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Dic3963 #30629327
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1328 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328);(1,3,2,4)(6,7)(9,1328)(10,1327)(11,1326)(12,1325)(13,1324)(14,1323)(15,1322)(16,1321)(17,1320)(18,1319)(19,1318)(20,1317)(21,1316)(22,1315)(23,1314)(24,1313)(25,1312)(26,1311)(27,1310)(28,1309)(29,1308)(30,1307)(31,1306)(32,1305)(33,1304)(34,1303)(35,1302)(36,1301)(37,1300)(38,1299)(39,1298)(40,1297)(41,1296)(42,1295)(43,1294)(44,1293)(45,1292)(46,1291)(47,1290)(48,1289)(49,1288)(50,1287)(51,1286)(52,1285)(53,1284)(54,1283)(55,1282)(56,1281)(57,1280)(58,1279)(59,1278)(60,1277)(61,1276)(62,1275)(63,1274)(64,1273)(65,1272)(66,1271)(67,1270)(68,1269)(69,1268)(70,1267)(71,1266)(72,1265)(73,1264)(74,1263)(75,1262)(76,1261)(77,1260)(78,1259)(79,1258)(80,1257)(81,1256)(82,1255)(83,1254)(84,1253)(85,1252)(86,1251)(87,1250)(88,1249)(89,1248)(90,1247)(91,1246)(92,1245)(93,1244)(94,1243)(95,1242)(96,1241)(97,1240)(98,1239)(99,1238)(100,1237)(101,1236)(102,1235)(103,1234)(104,1233)(105,1232)(106,1231)(107,1230)(108,1229)(109,1228)(110,1227)(111,1226)(112,1225)(113,1224)(114,1223)(115,1222)(116,1221)(117,1220)(118,1219)(119,1218)(120,1217)(121,1216)(122,1215)(123,1214)(124,1213)(125,1212)(126,1211)(127,1210)(128,1209)(129,1208)(130,1207)(131,1206)(132,1205)(133,1204)(134,1203)(135,1202)(136,1201)(137,1200)(138,1199)(139,1198)(140,1197)(141,1196)(142,1195)(143,1194)(144,1193)(145,1192)(146,1191)(147,1190)(148,1189)(149,1188)(150,1187)(151,1186)(152,1185)(153,1184)(154,1183)(155,1182)(156,1181)(157,1180)(158,1179)(159,1178)(160,1177)(161,1176)(162,1175)(163,1174)(164,1173)(165,1172)(166,1171)(167,1170)(168,1169)(169,1168)(170,1167)(171,1166)(172,1165)(173,1164)(174,1163)(175,1162)(176,1161)(177,1160)(178,1159)(179,1158)(180,1157)(181,1156)(182,1155)(183,1154)(184,1153)(185,1152)(186,1151)(187,1150)(188,1149)(189,1148)(190,1147)(191,1146)(192,1145)(193,1144)(194,1143)(195,1142)(196,1141)(197,1140)(198,1139)(199,1138)(200,1137)(201,1136)(202,1135)(203,1134)(204,1133)(205,1132)(206,1131)(207,1130)(208,1129)(209,1128)(210,1127)(211,1126)(212,1125)(213,1124)(214,1123)(215,1122)(216,1121)(217,1120)(218,1119)(219,1118)(220,1117)(221,1116)(222,1115)(223,1114)(224,1113)(225,1112)(226,1111)(227,1110)(228,1109)(229,1108)(230,1107)(231,1106)(232,1105)(233,1104)(234,1103)(235,1102)(236,1101)(237,1100)(238,1099)(239,1098)(240,1097)(241,1096)(242,1095)(243,1094)(244,1093)(245,1092)(246,1091)(247,1090)(248,1089)(249,1088)(250,1087)(251,1086)(252,1085)(253,1084)(254,1083)(255,1082)(256,1081)(257,1080)(258,1079)(259,1078)(260,1077)(261,1076)(262,1075)(263,1074)(264,1073)(265,1072)(266,1071)(267,1070)(268,1069)(269,1068)(270,1067)(271,1066)(272,1065)(273,1064)(274,1063)(275,1062)(276,1061)(277,1060)(278,1059)(279,1058)(280,1057)(281,1056)(282,1055)(283,1054)(284,1053)(285,1052)(286,1051)(287,1050)(288,1049)(289,1048)(290,1047)(291,1046)(292,1045)(293,1044)(294,1043)(295,1042)(296,1041)(297,1040)(298,1039)(299,1038)(300,1037)(301,1036)(302,1035)(303,1034)(304,1033)(305,1032)(306,1031)(307,1030)(308,1029)(309,1028)(310,1027)(311,1026)(312,1025)(313,1024)(314,1023)(315,1022)(316,1021)(317,1020)(318,1019)(319,1018)(320,1017)(321,1016)(322,1015)(323,1014)(324,1013)(325,1012)(326,1011)(327,1010)(328,1009)(329,1008)(330,1007)(331,1006)(332,1005)(333,1004)(334,1003)(335,1002)(336,1001)(337,1000)(338,999)(339,998)(340,997)(341,996)(342,995)(343,994)(344,993)(345,992)(346,991)(347,990)(348,989)(349,988)(350,987)(351,986)(352,985)(353,984)(354,983)(355,982)(356,981)(357,980)(358,979)(359,978)(360,977)(361,976)(362,975)(363,974)(364,973)(365,972)(366,971)(367,970)(368,969)(369,968)(370,967)(371,966)(372,965)(373,964)(374,963)(375,962)(376,961)(377,960)(378,959)(379,958)(380,957)(381,956)(382,955)(383,954)(384,953)(385,952)(386,951)(387,950)(388,949)(389,948)(390,947)(391,946)(392,945)(393,944)(394,943)(395,942)(396,941)(397,940)(398,939)(399,938)(400,937)(401,936)(402,935)(403,934)(404,933)(405,932)(406,931)(407,930)(408,929)(409,928)(410,927)(411,926)(412,925)(413,924)(414,923)(415,922)(416,921)(417,920)(418,919)(419,918)(420,917)(421,916)(422,915)(423,914)(424,913)(425,912)(426,911)(427,910)(428,909)(429,908)(430,907)(431,906)(432,905)(433,904)(434,903)(435,902)(436,901)(437,900)(438,899)(439,898)(440,897)(441,896)(442,895)(443,894)(444,893)(445,892)(446,891)(447,890)(448,889)(449,888)(450,887)(451,886)(452,885)(453,884)(454,883)(455,882)(456,881)(457,880)(458,879)(459,878)(460,877)(461,876)(462,875)(463,874)(464,873)(465,872)(466,871)(467,870)(468,869)(469,868)(470,867)(471,866)(472,865)(473,864)(474,863)(475,862)(476,861)(477,860)(478,859)(479,858)(480,857)(481,856)(482,855)(483,854)(484,853)(485,852)(486,851)(487,850)(488,849)(489,848)(490,847)(491,846)(492,845)(493,844)(494,843)(495,842)(496,841)(497,840)(498,839)(499,838)(500,837)(501,836)(502,835)(503,834)(504,833)(505,832)(506,831)(507,830)(508,829)(509,828)(510,827)(511,826)(512,825)(513,824)(514,823)(515,822)(516,821)(517,820)(518,819)(519,818)(520,817)(521,816)(522,815)(523,814)(524,813)(525,812)(526,811)(527,810)(528,809)(529,808)(530,807)(531,806)(532,805)(533,804)(534,803)(535,802)(536,801)(537,800)(538,799)(539,798)(540,797)(541,796)(542,795)(543,794)(544,793)(545,792)(546,791)(547,790)(548,789)(549,788)(550,787)(551,786)(552,785)(553,784)(554,783)(555,782)(556,781)(557,780)(558,779)(559,778)(560,777)(561,776)(562,775)(563,774)(564,773)(565,772)(566,771)(567,770)(568,769)(569,768)(570,767)(571,766)(572,765)(573,764)(574,763)(575,762)(576,761)(577,760)(578,759)(579,758)(580,757)(581,756)(582,755)(583,754)(584,753)(585,752)(586,751)(587,750)(588,749)(589,748)(590,747)(591,746)(592,745)(593,744)(594,743)(595,742)(596,741)(597,740)(598,739)(599,738)(600,737)(601,736)(602,735)(603,734)(604,733)(605,732)(606,731)(607,730)(608,729)(609,728)(610,727)(611,726)(612,725)(613,724)(614,723)(615,722)(616,721)(617,720)(618,719)(619,718)(620,717)(621,716)(622,715)(623,714)(624,713)(625,712)(626,711)(627,710)(628,709)(629,708)(630,707)(631,706)(632,705)(633,704)(634,703)(635,702)(636,701)(637,700)(638,699)(639,698)(640,697)(641,696)(642,695)(643,694)(644,693)(645,692)(646,691)(647,690)(648,689)(649,688)(650,687)(651,686)(652,685)(653,684)(654,683)(655,682)(656,681)(657,680)(658,679)(659,678)(660,677)(661,676)(662,675)(663,674)(664,673)(665,672)(666,671)(667,670)(668,669)
Polycyclic presentation:
2,3,1321,2|a^2=d,b^a=b^2,c^a=c^1320
Conjugacy classes & character table
3966 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15852, 6);
Finite Group Databasebeta