Finite Group Databasebeta

?

← Prev (#34090123) Next (#34090125) →

Dic₄₉₄₈ #34090124

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

Polycyclic presentation:

2^4,1237|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^1236,c^b=cd,e^b=e^1236

Conjugacy classes & character table

4951 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19792, 31);