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Aliases
Splittings
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 921 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);(4,921)(5,920)(6,919)(7,918)(8,917)(9,916)(10,915)(11,914)(12,913)(13,912)(14,911)(15,910)(16,909)(17,908)(18,907)(19,906)(20,905)(21,904)(22,903)(23,902)(24,901)(25,900)(26,899)(27,898)(28,897)(29,896)(30,895)(31,894)(32,893)(33,892)(34,891)(35,890)(36,889)(37,888)(38,887)(39,886)(40,885)(41,884)(42,883)(43,882)(44,881)(45,880)(46,879)(47,878)(48,877)(49,876)(50,875)(51,874)(52,873)(53,872)(54,871)(55,870)(56,869)(57,868)(58,867)(59,866)(60,865)(61,864)(62,863)(63,862)(64,861)(65,860)(66,859)(67,858)(68,857)(69,856)(70,855)(71,854)(72,853)(73,852)(74,851)(75,850)(76,849)(77,848)(78,847)(79,846)(80,845)(81,844)(82,843)(83,842)(84,841)(85,840)(86,839)(87,838)(88,837)(89,836)(90,835)(91,834)(92,833)(93,832)(94,831)(95,830)(96,829)(97,828)(98,827)(99,826)(100,825)(101,824)(102,823)(103,822)(104,821)(105,820)(106,819)(107,818)(108,817)(109,816)(110,815)(111,814)(112,813)(113,812)(114,811)(115,810)(116,809)(117,808)(118,807)(119,806)(120,805)(121,804)(122,803)(123,802)(124,801)(125,800)(126,799)(127,798)(128,797)(129,796)(130,795)(131,794)(132,793)(133,792)(134,791)(135,790)(136,789)(137,788)(138,787)(139,786)(140,785)(141,784)(142,783)(143,782)(144,781)(145,780)(146,779)(147,778)(148,777)(149,776)(150,775)(151,774)(152,773)(153,772)(154,771)(155,770)(156,769)(157,768)(158,767)(159,766)(160,765)(161,764)(162,763)(163,762)(164,761)(165,760)(166,759)(167,758)(168,757)(169,756)(170,755)(171,754)(172,753)(173,752)(174,751)(175,750)(176,749)(177,748)(178,747)(179,746)(180,745)(181,744)(182,743)(183,742)(184,741)(185,740)(186,739)(187,738)(188,737)(189,736)(190,735)(191,734)(192,733)(193,732)(194,731)(195,730)(196,729)(197,728)(198,727)(199,726)(200,725)(201,724)(202,723)(203,722)(204,721)(205,720)(206,719)(207,718)(208,717)(209,716)(210,715)(211,714)(212,713)(213,712)(214,711)(215,710)(216,709)(217,708)(218,707)(219,706)(220,705)(221,704)(222,703)(223,702)(224,701)(225,700)(226,699)(227,698)(228,697)(229,696)(230,695)(231,694)(232,693)(233,692)(234,691)(235,690)(236,689)(237,688)(238,687)(239,686)(240,685)(241,684)(242,683)(243,682)(244,681)(245,680)(246,679)(247,678)(248,677)(249,676)(250,675)(251,674)(252,673)(253,672)(254,671)(255,670)(256,669)(257,668)(258,667)(259,666)(260,665)(261,664)(262,663)(263,662)(264,661)(265,660)(266,659)(267,658)(268,657)(269,656)(270,655)(271,654)(272,653)(273,652)(274,651)(275,650)(276,649)(277,648)(278,647)(279,646)(280,645)(281,644)(282,643)(283,642)(284,641)(285,640)(286,639)(287,638)(288,637)(289,636)(290,635)(291,634)(292,633)(293,632)(294,631)(295,630)(296,629)(297,628)(298,627)(299,626)(300,625)(301,624)(302,623)(303,622)(304,621)(305,620)(306,619)(307,618)(308,617)(309,616)(310,615)(311,614)(312,613)(313,612)(314,611)(315,610)(316,609)(317,608)(318,607)(319,606)(320,605)(321,604)(322,603)(323,602)(324,601)(325,600)(326,599)(327,598)(328,597)(329,596)(330,595)(331,594)(332,593)(333,592)(334,591)(335,590)(336,589)(337,588)(338,587)(339,586)(340,585)(341,584)(342,583)(343,582)(344,581)(345,580)(346,579)(347,578)(348,577)(349,576)(350,575)(351,574)(352,573)(353,572)(354,571)(355,570)(356,569)(357,568)(358,567)(359,566)(360,565)(361,564)(362,563)(363,562)(364,561)(365,560)(366,559)(367,558)(368,557)(369,556)(370,555)(371,554)(372,553)(373,552)(374,551)(375,550)(376,549)(377,548)(378,547)(379,546)(380,545)(381,544)(382,543)(383,542)(384,541)(385,540)(386,539)(387,538)(388,537)(389,536)(390,535)(391,534)(392,533)(393,532)(394,531)(395,530)(396,529)(397,528)(398,527)(399,526)(400,525)(401,524)(402,523)(403,522)(404,521)(405,520)(406,519)(407,518)(408,517)(409,516)(410,515)(411,514)(412,513)(413,512)(414,511)(415,510)(416,509)(417,508)(418,507)(419,506)(420,505)(421,504)(422,503)(423,502)(424,501)(425,500)(426,499)(427,498)(428,497)(429,496)(430,495)(431,494)(432,493)(433,492)(434,491)(435,490)(436,489)(437,488)(438,487)(439,486)(440,485)(441,484)(442,483)(443,482)(444,481)(445,480)(446,479)(447,478)(448,477)(449,476)(450,475)(451,474)(452,473)(453,472)(454,471)(455,470)(456,469)(457,468)(458,467)(459,466)(460,465)(461,464)(462,463)
Conjugacy classes & character table
922 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3676, 3);
Finite Group Databasebeta