Finite Group Databasebeta

C2×D14267 #72292155

order57068
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

dihedralD28534
direct productC2×D14267

Splittings

Fitting, socleC2×C11×C1297 ⋊ C2
derived, HallC11×C1297 ⋊ C22
SylowC1297 ⋊ C2×D11
SylowC11 ⋊ C2×D1297

Subgroups

subgroupG/H
center, hypercenterC2D14267
commutator, cosocle, hypocenterC11×C1297C22
FrattiniC1G
Fitting, socleC2×C11×C1297C2
LCSG ▷ C11×C1297
UCSC1 ◁ C2

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 1310
transitive degreeμt(G) = 28534

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

Conjugacy classes & character table

14270 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((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), 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