Finite Group Databasebeta

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Dic₅₁₈₈ #35209246

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

Polycyclic presentation:

2^4,1297|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1296,c^b=cd,e^b=e^1296

Conjugacy classes & character table

5191 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20752, 31);