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Dic6505 #39907307
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
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);(1,3,2,4)(6,9)(7,8)(11,1310)(12,1309)(13,1308)(14,1307)(15,1306)(16,1305)(17,1304)(18,1303)(19,1302)(20,1301)(21,1300)(22,1299)(23,1298)(24,1297)(25,1296)(26,1295)(27,1294)(28,1293)(29,1292)(30,1291)(31,1290)(32,1289)(33,1288)(34,1287)(35,1286)(36,1285)(37,1284)(38,1283)(39,1282)(40,1281)(41,1280)(42,1279)(43,1278)(44,1277)(45,1276)(46,1275)(47,1274)(48,1273)(49,1272)(50,1271)(51,1270)(52,1269)(53,1268)(54,1267)(55,1266)(56,1265)(57,1264)(58,1263)(59,1262)(60,1261)(61,1260)(62,1259)(63,1258)(64,1257)(65,1256)(66,1255)(67,1254)(68,1253)(69,1252)(70,1251)(71,1250)(72,1249)(73,1248)(74,1247)(75,1246)(76,1245)(77,1244)(78,1243)(79,1242)(80,1241)(81,1240)(82,1239)(83,1238)(84,1237)(85,1236)(86,1235)(87,1234)(88,1233)(89,1232)(90,1231)(91,1230)(92,1229)(93,1228)(94,1227)(95,1226)(96,1225)(97,1224)(98,1223)(99,1222)(100,1221)(101,1220)(102,1219)(103,1218)(104,1217)(105,1216)(106,1215)(107,1214)(108,1213)(109,1212)(110,1211)(111,1210)(112,1209)(113,1208)(114,1207)(115,1206)(116,1205)(117,1204)(118,1203)(119,1202)(120,1201)(121,1200)(122,1199)(123,1198)(124,1197)(125,1196)(126,1195)(127,1194)(128,1193)(129,1192)(130,1191)(131,1190)(132,1189)(133,1188)(134,1187)(135,1186)(136,1185)(137,1184)(138,1183)(139,1182)(140,1181)(141,1180)(142,1179)(143,1178)(144,1177)(145,1176)(146,1175)(147,1174)(148,1173)(149,1172)(150,1171)(151,1170)(152,1169)(153,1168)(154,1167)(155,1166)(156,1165)(157,1164)(158,1163)(159,1162)(160,1161)(161,1160)(162,1159)(163,1158)(164,1157)(165,1156)(166,1155)(167,1154)(168,1153)(169,1152)(170,1151)(171,1150)(172,1149)(173,1148)(174,1147)(175,1146)(176,1145)(177,1144)(178,1143)(179,1142)(180,1141)(181,1140)(182,1139)(183,1138)(184,1137)(185,1136)(186,1135)(187,1134)(188,1133)(189,1132)(190,1131)(191,1130)(192,1129)(193,1128)(194,1127)(195,1126)(196,1125)(197,1124)(198,1123)(199,1122)(200,1121)(201,1120)(202,1119)(203,1118)(204,1117)(205,1116)(206,1115)(207,1114)(208,1113)(209,1112)(210,1111)(211,1110)(212,1109)(213,1108)(214,1107)(215,1106)(216,1105)(217,1104)(218,1103)(219,1102)(220,1101)(221,1100)(222,1099)(223,1098)(224,1097)(225,1096)(226,1095)(227,1094)(228,1093)(229,1092)(230,1091)(231,1090)(232,1089)(233,1088)(234,1087)(235,1086)(236,1085)(237,1084)(238,1083)(239,1082)(240,1081)(241,1080)(242,1079)(243,1078)(244,1077)(245,1076)(246,1075)(247,1074)(248,1073)(249,1072)(250,1071)(251,1070)(252,1069)(253,1068)(254,1067)(255,1066)(256,1065)(257,1064)(258,1063)(259,1062)(260,1061)(261,1060)(262,1059)(263,1058)(264,1057)(265,1056)(266,1055)(267,1054)(268,1053)(269,1052)(270,1051)(271,1050)(272,1049)(273,1048)(274,1047)(275,1046)(276,1045)(277,1044)(278,1043)(279,1042)(280,1041)(281,1040)(282,1039)(283,1038)(284,1037)(285,1036)(286,1035)(287,1034)(288,1033)(289,1032)(290,1031)(291,1030)(292,1029)(293,1028)(294,1027)(295,1026)(296,1025)(297,1024)(298,1023)(299,1022)(300,1021)(301,1020)(302,1019)(303,1018)(304,1017)(305,1016)(306,1015)(307,1014)(308,1013)(309,1012)(310,1011)(311,1010)(312,1009)(313,1008)(314,1007)(315,1006)(316,1005)(317,1004)(318,1003)(319,1002)(320,1001)(321,1000)(322,999)(323,998)(324,997)(325,996)(326,995)(327,994)(328,993)(329,992)(330,991)(331,990)(332,989)(333,988)(334,987)(335,986)(336,985)(337,984)(338,983)(339,982)(340,981)(341,980)(342,979)(343,978)(344,977)(345,976)(346,975)(347,974)(348,973)(349,972)(350,971)(351,970)(352,969)(353,968)(354,967)(355,966)(356,965)(357,964)(358,963)(359,962)(360,961)(361,960)(362,959)(363,958)(364,957)(365,956)(366,955)(367,954)(368,953)(369,952)(370,951)(371,950)(372,949)(373,948)(374,947)(375,946)(376,945)(377,944)(378,943)(379,942)(380,941)(381,940)(382,939)(383,938)(384,937)(385,936)(386,935)(387,934)(388,933)(389,932)(390,931)(391,930)(392,929)(393,928)(394,927)(395,926)(396,925)(397,924)(398,923)(399,922)(400,921)(401,920)(402,919)(403,918)(404,917)(405,916)(406,915)(407,914)(408,913)(409,912)(410,911)(411,910)(412,909)(413,908)(414,907)(415,906)(416,905)(417,904)(418,903)(419,902)(420,901)(421,900)(422,899)(423,898)(424,897)(425,896)(426,895)(427,894)(428,893)(429,892)(430,891)(431,890)(432,889)(433,888)(434,887)(435,886)(436,885)(437,884)(438,883)(439,882)(440,881)(441,880)(442,879)(443,878)(444,877)(445,876)(446,875)(447,874)(448,873)(449,872)(450,871)(451,870)(452,869)(453,868)(454,867)(455,866)(456,865)(457,864)(458,863)(459,862)(460,861)(461,860)(462,859)(463,858)(464,857)(465,856)(466,855)(467,854)(468,853)(469,852)(470,851)(471,850)(472,849)(473,848)(474,847)(475,846)(476,845)(477,844)(478,843)(479,842)(480,841)(481,840)(482,839)(483,838)(484,837)(485,836)(486,835)(487,834)(488,833)(489,832)(490,831)(491,830)(492,829)(493,828)(494,827)(495,826)(496,825)(497,824)(498,823)(499,822)(500,821)(501,820)(502,819)(503,818)(504,817)(505,816)(506,815)(507,814)(508,813)(509,812)(510,811)(511,810)(512,809)(513,808)(514,807)(515,806)(516,805)(517,804)(518,803)(519,802)(520,801)(521,800)(522,799)(523,798)(524,797)(525,796)(526,795)(527,794)(528,793)(529,792)(530,791)(531,790)(532,789)(533,788)(534,787)(535,786)(536,785)(537,784)(538,783)(539,782)(540,781)(541,780)(542,779)(543,778)(544,777)(545,776)(546,775)(547,774)(548,773)(549,772)(550,771)(551,770)(552,769)(553,768)(554,767)(555,766)(556,765)(557,764)(558,763)(559,762)(560,761)(561,760)(562,759)(563,758)(564,757)(565,756)(566,755)(567,754)(568,753)(569,752)(570,751)(571,750)(572,749)(573,748)(574,747)(575,746)(576,745)(577,744)(578,743)(579,742)(580,741)(581,740)(582,739)(583,738)(584,737)(585,736)(586,735)(587,734)(588,733)(589,732)(590,731)(591,730)(592,729)(593,728)(594,727)(595,726)(596,725)(597,724)(598,723)(599,722)(600,721)(601,720)(602,719)(603,718)(604,717)(605,716)(606,715)(607,714)(608,713)(609,712)(610,711)(611,710)(612,709)(613,708)(614,707)(615,706)(616,705)(617,704)(618,703)(619,702)(620,701)(621,700)(622,699)(623,698)(624,697)(625,696)(626,695)(627,694)(628,693)(629,692)(630,691)(631,690)(632,689)(633,688)(634,687)(635,686)(636,685)(637,684)(638,683)(639,682)(640,681)(641,680)(642,679)(643,678)(644,677)(645,676)(646,675)(647,674)(648,673)(649,672)(650,671)(651,670)(652,669)(653,668)(654,667)(655,666)(656,665)(657,664)(658,663)(659,662)(660,661)
Polycyclic presentation:
2,5,1301,2|a^2=d,b^a=b^4,c^a=c^1300
Conjugacy classes & character table
6508 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26020, 6);
Finite Group Databasebeta