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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1132 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);(4,9)(5,8)(6,7)(11,1132)(12,1131)(13,1130)(14,1129)(15,1128)(16,1127)(17,1126)(18,1125)(19,1124)(20,1123)(21,1122)(22,1121)(23,1120)(24,1119)(25,1118)(26,1117)(27,1116)(28,1115)(29,1114)(30,1113)(31,1112)(32,1111)(33,1110)(34,1109)(35,1108)(36,1107)(37,1106)(38,1105)(39,1104)(40,1103)(41,1102)(42,1101)(43,1100)(44,1099)(45,1098)(46,1097)(47,1096)(48,1095)(49,1094)(50,1093)(51,1092)(52,1091)(53,1090)(54,1089)(55,1088)(56,1087)(57,1086)(58,1085)(59,1084)(60,1083)(61,1082)(62,1081)(63,1080)(64,1079)(65,1078)(66,1077)(67,1076)(68,1075)(69,1074)(70,1073)(71,1072)(72,1071)(73,1070)(74,1069)(75,1068)(76,1067)(77,1066)(78,1065)(79,1064)(80,1063)(81,1062)(82,1061)(83,1060)(84,1059)(85,1058)(86,1057)(87,1056)(88,1055)(89,1054)(90,1053)(91,1052)(92,1051)(93,1050)(94,1049)(95,1048)(96,1047)(97,1046)(98,1045)(99,1044)(100,1043)(101,1042)(102,1041)(103,1040)(104,1039)(105,1038)(106,1037)(107,1036)(108,1035)(109,1034)(110,1033)(111,1032)(112,1031)(113,1030)(114,1029)(115,1028)(116,1027)(117,1026)(118,1025)(119,1024)(120,1023)(121,1022)(122,1021)(123,1020)(124,1019)(125,1018)(126,1017)(127,1016)(128,1015)(129,1014)(130,1013)(131,1012)(132,1011)(133,1010)(134,1009)(135,1008)(136,1007)(137,1006)(138,1005)(139,1004)(140,1003)(141,1002)(142,1001)(143,1000)(144,999)(145,998)(146,997)(147,996)(148,995)(149,994)(150,993)(151,992)(152,991)(153,990)(154,989)(155,988)(156,987)(157,986)(158,985)(159,984)(160,983)(161,982)(162,981)(163,980)(164,979)(165,978)(166,977)(167,976)(168,975)(169,974)(170,973)(171,972)(172,971)(173,970)(174,969)(175,968)(176,967)(177,966)(178,965)(179,964)(180,963)(181,962)(182,961)(183,960)(184,959)(185,958)(186,957)(187,956)(188,955)(189,954)(190,953)(191,952)(192,951)(193,950)(194,949)(195,948)(196,947)(197,946)(198,945)(199,944)(200,943)(201,942)(202,941)(203,940)(204,939)(205,938)(206,937)(207,936)(208,935)(209,934)(210,933)(211,932)(212,931)(213,930)(214,929)(215,928)(216,927)(217,926)(218,925)(219,924)(220,923)(221,922)(222,921)(223,920)(224,919)(225,918)(226,917)(227,916)(228,915)(229,914)(230,913)(231,912)(232,911)(233,910)(234,909)(235,908)(236,907)(237,906)(238,905)(239,904)(240,903)(241,902)(242,901)(243,900)(244,899)(245,898)(246,897)(247,896)(248,895)(249,894)(250,893)(251,892)(252,891)(253,890)(254,889)(255,888)(256,887)(257,886)(258,885)(259,884)(260,883)(261,882)(262,881)(263,880)(264,879)(265,878)(266,877)(267,876)(268,875)(269,874)(270,873)(271,872)(272,871)(273,870)(274,869)(275,868)(276,867)(277,866)(278,865)(279,864)(280,863)(281,862)(282,861)(283,860)(284,859)(285,858)(286,857)(287,856)(288,855)(289,854)(290,853)(291,852)(292,851)(293,850)(294,849)(295,848)(296,847)(297,846)(298,845)(299,844)(300,843)(301,842)(302,841)(303,840)(304,839)(305,838)(306,837)(307,836)(308,835)(309,834)(310,833)(311,832)(312,831)(313,830)(314,829)(315,828)(316,827)(317,826)(318,825)(319,824)(320,823)(321,822)(322,821)(323,820)(324,819)(325,818)(326,817)(327,816)(328,815)(329,814)(330,813)(331,812)(332,811)(333,810)(334,809)(335,808)(336,807)(337,806)(338,805)(339,804)(340,803)(341,802)(342,801)(343,800)(344,799)(345,798)(346,797)(347,796)(348,795)(349,794)(350,793)(351,792)(352,791)(353,790)(354,789)(355,788)(356,787)(357,786)(358,785)(359,784)(360,783)(361,782)(362,781)(363,780)(364,779)(365,778)(366,777)(367,776)(368,775)(369,774)(370,773)(371,772)(372,771)(373,770)(374,769)(375,768)(376,767)(377,766)(378,765)(379,764)(380,763)(381,762)(382,761)(383,760)(384,759)(385,758)(386,757)(387,756)(388,755)(389,754)(390,753)(391,752)(392,751)(393,750)(394,749)(395,748)(396,747)(397,746)(398,745)(399,744)(400,743)(401,742)(402,741)(403,740)(404,739)(405,738)(406,737)(407,736)(408,735)(409,734)(410,733)(411,732)(412,731)(413,730)(414,729)(415,728)(416,727)(417,726)(418,725)(419,724)(420,723)(421,722)(422,721)(423,720)(424,719)(425,718)(426,717)(427,716)(428,715)(429,714)(430,713)(431,712)(432,711)(433,710)(434,709)(435,708)(436,707)(437,706)(438,705)(439,704)(440,703)(441,702)(442,701)(443,700)(444,699)(445,698)(446,697)(447,696)(448,695)(449,694)(450,693)(451,692)(452,691)(453,690)(454,689)(455,688)(456,687)(457,686)(458,685)(459,684)(460,683)(461,682)(462,681)(463,680)(464,679)(465,678)(466,677)(467,676)(468,675)(469,674)(470,673)(471,672)(472,671)(473,670)(474,669)(475,668)(476,667)(477,666)(478,665)(479,664)(480,663)(481,662)(482,661)(483,660)(484,659)(485,658)(486,657)(487,656)(488,655)(489,654)(490,653)(491,652)(492,651)(493,650)(494,649)(495,648)(496,647)(497,646)(498,645)(499,644)(500,643)(501,642)(502,641)(503,640)(504,639)(505,638)(506,637)(507,636)(508,635)(509,634)(510,633)(511,632)(512,631)(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,624)(520,623)(521,622)(522,621)(523,620)(524,619)(525,618)(526,617)(527,616)(528,615)(529,614)(530,613)(531,612)(532,611)(533,610)(534,609)(535,608)(536,607)(537,606)(538,605)(539,604)(540,603)(541,602)(542,601)(543,600)(544,599)(545,598)(546,597)(547,596)(548,595)(549,594)(550,593)(551,592)(552,591)(553,590)(554,589)(555,588)(556,587)(557,586)(558,585)(559,584)(560,583)(561,582)(562,581)(563,580)(564,579)(565,578)(566,577)(567,576)(568,575)(569,574)(570,573)(571,572)
Conjugacy classes & character table
7864 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31444, 9);
Finite Group Databasebeta