Finite Group Databasebeta

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Dic₆₂₃₆ #38735604

• 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 1575 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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49)(345,1248)(346,1247)(347,1246)(348,1245)(349,1244)(350,1243)(351,1242)(352,1241)(353,1240)(354,1239)(355,1238)(356,1237)(357,1236)(358,1235)(359,1234)(360,1233)(361,1232)(362,1231)(363,1230)(364,1229)(365,1228)(366,1227)(367,1226)(368,1225)(369,1224)(370,1223)(371,1222)(372,1221)(373,1220)(374,1219)(375,1218)(376,1217)(377,1216)(378,1215)(379,1214)(380,1213)(381,1212)(382,1211)(383,1210)(384,1209)(385,1208)(386,1207)(387,1206)(388,1205)(389,1204)(390,1203)(391,1202)(392,1201)(393,1200)(394,1199)(395,1198)(396,1197)(397,1196)(398,1195)(399,1194)(400,1193)(401,1192)(402,1191)(403,1190)(404,1189)(405,1188)(406,1187)(407,1186)(408,1185)(409,1184)(410,1183)(411,1182)(412,1181)(413,1180)(414,1179)(415,1178)(416,1177)(417,1176)(418,1175)(419,1174)(420,1173)(421,1172)(422,1171)(423,1170)(424,1169)(425,1168)(426,1167)(427,1166)(428,1165)(429,1164)(430,1163)(431,1162)(432,1161)(433,1160)(434,1159)(435,1158)(436,1157)(437,1156)(438,1155)(439,1154)(440,1153)(441,1152)(442,1151)(443,1150)(444,1149)(445,1148)(446,1147)(447,1146)(448,1145)(449,1144)(450,1143)(451,1142)(452,1141)(453,1140)(454,1139)(455,1138)(456,1137)(457,1136)(458,1135)(459,1134)(460,1133)(461,1132)(462,1131)(463,1130)(464,1129)(465,1128)(466,1127)(467,1126)(468,1125)(469,1124)(470,1123)(471,1122)(472,1121)(473,1120)(474,1119)(475,1118)(476,1117)(477,1116)(478,1115)(479,1114)(480,1113)(481,1112)(482,1111)(483,1110)(484,1109)(485,1108)(486,1107)(487,1106)(488,1105)(489,1104)(490,1103)(491,1102)(492,1101)(493,1100)(494,1099)(495,1098)(496,1097)(497,1096)(498,1095)(499,1094)(500,1093)(501,1092)(502,1091)(503,1090)(504,1089)(505,1088)(506,1087)(507,1086)(508,1085)(509,1084)(510,1083)(511,1082)(512,1081)(513,1080)(514,1079)(515,1078)(516,1077)(517,1076)(518,1075)(519,1074)(520,1073)(521,1072)(522,1071)(523,1070)(524,1069)(525,1068)(526,1067)(527,1066)(528,1065)(529,1064)(530,1063)(531,1062)(532,1061)(533,1060)(534,1059)(535,1058)(536,1057)(537,1056)(538,1055)(539,1054)(540,1053)(541,1052)(542,1051)(543,1050)(544,1049)(545,1048)(546,1047)(547,1046)(548,1045)(549,1044)(550,1043)(551,1042)(552,1041)(553,1040)(554,1039)(555,1038)(556,1037)(557,1036)(558,1035)(559,1034)(560,1033)(561,1032)(562,1031)(563,1030)(564,1029)(565,1028)(566,1027)(567,1026)(568,1025)(569,1024)(570,1023)(571,1022)(572,1021)(573,1020)(574,1019)(575,1018)(576,1017)(577,1016)(578,1015)(579,1014)(580,1013)(581,1012)(582,1011)(583,1010)(584,1009)(585,1008)(586,1007)(587,1006)(588,1005)(589,1004)(590,1003)(591,1002)(592,1001)(593,1000)(594,999)(595,998)(596,997)(597,996)(598,995)(599,994)(600,993)(601,992)(602,991)(603,990)(604,989)(605,988)(606,987)(607,986)(608,985)(609,984)(610,983)(611,982)(612,981)(613,980)(614,979)(615,978)(616,977)(617,976)(618,975)(619,974)(620,973)(621,972)(622,971)(623,970)(624,969)(625,968)(626,967)(627,966)(628,965)(629,964)(630,963)(631,962)(632,961)(633,960)(634,959)(635,958)(636,957)(637,956)(638,955)(639,954)(640,953)(641,952)(642,951)(643,950)(644,949)(645,948)(646,947)(647,946)(648,945)(649,944)(650,943)(651,942)(652,941)(653,940)(654,939)(655,938)(656,937)(657,936)(658,935)(659,934)(660,933)(661,932)(662,931)(663,930)(664,929)(665,928)(666,927)(667,926)(668,925)(669,924)(670,923)(671,922)(672,921)(673,920)(674,919)(675,918)(676,917)(677,916)(678,915)(679,914)(680,913)(681,912)(682,911)(683,910)(684,909)(685,908)(686,907)(687,906)(688,905)(689,904)(690,903)(691,902)(692,901)(693,900)(694,899)(695,898)(696,897)(697,896)(698,895)(699,894)(700,893)(701,892)(702,891)(703,890)(704,889)(705,888)(706,887)(707,886)(708,885)(709,884)(710,883)(711,882)(712,881)(713,880)(714,879)(715,878)(716,877)(717,876)(718,875)(719,874)(720,873)(721,872)(722,871)(723,870)(724,869)(725,868)(726,867)(727,866)(728,865)(729,864)(730,863)(731,862)(732,861)(733,860)(734,859)(735,858)(736,857)(737,856)(738,855)(739,854)(740,853)(741,852)(742,851)(743,850)(744,849)(745,848)(746,847)(747,846)(748,845)(749,844)(750,843)(751,842)(752,841)(753,840)(754,839)(755,838)(756,837)(757,836)(758,835)(759,834)(760,833)(761,832)(762,831)(763,830)(764,829)(765,828)(766,827)(767,826)(768,825)(769,824)(770,823)(771,822)(772,821)(773,820)(774,819)(775,818)(776,817)(777,816)(778,815)(779,814)(780,813)(781,812)(782,811)(783,810)(784,809)(785,808)(786,807)(787,806)(788,805)(789,804)(790,803)(791,802)(792,801)(793,800)(794,799)(795,798)(796,797)

Polycyclic presentation:

2^4,1559|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1558,c^b=cd,e^b=e^1558

Conjugacy classes & character table

6239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24944, 31);