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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 929 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);(5,10)(6,9)(7,8)(12,929)(13,928)(14,927)(15,926)(16,925)(17,924)(18,923)(19,922)(20,921)(21,920)(22,919)(23,918)(24,917)(25,916)(26,915)(27,914)(28,913)(29,912)(30,911)(31,910)(32,909)(33,908)(34,907)(35,906)(36,905)(37,904)(38,903)(39,902)(40,901)(41,900)(42,899)(43,898)(44,897)(45,896)(46,895)(47,894)(48,893)(49,892)(50,891)(51,890)(52,889)(53,888)(54,887)(55,886)(56,885)(57,884)(58,883)(59,882)(60,881)(61,880)(62,879)(63,878)(64,877)(65,876)(66,875)(67,874)(68,873)(69,872)(70,871)(71,870)(72,869)(73,868)(74,867)(75,866)(76,865)(77,864)(78,863)(79,862)(80,861)(81,860)(82,859)(83,858)(84,857)(85,856)(86,855)(87,854)(88,853)(89,852)(90,851)(91,850)(92,849)(93,848)(94,847)(95,846)(96,845)(97,844)(98,843)(99,842)(100,841)(101,840)(102,839)(103,838)(104,837)(105,836)(106,835)(107,834)(108,833)(109,832)(110,831)(111,830)(112,829)(113,828)(114,827)(115,826)(116,825)(117,824)(118,823)(119,822)(120,821)(121,820)(122,819)(123,818)(124,817)(125,816)(126,815)(127,814)(128,813)(129,812)(130,811)(131,810)(132,809)(133,808)(134,807)(135,806)(136,805)(137,804)(138,803)(139,802)(140,801)(141,800)(142,799)(143,798)(144,797)(145,796)(146,795)(147,794)(148,793)(149,792)(150,791)(151,790)(152,789)(153,788)(154,787)(155,786)(156,785)(157,784)(158,783)(159,782)(160,781)(161,780)(162,779)(163,778)(164,777)(165,776)(166,775)(167,774)(168,773)(169,772)(170,771)(171,770)(172,769)(173,768)(174,767)(175,766)(176,765)(177,764)(178,763)(179,762)(180,761)(181,760)(182,759)(183,758)(184,757)(185,756)(186,755)(187,754)(188,753)(189,752)(190,751)(191,750)(192,749)(193,748)(194,747)(195,746)(196,745)(197,744)(198,743)(199,742)(200,741)(201,740)(202,739)(203,738)(204,737)(205,736)(206,735)(207,734)(208,733)(209,732)(210,731)(211,730)(212,729)(213,728)(214,727)(215,726)(216,725)(217,724)(218,723)(219,722)(220,721)(221,720)(222,719)(223,718)(224,717)(225,716)(226,715)(227,714)(228,713)(229,712)(230,711)(231,710)(232,709)(233,708)(234,707)(235,706)(236,705)(237,704)(238,703)(239,702)(240,701)(241,700)(242,699)(243,698)(244,697)(245,696)(246,695)(247,694)(248,693)(249,692)(250,691)(251,690)(252,689)(253,688)(254,687)(255,686)(256,685)(257,684)(258,683)(259,682)(260,681)(261,680)(262,679)(263,678)(264,677)(265,676)(266,675)(267,674)(268,673)(269,672)(270,671)(271,670)(272,669)(273,668)(274,667)(275,666)(276,665)(277,664)(278,663)(279,662)(280,661)(281,660)(282,659)(283,658)(284,657)(285,656)(286,655)(287,654)(288,653)(289,652)(290,651)(291,650)(292,649)(293,648)(294,647)(295,646)(296,645)(297,644)(298,643)(299,642)(300,641)(301,640)(302,639)(303,638)(304,637)(305,636)(306,635)(307,634)(308,633)(309,632)(310,631)(311,630)(312,629)(313,628)(314,627)(315,626)(316,625)(317,624)(318,623)(319,622)(320,621)(321,620)(322,619)(323,618)(324,617)(325,616)(326,615)(327,614)(328,613)(329,612)(330,611)(331,610)(332,609)(333,608)(334,607)(335,606)(336,605)(337,604)(338,603)(339,602)(340,601)(341,600)(342,599)(343,598)(344,597)(345,596)(346,595)(347,594)(348,593)(349,592)(350,591)(351,590)(352,589)(353,588)(354,587)(355,586)(356,585)(357,584)(358,583)(359,582)(360,581)(361,580)(362,579)(363,578)(364,577)(365,576)(366,575)(367,574)(368,573)(369,572)(370,571)(371,570)(372,569)(373,568)(374,567)(375,566)(376,565)(377,564)(378,563)(379,562)(380,561)(381,560)(382,559)(383,558)(384,557)(385,556)(386,555)(387,554)(388,553)(389,552)(390,551)(391,550)(392,549)(393,548)(394,547)(395,546)(396,545)(397,544)(398,543)(399,542)(400,541)(401,540)(402,539)(403,538)(404,537)(405,536)(406,535)(407,534)(408,533)(409,532)(410,531)(411,530)(412,529)(413,528)(414,527)(415,526)(416,525)(417,524)(418,523)(419,522)(420,521)(421,520)(422,519)(423,518)(424,517)(425,516)(426,515)(427,514)(428,513)(429,512)(430,511)(431,510)(432,509)(433,508)(434,507)(435,506)(436,505)(437,504)(438,503)(439,502)(440,501)(441,500)(442,499)(443,498)(444,497)(445,496)(446,495)(447,494)(448,493)(449,492)(450,491)(451,490)(452,489)(453,488)(454,487)(455,486)(456,485)(457,484)(458,483)(459,482)(460,481)(461,480)(462,479)(463,478)(464,477)(465,476)(466,475)(467,474)(468,473)(469,472)(470,471)
Conjugacy classes & character table
9654 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38598, 8);
Finite Group Databasebeta