412)(40,1411)(41,1410)(42,1409)(43,1408)(44,1407)(45,1406)(46,1405)(47,1404)(48,1403)(49,1402)(50,1401)(51,1400)(52,1399)(53,1398)(54,1397)(55,1396)(56,1395)(57,1394)(58,1393)(59,1392)(60,1391)(61,1390)(62,1389)(63,1388)(64,1387)(65,1386)(66,1385)(67,1384)(68,1383)(69,1382)(70,1381)(71,1380)(72,1379)(73,1378)(74,1377)(75,1376)(76,1375)(77,1374)(78,1373)(79,1372)(80,1371)(81,1370)(82,1369)(83,1368)(84,1367)(85,1366)(86,1365)(87,1364)(88,1363)(89,1362)(90,1361)(91,1360)(92,1359)(93,1358)(94,1357)(95,1356)(96,1355)(97,1354)(98,1353)(99,1352)(100,1351)(101,1350)(102,1349)(103,1348)(104,1347)(105,1346)(106,1345)(107,1344)(108,1343)(109,1342)(110,1341)(111,1340)(112,1339)(113,1338)(114,1337)(115,1336)(116,1335)(117,1334)(118,1333)(119,1332)(120,1331)(121,1330)(122,1329)(123,1328)(124,1327)(125,1326)(126,1325)(127,1324)(128,1323)(129,1322)(130,1321)(131,1320)(132,1319)(133,1318)(134,1317)(135,1316)(136,1315)(137,1314)(138,1313)(139,1312)(140,1311)(141,1310)(142,1309)(143,1308)(144,1307)(145,1306)(146,1305)(147,1304)(148,1303)(149,1302)(150,1301)(151,1300)(152,1299)(153,1298)(154,1297)(155,1296)(156,1295)(157,1294)(158,1293)(159,1292)(160,1291)(161,1290)(162,1289)(163,1288)(164,1287)(165,1286)(166,1285)(167,1284)(168,1283)(169,1282)(170,1281)(171,1280)(172,1279)(173,1278)(174,1277)(175,1276)(176,1275)(177,1274)(178,1273)(179,1272)(180,1271)(181,1270)(182,1269)(183,1268)(184,1267)(185,1266)(186,1265)(187,1264)(188,1263)(189,1262)(190,1261)(191,1260)(192,1259)(193,1258)(194,1257)(195,1256)(196,1255)(197,1254)(198,1253)(199,1252)(200,1251)(201,1250)(202,1249)(203,1248)(204,1247)(205,1246)(206,1245)(207,1244)(208,1243)(209,1242)(210,1241)(211,1240)(212,1239)(213,1238)(214,1237)(215,1236)(216,1235)(217,1234)(218,1233)(219,1232)(220,1231)(221,1230)(222,1229)(223,1228)(224,1227)(225,1226)(226,1225)(227,1224)(228,1223)(229,1222)(230,1221)(231,1220)(232,1219)(233,1218)(234,1217)(235,1216)(236,1215)(237,1214)(238,1213)(239,1212)(240,1211)(241,1210)(242,1209)(243,1208)(244,1207)(245,1206)(246,1205)(247,1204)(248,1203)(249,1202)(250,1201)(251,1200)(252,1199)(253,1198)(254,1197)(255,1196)(256,1195)(257,1194)(258,1193)(259,1192)(260,1191)(261,1190)(262,1189)(263,1188)(264,1187)(265,1186)(266,1185)(267,1184)(268,1183)(269,1182)(270,1181)(271,1180)(272,1179)(273,1178)(274,1177)(275,1176)(276,1175)(277,1174)(278,1173)(279,1172)(280,1171)(281,1170)(282,1169)(283,1168)(284,1167)(285,1166)(286,1165)(287,1164)(288,1163)(289,1162)(290,1161)(291,1160)(292,1159)(293,1158)(294,1157)(295,1156)(296,1155)(297,1154)(298,1153)(299,1152)(300,1151)(301,1150)(302,1149)(303,1148)(304,1147)(305,1146)(306,1145)(307,1144)(308,1143)(309,1142)(310,1141)(311,1140)(312,1139)(313,1138)(314,1137)(315,1136)(316,1135)(317,1134)(318,1133)(319,1132)(320,1131)(321,1130)(322,1129)(323,1128)(324,1127)(325,1126)(326,1125)(327,1124)(328,1123)(329,1122)(330,1121)(331,1120)(332,1119)(333,1118)(334,1117)(335,1116)(336,1115)(337,1114)(338,1113)(339,1112)(340,1111)(341,1110)(342,1109)(343,1108)(344,1107)(345,1106)(346,1105)(347,1104)(348,1103)(349,1102)(350,1101)(351,1100)(352,1099)(353,1098)(354,1097)(355,1096)(356,1095)(357,1094)(358,1093)(359,1092)(360,1091)(361,1090)(362,1089)(363,1088)(364,1087)(365,1086)(366,1085)(367,1084)(368,1083)(369,1082)(370,1081)(371,1080)(372,1079)(373,1078)(374,1077)(375,1076)(376,1075)(377,1074)(378,1073)(379,1072)(380,1071)(381,1070)(382,1069)(383,1068)(384,1067)(385,1066)(386,1065)(387,1064)(388,1063)(389,1062)(390,1061)(391,1060)(392,1059)(393,1058)(394,1057)(395,1056)(396,1055)(397,1054)(398,1053)(399,1052)(400,1051)(401,1050)(402,1049)(403,1048)(404,1047)(405,1046)(406,1045)(407,1044)(408,1043)(409,1042)(410,1041)(411,1040)(412,1039)(413,1038)(414,1037)(415,1036)(416,1035)(417,1034)(418,1033)(419,1032)(420,1031)(421,1030)(422,1029)(423,1028)(424,1027)(425,1026)(426,1025)(427,1024)(428,1023)(429,1022)(430,1021)(431,1020)(432,1019)(433,1018)(434,1017)(435,1016)(436,1015)(437,1014)(438,1013)(439,1012)(440,1011)(441,1010)(442,1009)(443,1008)(444,1007)(445,1006)(446,1005)(447,1004)(448,1003)(449,1002)(450,1001)(451,1000)(452,999)(453,998)(454,997)(455,996)(456,995)(457,994)(458,993)(459,992)(460,991)(461,990)(462,989)(463,988)(464,987)(465,986)(466,985)(467,984)(468,983)(469,982)(470,981)(471,980)(472,979)(473,978)(474,977)(475,976)(476,975)(477,974)(478,973)(479,972)(480,971)(481,970)(482,969)(483,968)(484,967)(485,966)(486,965)(487,964)(488,963)(489,962)(490,961)(491,960)(492,959)(493,958)(494,957)(495,956)(496,955)(497,954)(498,953)(499,952)(500,951)(501,950)(502,949)(503,948)(504,947)(505,946)(506,945)(507,944)(508,943)(509,942)(510,941)(511,940)(512,939)(513,938)(514,937)(515,936)(516,935)(517,934)(518,933)(519,932)(520,931)(521,930)(522,929)(523,928)(524,927)(525,926)(526,925)(527,924)(528,923)(529,922)(530,921)(531,920)(532,919)(533,918)(534,917)(535,916)(536,915)(537,914)(538,913)(539,912)(540,911)(541,910)(542,909)(543,908)(544,907)(545,906)(546,905)(547,904)(548,903)(549,902)(550,901)(551,900)(552,899)(553,898)(554,897)(555,896)(556,895)(557,894)(558,893)(559,892)(560,891)(561,890)(562,889)(563,888)(564,887)(565,886)(566,885)(567,884)(568,883)(569,882)(570,881)(571,880)(572,879)(573,878)(574,877)(575,876)(576,875)(577,874)(578,873)(579,872)(580,871)(581,870)(582,869)(583,868)(584,867)(585,866)(586,865)(587,864)(588,863)(589,862)(590,861)(591,860)(592,859)(593,858)(594,857)(595,856)(596,855)(597,854)(598,853)(599,852)(600,851)(601,850)(602,849)(603,848)(604,847)(605,846)(606,845)(607,844)(608,843)(609,842)(610,841)(611,840)(612,839)(613,838)(614,837)(615,836)(616,835)(617,834)(618,833)(619,832)(620,831)(621,830)(622,829)(623,828)(624,827)(625,826)(626,825)(627,824)(628,823)(629,822)(630,821)(631,820)(632,819)(633,818)(634,817)(635,816)(636,815)(637,814)(638,813)(639,812)(640,811)(641,810)(642,809)(643,808)(644,807)(645,806)(646,805)(647,804)(648,803)(649,802)(650,801)(651,800)(652,799)(653,798)(654,797)(655,796)(656,795)(657,794)(658,793)(659,792)(660,791)(661,790)(662,789)(663,788)(664,787)(665,786)(666,785)(667,784)(668,783)(669,782)(670,781)(671,780)(672,779)(673,778)(674,777)(675,776)(676,775)(677,774)(678,773)(679,772)(680,771)(681,770)(682,769)(683,768)(684,767)(685,766)(686,765)(687,764)(688,763)(689,762)(690,761)(691,760)(692,759)(693,758)(694,757)(695,756)(696,755)(697,754)(698,753)(699,752)(700,751)(701,750)(702,749)(703,748)(704,747)(705,746)(706,745)(707,744)(708,743)(709,742)(710,741)(711,740)(712,739)(713,738)(714,737)(715,736)(716,735)(717,734)(718,733)(719,732)(720,731)(721,730)(722,729)(723,728)(724,727)(725,726)

Polycyclic presentation:

2,11,1427|b^a=b^10,c^a=c^1426

Conjugacy classes & character table

7850 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31394, 3);