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D1303 #14579656
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1303 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);(2,1303)(3,1302)(4,1301)(5,1300)(6,1299)(7,1298)(8,1297)(9,1296)(10,1295)(11,1294)(12,1293)(13,1292)(14,1291)(15,1290)(16,1289)(17,1288)(18,1287)(19,1286)(20,1285)(21,1284)(22,1283)(23,1282)(24,1281)(25,1280)(26,1279)(27,1278)(28,1277)(29,1276)(30,1275)(31,1274)(32,1273)(33,1272)(34,1271)(35,1270)(36,1269)(37,1268)(38,1267)(39,1266)(40,1265)(41,1264)(42,1263)(43,1262)(44,1261)(45,1260)(46,1259)(47,1258)(48,1257)(49,1256)(50,1255)(51,1254)(52,1253)(53,1252)(54,1251)(55,1250)(56,1249)(57,1248)(58,1247)(59,1246)(60,1245)(61,1244)(62,1243)(63,1242)(64,1241)(65,1240)(66,1239)(67,1238)(68,1237)(69,1236)(70,1235)(71,1234)(72,1233)(73,1232)(74,1231)(75,1230)(76,1229)(77,1228)(78,1227)(79,1226)(80,1225)(81,1224)(82,1223)(83,1222)(84,1221)(85,1220)(86,1219)(87,1218)(88,1217)(89,1216)(90,1215)(91,1214)(92,1213)(93,1212)(94,1211)(95,1210)(96,1209)(97,1208)(98,1207)(99,1206)(100,1205)(101,1204)(102,1203)(103,1202)(104,1201)(105,1200)(106,1199)(107,1198)(108,1197)(109,1196)(110,1195)(111,1194)(112,1193)(113,1192)(114,1191)(115,1190)(116,1189)(117,1188)(118,1187)(119,1186)(120,1185)(121,1184)(122,1183)(123,1182)(124,1181)(125,1180)(126,1179)(127,1178)(128,1177)(129,1176)(130,1175)(131,1174)(132,1173)(133,1172)(134,1171)(135,1170)(136,1169)(137,1168)(138,1167)(139,1166)(140,1165)(141,1164)(142,1163)(143,1162)(144,1161)(145,1160)(146,1159)(147,1158)(148,1157)(149,1156)(150,1155)(151,1154)(152,1153)(153,1152)(154,1151)(155,1150)(156,1149)(157,1148)(158,1147)(159,1146)(160,1145)(161,1144)(162,1143)(163,1142)(164,1141)(165,1140)(166,1139)(167,1138)(168,1137)(169,1136)(170,1135)(171,1134)(172,1133)(173,1132)(174,1131)(175,1130)(176,1129)(177,1128)(178,1127)(179,1126)(180,1125)(181,1124)(182,1123)(183,1122)(184,1121)(185,1120)(186,1119)(187,1118)(188,1117)(189,1116)(190,1115)(191,1114)(192,1113)(193,1112)(194,1111)(195,1110)(196,1109)(197,1108)(198,1107)(199,1106)(200,1105)(201,1104)(202,1103)(203,1102)(204,1101)(205,1100)(206,1099)(207,1098)(208,1097)(209,1096)(210,1095)(211,1094)(212,1093)(213,1092)(214,1091)(215,1090)(216,1089)(217,1088)(218,1087)(219,1086)(220,1085)(221,1084)(222,1083)(223,1082)(224,1081)(225,1080)(226,1079)(227,1078)(228,1077)(229,1076)(230,1075)(231,1074)(232,1073)(233,1072)(234,1071)(235,1070)(236,1069)(237,1068)(238,1067)(239,1066)(240,1065)(241,1064)(242,1063)(243,1062)(244,1061)(245,1060)(246,1059)(247,1058)(248,1057)(249,1056)(250,1055)(251,1054)(252,1053)(253,1052)(254,1051)(255,1050)(256,1049)(257,1048)(258,1047)(259,1046)(260,1045)(261,1044)(262,1043)(263,1042)(264,1041)(265,1040)(266,1039)(267,1038)(268,1037)(269,1036)(270,1035)(271,1034)(272,1033)(273,1032)(274,1031)(275,1030)(276,1029)(277,1028)(278,1027)(279,1026)(280,1025)(281,1024)(282,1023)(283,1022)(284,1021)(285,1020)(286,1019)(287,1018)(288,1017)(289,1016)(290,1015)(291,1014)(292,1013)(293,1012)(294,1011)(295,1010)(296,1009)(297,1008)(298,1007)(299,1006)(300,1005)(301,1004)(302,1003)(303,1002)(304,1001)(305,1000)(306,999)(307,998)(308,997)(309,996)(310,995)(311,994)(312,993)(313,992)(314,991)(315,990)(316,989)(317,988)(318,987)(319,986)(320,985)(321,984)(322,983)(323,982)(324,981)(325,980)(326,979)(327,978)(328,977)(329,976)(330,975)(331,974)(332,973)(333,972)(334,971)(335,970)(336,969)(337,968)(338,967)(339,966)(340,965)(341,964)(342,963)(343,962)(344,961)(345,960)(346,959)(347,958)(348,957)(349,956)(350,955)(351,954)(352,953)(353,952)(354,951)(355,950)(356,949)(357,948)(358,947)(359,946)(360,945)(361,944)(362,943)(363,942)(364,941)(365,940)(366,939)(367,938)(368,937)(369,936)(370,935)(371,934)(372,933)(373,932)(374,931)(375,930)(376,929)(377,928)(378,927)(379,926)(380,925)(381,924)(382,923)(383,922)(384,921)(385,920)(386,919)(387,918)(388,917)(389,916)(390,915)(391,914)(392,913)(393,912)(394,911)(395,910)(396,909)(397,908)(398,907)(399,906)(400,905)(401,904)(402,903)(403,902)(404,901)(405,900)(406,899)(407,898)(408,897)(409,896)(410,895)(411,894)(412,893)(413,892)(414,891)(415,890)(416,889)(417,888)(418,887)(419,886)(420,885)(421,884)(422,883)(423,882)(424,881)(425,880)(426,879)(427,878)(428,877)(429,876)(430,875)(431,874)(432,873)(433,872)(434,871)(435,870)(436,869)(437,868)(438,867)(439,866)(440,865)(441,864)(442,863)(443,862)(444,861)(445,860)(446,859)(447,858)(448,857)(449,856)(450,855)(451,854)(452,853)(453,852)(454,851)(455,850)(456,849)(457,848)(458,847)(459,846)(460,845)(461,844)(462,843)(463,842)(464,841)(465,840)(466,839)(467,838)(468,837)(469,836)(470,835)(471,834)(472,833)(473,832)(474,831)(475,830)(476,829)(477,828)(478,827)(479,826)(480,825)(481,824)(482,823)(483,822)(484,821)(485,820)(486,819)(487,818)(488,817)(489,816)(490,815)(491,814)(492,813)(493,812)(494,811)(495,810)(496,809)(497,808)(498,807)(499,806)(500,805)(501,804)(502,803)(503,802)(504,801)(505,800)(506,799)(507,798)(508,797)(509,796)(510,795)(511,794)(512,793)(513,792)(514,791)(515,790)(516,789)(517,788)(518,787)(519,786)(520,785)(521,784)(522,783)(523,782)(524,781)(525,780)(526,779)(527,778)(528,777)(529,776)(530,775)(531,774)(532,773)(533,772)(534,771)(535,770)(536,769)(537,768)(538,767)(539,766)(540,765)(541,764)(542,763)(543,762)(544,761)(545,760)(546,759)(547,758)(548,757)(549,756)(550,755)(551,754)(552,753)(553,752)(554,751)(555,750)(556,749)(557,748)(558,747)(559,746)(560,745)(561,744)(562,743)(563,742)(564,741)(565,740)(566,739)(567,738)(568,737)(569,736)(570,735)(571,734)(572,733)(573,732)(574,731)(575,730)(576,729)(577,728)(578,727)(579,726)(580,725)(581,724)(582,723)(583,722)(584,721)(585,720)(586,719)(587,718)(588,717)(589,716)(590,715)(591,714)(592,713)(593,712)(594,711)(595,710)(596,709)(597,708)(598,707)(599,706)(600,705)(601,704)(602,703)(603,702)(604,701)(605,700)(606,699)(607,698)(608,697)(609,696)(610,695)(611,694)(612,693)(613,692)(614,691)(615,690)(616,689)(617,688)(618,687)(619,686)(620,685)(621,684)(622,683)(623,682)(624,681)(625,680)(626,679)(627,678)(628,677)(629,676)(630,675)(631,674)(632,673)(633,672)(634,671)(635,670)(636,669)(637,668)(638,667)(639,666)(640,665)(641,664)(642,663)(643,662)(644,661)(645,660)(646,659)(647,658)(648,657)(649,656)(650,655)(651,654)(652,653)
Polycyclic presentation:
2,1303|b^a=b^1302
Conjugacy classes & character table
653 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2606, 1);
Finite Group Databasebeta