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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1138 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);(4,9)(5,8)(6,7)(11,1138)(12,1137)(13,1136)(14,1135)(15,1134)(16,1133)(17,1132)(18,1131)(19,1130)(20,1129)(21,1128)(22,1127)(23,1126)(24,1125)(25,1124)(26,1123)(27,1122)(28,1121)(29,1120)(30,1119)(31,1118)(32,1117)(33,1116)(34,1115)(35,1114)(36,1113)(37,1112)(38,1111)(39,1110)(40,1109)(41,1108)(42,1107)(43,1106)(44,1105)(45,1104)(46,1103)(47,1102)(48,1101)(49,1100)(50,1099)(51,1098)(52,1097)(53,1096)(54,1095)(55,1094)(56,1093)(57,1092)(58,1091)(59,1090)(60,1089)(61,1088)(62,1087)(63,1086)(64,1085)(65,1084)(66,1083)(67,1082)(68,1081)(69,1080)(70,1079)(71,1078)(72,1077)(73,1076)(74,1075)(75,1074)(76,1073)(77,1072)(78,1071)(79,1070)(80,1069)(81,1068)(82,1067)(83,1066)(84,1065)(85,1064)(86,1063)(87,1062)(88,1061)(89,1060)(90,1059)(91,1058)(92,1057)(93,1056)(94,1055)(95,1054)(96,1053)(97,1052)(98,1051)(99,1050)(100,1049)(101,1048)(102,1047)(103,1046)(104,1045)(105,1044)(106,1043)(107,1042)(108,1041)(109,1040)(110,1039)(111,1038)(112,1037)(113,1036)(114,1035)(115,1034)(116,1033)(117,1032)(118,1031)(119,1030)(120,1029)(121,1028)(122,1027)(123,1026)(124,1025)(125,1024)(126,1023)(127,1022)(128,1021)(129,1020)(130,1019)(131,1018)(132,1017)(133,1016)(134,1015)(135,1014)(136,1013)(137,1012)(138,1011)(139,1010)(140,1009)(141,1008)(142,1007)(143,1006)(144,1005)(145,1004)(146,1003)(147,1002)(148,1001)(149,1000)(150,999)(151,998)(152,997)(153,996)(154,995)(155,994)(156,993)(157,992)(158,991)(159,990)(160,989)(161,988)(162,987)(163,986)(164,985)(165,984)(166,983)(167,982)(168,981)(169,980)(170,979)(171,978)(172,977)(173,976)(174,975)(175,974)(176,973)(177,972)(178,971)(179,970)(180,969)(181,968)(182,967)(183,966)(184,965)(185,964)(186,963)(187,962)(188,961)(189,960)(190,959)(191,958)(192,957)(193,956)(194,955)(195,954)(196,953)(197,952)(198,951)(199,950)(200,949)(201,948)(202,947)(203,946)(204,945)(205,944)(206,943)(207,942)(208,941)(209,940)(210,939)(211,938)(212,937)(213,936)(214,935)(215,934)(216,933)(217,932)(218,931)(219,930)(220,929)(221,928)(222,927)(223,926)(224,925)(225,924)(226,923)(227,922)(228,921)(229,920)(230,919)(231,918)(232,917)(233,916)(234,915)(235,914)(236,913)(237,912)(238,911)(239,910)(240,909)(241,908)(242,907)(243,906)(244,905)(245,904)(246,903)(247,902)(248,901)(249,900)(250,899)(251,898)(252,897)(253,896)(254,895)(255,894)(256,893)(257,892)(258,891)(259,890)(260,889)(261,888)(262,887)(263,886)(264,885)(265,884)(266,883)(267,882)(268,881)(269,880)(270,879)(271,878)(272,877)(273,876)(274,875)(275,874)(276,873)(277,872)(278,871)(279,870)(280,869)(281,868)(282,867)(283,866)(284,865)(285,864)(286,863)(287,862)(288,861)(289,860)(290,859)(291,858)(292,857)(293,856)(294,855)(295,854)(296,853)(297,852)(298,851)(299,850)(300,849)(301,848)(302,847)(303,846)(304,845)(305,844)(306,843)(307,842)(308,841)(309,840)(310,839)(311,838)(312,837)(313,836)(314,835)(315,834)(316,833)(317,832)(318,831)(319,830)(320,829)(321,828)(322,827)(323,826)(324,825)(325,824)(326,823)(327,822)(328,821)(329,820)(330,819)(331,818)(332,817)(333,816)(334,815)(335,814)(336,813)(337,812)(338,811)(339,810)(340,809)(341,808)(342,807)(343,806)(344,805)(345,804)(346,803)(347,802)(348,801)(349,800)(350,799)(351,798)(352,797)(353,796)(354,795)(355,794)(356,793)(357,792)(358,791)(359,790)(360,789)(361,788)(362,787)(363,786)(364,785)(365,784)(366,783)(367,782)(368,781)(369,780)(370,779)(371,778)(372,777)(373,776)(374,775)(375,774)(376,773)(377,772)(378,771)(379,770)(380,769)(381,768)(382,767)(383,766)(384,765)(385,764)(386,763)(387,762)(388,761)(389,760)(390,759)(391,758)(392,757)(393,756)(394,755)(395,754)(396,753)(397,752)(398,751)(399,750)(400,749)(401,748)(402,747)(403,746)(404,745)(405,744)(406,743)(407,742)(408,741)(409,740)(410,739)(411,738)(412,737)(413,736)(414,735)(415,734)(416,733)(417,732)(418,731)(419,730)(420,729)(421,728)(422,727)(423,726)(424,725)(425,724)(426,723)(427,722)(428,721)(429,720)(430,719)(431,718)(432,717)(433,716)(434,715)(435,714)(436,713)(437,712)(438,711)(439,710)(440,709)(441,708)(442,707)(443,706)(444,705)(445,704)(446,703)(447,702)(448,701)(449,700)(450,699)(451,698)(452,697)(453,696)(454,695)(455,694)(456,693)(457,692)(458,691)(459,690)(460,689)(461,688)(462,687)(463,686)(464,685)(465,684)(466,683)(467,682)(468,681)(469,680)(470,679)(471,678)(472,677)(473,676)(474,675)(475,674)(476,673)(477,672)(478,671)(479,670)(480,669)(481,668)(482,667)(483,666)(484,665)(485,664)(486,663)(487,662)(488,661)(489,660)(490,659)(491,658)(492,657)(493,656)(494,655)(495,654)(496,653)(497,652)(498,651)(499,650)(500,649)(501,648)(502,647)(503,646)(504,645)(505,644)(506,643)(507,642)(508,641)(509,640)(510,639)(511,638)(512,637)(513,636)(514,635)(515,634)(516,633)(517,632)(518,631)(519,630)(520,629)(521,628)(522,627)(523,626)(524,625)(525,624)(526,623)(527,622)(528,621)(529,620)(530,619)(531,618)(532,617)(533,616)(534,615)(535,614)(536,613)(537,612)(538,611)(539,610)(540,609)(541,608)(542,607)(543,606)(544,605)(545,604)(546,603)(547,602)(548,601)(549,600)(550,599)(551,598)(552,597)(553,596)(554,595)(555,594)(556,593)(557,592)(558,591)(559,590)(560,589)(561,588)(562,587)(563,586)(564,585)(565,584)(566,583)(567,582)(568,581)(569,580)(570,579)(571,578)(572,577)(573,576)(574,575)
Conjugacy classes & character table
7906 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31612, 11);
Finite Group Databasebeta