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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1126 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);(4,9)(5,8)(6,7)(11,1126)(12,1125)(13,1124)(14,1123)(15,1122)(16,1121)(17,1120)(18,1119)(19,1118)(20,1117)(21,1116)(22,1115)(23,1114)(24,1113)(25,1112)(26,1111)(27,1110)(28,1109)(29,1108)(30,1107)(31,1106)(32,1105)(33,1104)(34,1103)(35,1102)(36,1101)(37,1100)(38,1099)(39,1098)(40,1097)(41,1096)(42,1095)(43,1094)(44,1093)(45,1092)(46,1091)(47,1090)(48,1089)(49,1088)(50,1087)(51,1086)(52,1085)(53,1084)(54,1083)(55,1082)(56,1081)(57,1080)(58,1079)(59,1078)(60,1077)(61,1076)(62,1075)(63,1074)(64,1073)(65,1072)(66,1071)(67,1070)(68,1069)(69,1068)(70,1067)(71,1066)(72,1065)(73,1064)(74,1063)(75,1062)(76,1061)(77,1060)(78,1059)(79,1058)(80,1057)(81,1056)(82,1055)(83,1054)(84,1053)(85,1052)(86,1051)(87,1050)(88,1049)(89,1048)(90,1047)(91,1046)(92,1045)(93,1044)(94,1043)(95,1042)(96,1041)(97,1040)(98,1039)(99,1038)(100,1037)(101,1036)(102,1035)(103,1034)(104,1033)(105,1032)(106,1031)(107,1030)(108,1029)(109,1028)(110,1027)(111,1026)(112,1025)(113,1024)(114,1023)(115,1022)(116,1021)(117,1020)(118,1019)(119,1018)(120,1017)(121,1016)(122,1015)(123,1014)(124,1013)(125,1012)(126,1011)(127,1010)(128,1009)(129,1008)(130,1007)(131,1006)(132,1005)(133,1004)(134,1003)(135,1002)(136,1001)(137,1000)(138,999)(139,998)(140,997)(141,996)(142,995)(143,994)(144,993)(145,992)(146,991)(147,990)(148,989)(149,988)(150,987)(151,986)(152,985)(153,984)(154,983)(155,982)(156,981)(157,980)(158,979)(159,978)(160,977)(161,976)(162,975)(163,974)(164,973)(165,972)(166,971)(167,970)(168,969)(169,968)(170,967)(171,966)(172,965)(173,964)(174,963)(175,962)(176,961)(177,960)(178,959)(179,958)(180,957)(181,956)(182,955)(183,954)(184,953)(185,952)(186,951)(187,950)(188,949)(189,948)(190,947)(191,946)(192,945)(193,944)(194,943)(195,942)(196,941)(197,940)(198,939)(199,938)(200,937)(201,936)(202,935)(203,934)(204,933)(205,932)(206,931)(207,930)(208,929)(209,928)(210,927)(211,926)(212,925)(213,924)(214,923)(215,922)(216,921)(217,920)(218,919)(219,918)(220,917)(221,916)(222,915)(223,914)(224,913)(225,912)(226,911)(227,910)(228,909)(229,908)(230,907)(231,906)(232,905)(233,904)(234,903)(235,902)(236,901)(237,900)(238,899)(239,898)(240,897)(241,896)(242,895)(243,894)(244,893)(245,892)(246,891)(247,890)(248,889)(249,888)(250,887)(251,886)(252,885)(253,884)(254,883)(255,882)(256,881)(257,880)(258,879)(259,878)(260,877)(261,876)(262,875)(263,874)(264,873)(265,872)(266,871)(267,870)(268,869)(269,868)(270,867)(271,866)(272,865)(273,864)(274,863)(275,862)(276,861)(277,860)(278,859)(279,858)(280,857)(281,856)(282,855)(283,854)(284,853)(285,852)(286,851)(287,850)(288,849)(289,848)(290,847)(291,846)(292,845)(293,844)(294,843)(295,842)(296,841)(297,840)(298,839)(299,838)(300,837)(301,836)(302,835)(303,834)(304,833)(305,832)(306,831)(307,830)(308,829)(309,828)(310,827)(311,826)(312,825)(313,824)(314,823)(315,822)(316,821)(317,820)(318,819)(319,818)(320,817)(321,816)(322,815)(323,814)(324,813)(325,812)(326,811)(327,810)(328,809)(329,808)(330,807)(331,806)(332,805)(333,804)(334,803)(335,802)(336,801)(337,800)(338,799)(339,798)(340,797)(341,796)(342,795)(343,794)(344,793)(345,792)(346,791)(347,790)(348,789)(349,788)(350,787)(351,786)(352,785)(353,784)(354,783)(355,782)(356,781)(357,780)(358,779)(359,778)(360,777)(361,776)(362,775)(363,774)(364,773)(365,772)(366,771)(367,770)(368,769)(369,768)(370,767)(371,766)(372,765)(373,764)(374,763)(375,762)(376,761)(377,760)(378,759)(379,758)(380,757)(381,756)(382,755)(383,754)(384,753)(385,752)(386,751)(387,750)(388,749)(389,748)(390,747)(391,746)(392,745)(393,744)(394,743)(395,742)(396,741)(397,740)(398,739)(399,738)(400,737)(401,736)(402,735)(403,734)(404,733)(405,732)(406,731)(407,730)(408,729)(409,728)(410,727)(411,726)(412,725)(413,724)(414,723)(415,722)(416,721)(417,720)(418,719)(419,718)(420,717)(421,716)(422,715)(423,714)(424,713)(425,712)(426,711)(427,710)(428,709)(429,708)(430,707)(431,706)(432,705)(433,704)(434,703)(435,702)(436,701)(437,700)(438,699)(439,698)(440,697)(441,696)(442,695)(443,694)(444,693)(445,692)(446,691)(447,690)(448,689)(449,688)(450,687)(451,686)(452,685)(453,684)(454,683)(455,682)(456,681)(457,680)(458,679)(459,678)(460,677)(461,676)(462,675)(463,674)(464,673)(465,672)(466,671)(467,670)(468,669)(469,668)(470,667)(471,666)(472,665)(473,664)(474,663)(475,662)(476,661)(477,660)(478,659)(479,658)(480,657)(481,656)(482,655)(483,654)(484,653)(485,652)(486,651)(487,650)(488,649)(489,648)(490,647)(491,646)(492,645)(493,644)(494,643)(495,642)(496,641)(497,640)(498,639)(499,638)(500,637)(501,636)(502,635)(503,634)(504,633)(505,632)(506,631)(507,630)(508,629)(509,628)(510,627)(511,626)(512,625)(513,624)(514,623)(515,622)(516,621)(517,620)(518,619)(519,618)(520,617)(521,616)(522,615)(523,614)(524,613)(525,612)(526,611)(527,610)(528,609)(529,608)(530,607)(531,606)(532,605)(533,604)(534,603)(535,602)(536,601)(537,600)(538,599)(539,598)(540,597)(541,596)(542,595)(543,594)(544,593)(545,592)(546,591)(547,590)(548,589)(549,588)(550,587)(551,586)(552,585)(553,584)(554,583)(555,582)(556,581)(557,580)(558,579)(559,578)(560,577)(561,576)(562,575)(563,574)(564,573)(565,572)(566,571)(567,570)(568,569)
Conjugacy classes & character table
7822 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31276, 11);
Finite Group Databasebeta