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Dic3921 #30627960
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1314 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);(1,3,2,4)(6,7)(9,1314)(10,1313)(11,1312)(12,1311)(13,1310)(14,1309)(15,1308)(16,1307)(17,1306)(18,1305)(19,1304)(20,1303)(21,1302)(22,1301)(23,1300)(24,1299)(25,1298)(26,1297)(27,1296)(28,1295)(29,1294)(30,1293)(31,1292)(32,1291)(33,1290)(34,1289)(35,1288)(36,1287)(37,1286)(38,1285)(39,1284)(40,1283)(41,1282)(42,1281)(43,1280)(44,1279)(45,1278)(46,1277)(47,1276)(48,1275)(49,1274)(50,1273)(51,1272)(52,1271)(53,1270)(54,1269)(55,1268)(56,1267)(57,1266)(58,1265)(59,1264)(60,1263)(61,1262)(62,1261)(63,1260)(64,1259)(65,1258)(66,1257)(67,1256)(68,1255)(69,1254)(70,1253)(71,1252)(72,1251)(73,1250)(74,1249)(75,1248)(76,1247)(77,1246)(78,1245)(79,1244)(80,1243)(81,1242)(82,1241)(83,1240)(84,1239)(85,1238)(86,1237)(87,1236)(88,1235)(89,1234)(90,1233)(91,1232)(92,1231)(93,1230)(94,1229)(95,1228)(96,1227)(97,1226)(98,1225)(99,1224)(100,1223)(101,1222)(102,1221)(103,1220)(104,1219)(105,1218)(106,1217)(107,1216)(108,1215)(109,1214)(110,1213)(111,1212)(112,1211)(113,1210)(114,1209)(115,1208)(116,1207)(117,1206)(118,1205)(119,1204)(120,1203)(121,1202)(122,1201)(123,1200)(124,1199)(125,1198)(126,1197)(127,1196)(128,1195)(129,1194)(130,1193)(131,1192)(132,1191)(133,1190)(134,1189)(135,1188)(136,1187)(137,1186)(138,1185)(139,1184)(140,1183)(141,1182)(142,1181)(143,1180)(144,1179)(145,1178)(146,1177)(147,1176)(148,1175)(149,1174)(150,1173)(151,1172)(152,1171)(153,1170)(154,1169)(155,1168)(156,1167)(157,1166)(158,1165)(159,1164)(160,1163)(161,1162)(162,1161)(163,1160)(164,1159)(165,1158)(166,1157)(167,1156)(168,1155)(169,1154)(170,1153)(171,1152)(172,1151)(173,1150)(174,1149)(175,1148)(176,1147)(177,1146)(178,1145)(179,1144)(180,1143)(181,1142)(182,1141)(183,1140)(184,1139)(185,1138)(186,1137)(187,1136)(188,1135)(189,1134)(190,1133)(191,1132)(192,1131)(193,1130)(194,1129)(195,1128)(196,1127)(197,1126)(198,1125)(199,1124)(200,1123)(201,1122)(202,1121)(203,1120)(204,1119)(205,1118)(206,1117)(207,1116)(208,1115)(209,1114)(210,1113)(211,1112)(212,1111)(213,1110)(214,1109)(215,1108)(216,1107)(217,1106)(218,1105)(219,1104)(220,1103)(221,1102)(222,1101)(223,1100)(224,1099)(225,1098)(226,1097)(227,1096)(228,1095)(229,1094)(230,1093)(231,1092)(232,1091)(233,1090)(234,1089)(235,1088)(236,1087)(237,1086)(238,1085)(239,1084)(240,1083)(241,1082)(242,1081)(243,1080)(244,1079)(245,1078)(246,1077)(247,1076)(248,1075)(249,1074)(250,1073)(251,1072)(252,1071)(253,1070)(254,1069)(255,1068)(256,1067)(257,1066)(258,1065)(259,1064)(260,1063)(261,1062)(262,1061)(263,1060)(264,1059)(265,1058)(266,1057)(267,1056)(268,1055)(269,1054)(270,1053)(271,1052)(272,1051)(273,1050)(274,1049)(275,1048)(276,1047)(277,1046)(278,1045)(279,1044)(280,1043)(281,1042)(282,1041)(283,1040)(284,1039)(285,1038)(286,1037)(287,1036)(288,1035)(289,1034)(290,1033)(291,1032)(292,1031)(293,1030)(294,1029)(295,1028)(296,1027)(297,1026)(298,1025)(299,1024)(300,1023)(301,1022)(302,1021)(303,1020)(304,1019)(305,1018)(306,1017)(307,1016)(308,1015)(309,1014)(310,1013)(311,1012)(312,1011)(313,1010)(314,1009)(315,1008)(316,1007)(317,1006)(318,1005)(319,1004)(320,1003)(321,1002)(322,1001)(323,1000)(324,999)(325,998)(326,997)(327,996)(328,995)(329,994)(330,993)(331,992)(332,991)(333,990)(334,989)(335,988)(336,987)(337,986)(338,985)(339,984)(340,983)(341,982)(342,981)(343,980)(344,979)(345,978)(346,977)(347,976)(348,975)(349,974)(350,973)(351,972)(352,971)(353,970)(354,969)(355,968)(356,967)(357,966)(358,965)(359,964)(360,963)(361,962)(362,961)(363,960)(364,959)(365,958)(366,957)(367,956)(368,955)(369,954)(370,953)(371,952)(372,951)(373,950)(374,949)(375,948)(376,947)(377,946)(378,945)(379,944)(380,943)(381,942)(382,941)(383,940)(384,939)(385,938)(386,937)(387,936)(388,935)(389,934)(390,933)(391,932)(392,931)(393,930)(394,929)(395,928)(396,927)(397,926)(398,925)(399,924)(400,923)(401,922)(402,921)(403,920)(404,919)(405,918)(406,917)(407,916)(408,915)(409,914)(410,913)(411,912)(412,911)(413,910)(414,909)(415,908)(416,907)(417,906)(418,905)(419,904)(420,903)(421,902)(422,901)(423,900)(424,899)(425,898)(426,897)(427,896)(428,895)(429,894)(430,893)(431,892)(432,891)(433,890)(434,889)(435,888)(436,887)(437,886)(438,885)(439,884)(440,883)(441,882)(442,881)(443,880)(444,879)(445,878)(446,877)(447,876)(448,875)(449,874)(450,873)(451,872)(452,871)(453,870)(454,869)(455,868)(456,867)(457,866)(458,865)(459,864)(460,863)(461,862)(462,861)(463,860)(464,859)(465,858)(466,857)(467,856)(468,855)(469,854)(470,853)(471,852)(472,851)(473,850)(474,849)(475,848)(476,847)(477,846)(478,845)(479,844)(480,843)(481,842)(482,841)(483,840)(484,839)(485,838)(486,837)(487,836)(488,835)(489,834)(490,833)(491,832)(492,831)(493,830)(494,829)(495,828)(496,827)(497,826)(498,825)(499,824)(500,823)(501,822)(502,821)(503,820)(504,819)(505,818)(506,817)(507,816)(508,815)(509,814)(510,813)(511,812)(512,811)(513,810)(514,809)(515,808)(516,807)(517,806)(518,805)(519,804)(520,803)(521,802)(522,801)(523,800)(524,799)(525,798)(526,797)(527,796)(528,795)(529,794)(530,793)(531,792)(532,791)(533,790)(534,789)(535,788)(536,787)(537,786)(538,785)(539,784)(540,783)(541,782)(542,781)(543,780)(544,779)(545,778)(546,777)(547,776)(548,775)(549,774)(550,773)(551,772)(552,771)(553,770)(554,769)(555,768)(556,767)(557,766)(558,765)(559,764)(560,763)(561,762)(562,761)(563,760)(564,759)(565,758)(566,757)(567,756)(568,755)(569,754)(570,753)(571,752)(572,751)(573,750)(574,749)(575,748)(576,747)(577,746)(578,745)(579,744)(580,743)(581,742)(582,741)(583,740)(584,739)(585,738)(586,737)(587,736)(588,735)(589,734)(590,733)(591,732)(592,731)(593,730)(594,729)(595,728)(596,727)(597,726)(598,725)(599,724)(600,723)(601,722)(602,721)(603,720)(604,719)(605,718)(606,717)(607,716)(608,715)(609,714)(610,713)(611,712)(612,711)(613,710)(614,709)(615,708)(616,707)(617,706)(618,705)(619,704)(620,703)(621,702)(622,701)(623,700)(624,699)(625,698)(626,697)(627,696)(628,695)(629,694)(630,693)(631,692)(632,691)(633,690)(634,689)(635,688)(636,687)(637,686)(638,685)(639,684)(640,683)(641,682)(642,681)(643,680)(644,679)(645,678)(646,677)(647,676)(648,675)(649,674)(650,673)(651,672)(652,671)(653,670)(654,669)(655,668)(656,667)(657,666)(658,665)(659,664)(660,663)(661,662)
Polycyclic presentation:
2,3,1307,2|a^2=d,b^a=b^2,c^a=c^1306
Conjugacy classes & character table
3924 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15684, 4);
Finite Group Databasebeta