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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1122 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);(4,5)(7,1122)(8,1121)(9,1120)(10,1119)(11,1118)(12,1117)(13,1116)(14,1115)(15,1114)(16,1113)(17,1112)(18,1111)(19,1110)(20,1109)(21,1108)(22,1107)(23,1106)(24,1105)(25,1104)(26,1103)(27,1102)(28,1101)(29,1100)(30,1099)(31,1098)(32,1097)(33,1096)(34,1095)(35,1094)(36,1093)(37,1092)(38,1091)(39,1090)(40,1089)(41,1088)(42,1087)(43,1086)(44,1085)(45,1084)(46,1083)(47,1082)(48,1081)(49,1080)(50,1079)(51,1078)(52,1077)(53,1076)(54,1075)(55,1074)(56,1073)(57,1072)(58,1071)(59,1070)(60,1069)(61,1068)(62,1067)(63,1066)(64,1065)(65,1064)(66,1063)(67,1062)(68,1061)(69,1060)(70,1059)(71,1058)(72,1057)(73,1056)(74,1055)(75,1054)(76,1053)(77,1052)(78,1051)(79,1050)(80,1049)(81,1048)(82,1047)(83,1046)(84,1045)(85,1044)(86,1043)(87,1042)(88,1041)(89,1040)(90,1039)(91,1038)(92,1037)(93,1036)(94,1035)(95,1034)(96,1033)(97,1032)(98,1031)(99,1030)(100,1029)(101,1028)(102,1027)(103,1026)(104,1025)(105,1024)(106,1023)(107,1022)(108,1021)(109,1020)(110,1019)(111,1018)(112,1017)(113,1016)(114,1015)(115,1014)(116,1013)(117,1012)(118,1011)(119,1010)(120,1009)(121,1008)(122,1007)(123,1006)(124,1005)(125,1004)(126,1003)(127,1002)(128,1001)(129,1000)(130,999)(131,998)(132,997)(133,996)(134,995)(135,994)(136,993)(137,992)(138,991)(139,990)(140,989)(141,988)(142,987)(143,986)(144,985)(145,984)(146,983)(147,982)(148,981)(149,980)(150,979)(151,978)(152,977)(153,976)(154,975)(155,974)(156,973)(157,972)(158,971)(159,970)(160,969)(161,968)(162,967)(163,966)(164,965)(165,964)(166,963)(167,962)(168,961)(169,960)(170,959)(171,958)(172,957)(173,956)(174,955)(175,954)(176,953)(177,952)(178,951)(179,950)(180,949)(181,948)(182,947)(183,946)(184,945)(185,944)(186,943)(187,942)(188,941)(189,940)(190,939)(191,938)(192,937)(193,936)(194,935)(195,934)(196,933)(197,932)(198,931)(199,930)(200,929)(201,928)(202,927)(203,926)(204,925)(205,924)(206,923)(207,922)(208,921)(209,920)(210,919)(211,918)(212,917)(213,916)(214,915)(215,914)(216,913)(217,912)(218,911)(219,910)(220,909)(221,908)(222,907)(223,906)(224,905)(225,904)(226,903)(227,902)(228,901)(229,900)(230,899)(231,898)(232,897)(233,896)(234,895)(235,894)(236,893)(237,892)(238,891)(239,890)(240,889)(241,888)(242,887)(243,886)(244,885)(245,884)(246,883)(247,882)(248,881)(249,880)(250,879)(251,878)(252,877)(253,876)(254,875)(255,874)(256,873)(257,872)(258,871)(259,870)(260,869)(261,868)(262,867)(263,866)(264,865)(265,864)(266,863)(267,862)(268,861)(269,860)(270,859)(271,858)(272,857)(273,856)(274,855)(275,854)(276,853)(277,852)(278,851)(279,850)(280,849)(281,848)(282,847)(283,846)(284,845)(285,844)(286,843)(287,842)(288,841)(289,840)(290,839)(291,838)(292,837)(293,836)(294,835)(295,834)(296,833)(297,832)(298,831)(299,830)(300,829)(301,828)(302,827)(303,826)(304,825)(305,824)(306,823)(307,822)(308,821)(309,820)(310,819)(311,818)(312,817)(313,816)(314,815)(315,814)(316,813)(317,812)(318,811)(319,810)(320,809)(321,808)(322,807)(323,806)(324,805)(325,804)(326,803)(327,802)(328,801)(329,800)(330,799)(331,798)(332,797)(333,796)(334,795)(335,794)(336,793)(337,792)(338,791)(339,790)(340,789)(341,788)(342,787)(343,786)(344,785)(345,784)(346,783)(347,782)(348,781)(349,780)(350,779)(351,778)(352,777)(353,776)(354,775)(355,774)(356,773)(357,772)(358,771)(359,770)(360,769)(361,768)(362,767)(363,766)(364,765)(365,764)(366,763)(367,762)(368,761)(369,760)(370,759)(371,758)(372,757)(373,756)(374,755)(375,754)(376,753)(377,752)(378,751)(379,750)(380,749)(381,748)(382,747)(383,746)(384,745)(385,744)(386,743)(387,742)(388,741)(389,740)(390,739)(391,738)(392,737)(393,736)(394,735)(395,734)(396,733)(397,732)(398,731)(399,730)(400,729)(401,728)(402,727)(403,726)(404,725)(405,724)(406,723)(407,722)(408,721)(409,720)(410,719)(411,718)(412,717)(413,716)(414,715)(415,714)(416,713)(417,712)(418,711)(419,710)(420,709)(421,708)(422,707)(423,706)(424,705)(425,704)(426,703)(427,702)(428,701)(429,700)(430,699)(431,698)(432,697)(433,696)(434,695)(435,694)(436,693)(437,692)(438,691)(439,690)(440,689)(441,688)(442,687)(443,686)(444,685)(445,684)(446,683)(447,682)(448,681)(449,680)(450,679)(451,678)(452,677)(453,676)(454,675)(455,674)(456,673)(457,672)(458,671)(459,670)(460,669)(461,668)(462,667)(463,666)(464,665)(465,664)(466,663)(467,662)(468,661)(469,660)(470,659)(471,658)(472,657)(473,656)(474,655)(475,654)(476,653)(477,652)(478,651)(479,650)(480,649)(481,648)(482,647)(483,646)(484,645)(485,644)(486,643)(487,642)(488,641)(489,640)(490,639)(491,638)(492,637)(493,636)(494,635)(495,634)(496,633)(497,632)(498,631)(499,630)(500,629)(501,628)(502,627)(503,626)(504,625)(505,624)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,617)(513,616)(514,615)(515,614)(516,613)(517,612)(518,611)(519,610)(520,609)(521,608)(522,607)(523,606)(524,605)(525,604)(526,603)(527,602)(528,601)(529,600)(530,599)(531,598)(532,597)(533,596)(534,595)(535,594)(536,593)(537,592)(538,591)(539,590)(540,589)(541,588)(542,587)(543,586)(544,585)(545,584)(546,583)(547,582)(548,581)(549,580)(550,579)(551,578)(552,577)(553,576)(554,575)(555,574)(556,573)(557,572)(558,571)(559,570)(560,569)(561,568)(562,567)(563,566)(564,565)
Conjugacy classes & character table
3354 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13404, 16);
Finite Group Databasebeta