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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1158 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);(4,5)(7,1158)(8,1157)(9,1156)(10,1155)(11,1154)(12,1153)(13,1152)(14,1151)(15,1150)(16,1149)(17,1148)(18,1147)(19,1146)(20,1145)(21,1144)(22,1143)(23,1142)(24,1141)(25,1140)(26,1139)(27,1138)(28,1137)(29,1136)(30,1135)(31,1134)(32,1133)(33,1132)(34,1131)(35,1130)(36,1129)(37,1128)(38,1127)(39,1126)(40,1125)(41,1124)(42,1123)(43,1122)(44,1121)(45,1120)(46,1119)(47,1118)(48,1117)(49,1116)(50,1115)(51,1114)(52,1113)(53,1112)(54,1111)(55,1110)(56,1109)(57,1108)(58,1107)(59,1106)(60,1105)(61,1104)(62,1103)(63,1102)(64,1101)(65,1100)(66,1099)(67,1098)(68,1097)(69,1096)(70,1095)(71,1094)(72,1093)(73,1092)(74,1091)(75,1090)(76,1089)(77,1088)(78,1087)(79,1086)(80,1085)(81,1084)(82,1083)(83,1082)(84,1081)(85,1080)(86,1079)(87,1078)(88,1077)(89,1076)(90,1075)(91,1074)(92,1073)(93,1072)(94,1071)(95,1070)(96,1069)(97,1068)(98,1067)(99,1066)(100,1065)(101,1064)(102,1063)(103,1062)(104,1061)(105,1060)(106,1059)(107,1058)(108,1057)(109,1056)(110,1055)(111,1054)(112,1053)(113,1052)(114,1051)(115,1050)(116,1049)(117,1048)(118,1047)(119,1046)(120,1045)(121,1044)(122,1043)(123,1042)(124,1041)(125,1040)(126,1039)(127,1038)(128,1037)(129,1036)(130,1035)(131,1034)(132,1033)(133,1032)(134,1031)(135,1030)(136,1029)(137,1028)(138,1027)(139,1026)(140,1025)(141,1024)(142,1023)(143,1022)(144,1021)(145,1020)(146,1019)(147,1018)(148,1017)(149,1016)(150,1015)(151,1014)(152,1013)(153,1012)(154,1011)(155,1010)(156,1009)(157,1008)(158,1007)(159,1006)(160,1005)(161,1004)(162,1003)(163,1002)(164,1001)(165,1000)(166,999)(167,998)(168,997)(169,996)(170,995)(171,994)(172,993)(173,992)(174,991)(175,990)(176,989)(177,988)(178,987)(179,986)(180,985)(181,984)(182,983)(183,982)(184,981)(185,980)(186,979)(187,978)(188,977)(189,976)(190,975)(191,974)(192,973)(193,972)(194,971)(195,970)(196,969)(197,968)(198,967)(199,966)(200,965)(201,964)(202,963)(203,962)(204,961)(205,960)(206,959)(207,958)(208,957)(209,956)(210,955)(211,954)(212,953)(213,952)(214,951)(215,950)(216,949)(217,948)(218,947)(219,946)(220,945)(221,944)(222,943)(223,942)(224,941)(225,940)(226,939)(227,938)(228,937)(229,936)(230,935)(231,934)(232,933)(233,932)(234,931)(235,930)(236,929)(237,928)(238,927)(239,926)(240,925)(241,924)(242,923)(243,922)(244,921)(245,920)(246,919)(247,918)(248,917)(249,916)(250,915)(251,914)(252,913)(253,912)(254,911)(255,910)(256,909)(257,908)(258,907)(259,906)(260,905)(261,904)(262,903)(263,902)(264,901)(265,900)(266,899)(267,898)(268,897)(269,896)(270,895)(271,894)(272,893)(273,892)(274,891)(275,890)(276,889)(277,888)(278,887)(279,886)(280,885)(281,884)(282,883)(283,882)(284,881)(285,880)(286,879)(287,878)(288,877)(289,876)(290,875)(291,874)(292,873)(293,872)(294,871)(295,870)(296,869)(297,868)(298,867)(299,866)(300,865)(301,864)(302,863)(303,862)(304,861)(305,860)(306,859)(307,858)(308,857)(309,856)(310,855)(311,854)(312,853)(313,852)(314,851)(315,850)(316,849)(317,848)(318,847)(319,846)(320,845)(321,844)(322,843)(323,842)(324,841)(325,840)(326,839)(327,838)(328,837)(329,836)(330,835)(331,834)(332,833)(333,832)(334,831)(335,830)(336,829)(337,828)(338,827)(339,826)(340,825)(341,824)(342,823)(343,822)(344,821)(345,820)(346,819)(347,818)(348,817)(349,816)(350,815)(351,814)(352,813)(353,812)(354,811)(355,810)(356,809)(357,808)(358,807)(359,806)(360,805)(361,804)(362,803)(363,802)(364,801)(365,800)(366,799)(367,798)(368,797)(369,796)(370,795)(371,794)(372,793)(373,792)(374,791)(375,790)(376,789)(377,788)(378,787)(379,786)(380,785)(381,784)(382,783)(383,782)(384,781)(385,780)(386,779)(387,778)(388,777)(389,776)(390,775)(391,774)(392,773)(393,772)(394,771)(395,770)(396,769)(397,768)(398,767)(399,766)(400,765)(401,764)(402,763)(403,762)(404,761)(405,760)(406,759)(407,758)(408,757)(409,756)(410,755)(411,754)(412,753)(413,752)(414,751)(415,750)(416,749)(417,748)(418,747)(419,746)(420,745)(421,744)(422,743)(423,742)(424,741)(425,740)(426,739)(427,738)(428,737)(429,736)(430,735)(431,734)(432,733)(433,732)(434,731)(435,730)(436,729)(437,728)(438,727)(439,726)(440,725)(441,724)(442,723)(443,722)(444,721)(445,720)(446,719)(447,718)(448,717)(449,716)(450,715)(451,714)(452,713)(453,712)(454,711)(455,710)(456,709)(457,708)(458,707)(459,706)(460,705)(461,704)(462,703)(463,702)(464,701)(465,700)(466,699)(467,698)(468,697)(469,696)(470,695)(471,694)(472,693)(473,692)(474,691)(475,690)(476,689)(477,688)(478,687)(479,686)(480,685)(481,684)(482,683)(483,682)(484,681)(485,680)(486,679)(487,678)(488,677)(489,676)(490,675)(491,674)(492,673)(493,672)(494,671)(495,670)(496,669)(497,668)(498,667)(499,666)(500,665)(501,664)(502,663)(503,662)(504,661)(505,660)(506,659)(507,658)(508,657)(509,656)(510,655)(511,654)(512,653)(513,652)(514,651)(515,650)(516,649)(517,648)(518,647)(519,646)(520,645)(521,644)(522,643)(523,642)(524,641)(525,640)(526,639)(527,638)(528,637)(529,636)(530,635)(531,634)(532,633)(533,632)(534,631)(535,630)(536,629)(537,628)(538,627)(539,626)(540,625)(541,624)(542,623)(543,622)(544,621)(545,620)(546,619)(547,618)(548,617)(549,616)(550,615)(551,614)(552,613)(553,612)(554,611)(555,610)(556,609)(557,608)(558,607)(559,606)(560,605)(561,604)(562,603)(563,602)(564,601)(565,600)(566,599)(567,598)(568,597)(569,596)(570,595)(571,594)(572,593)(573,592)(574,591)(575,590)(576,589)(577,588)(578,587)(579,586)(580,585)(581,584)(582,583)
Conjugacy classes & character table
3462 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13836, 16);
Finite Group Databasebeta