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Dic829 #15693278
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 833 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);(1,3,2,4)(6,833)(7,832)(8,831)(9,830)(10,829)(11,828)(12,827)(13,826)(14,825)(15,824)(16,823)(17,822)(18,821)(19,820)(20,819)(21,818)(22,817)(23,816)(24,815)(25,814)(26,813)(27,812)(28,811)(29,810)(30,809)(31,808)(32,807)(33,806)(34,805)(35,804)(36,803)(37,802)(38,801)(39,800)(40,799)(41,798)(42,797)(43,796)(44,795)(45,794)(46,793)(47,792)(48,791)(49,790)(50,789)(51,788)(52,787)(53,786)(54,785)(55,784)(56,783)(57,782)(58,781)(59,780)(60,779)(61,778)(62,777)(63,776)(64,775)(65,774)(66,773)(67,772)(68,771)(69,770)(70,769)(71,768)(72,767)(73,766)(74,765)(75,764)(76,763)(77,762)(78,761)(79,760)(80,759)(81,758)(82,757)(83,756)(84,755)(85,754)(86,753)(87,752)(88,751)(89,750)(90,749)(91,748)(92,747)(93,746)(94,745)(95,744)(96,743)(97,742)(98,741)(99,740)(100,739)(101,738)(102,737)(103,736)(104,735)(105,734)(106,733)(107,732)(108,731)(109,730)(110,729)(111,728)(112,727)(113,726)(114,725)(115,724)(116,723)(117,722)(118,721)(119,720)(120,719)(121,718)(122,717)(123,716)(124,715)(125,714)(126,713)(127,712)(128,711)(129,710)(130,709)(131,708)(132,707)(133,706)(134,705)(135,704)(136,703)(137,702)(138,701)(139,700)(140,699)(141,698)(142,697)(143,696)(144,695)(145,694)(146,693)(147,692)(148,691)(149,690)(150,689)(151,688)(152,687)(153,686)(154,685)(155,684)(156,683)(157,682)(158,681)(159,680)(160,679)(161,678)(162,677)(163,676)(164,675)(165,674)(166,673)(167,672)(168,671)(169,670)(170,669)(171,668)(172,667)(173,666)(174,665)(175,664)(176,663)(177,662)(178,661)(179,660)(180,659)(181,658)(182,657)(183,656)(184,655)(185,654)(186,653)(187,652)(188,651)(189,650)(190,649)(191,648)(192,647)(193,646)(194,645)(195,644)(196,643)(197,642)(198,641)(199,640)(200,639)(201,638)(202,637)(203,636)(204,635)(205,634)(206,633)(207,632)(208,631)(209,630)(210,629)(211,628)(212,627)(213,626)(214,625)(215,624)(216,623)(217,622)(218,621)(219,620)(220,619)(221,618)(222,617)(223,616)(224,615)(225,614)(226,613)(227,612)(228,611)(229,610)(230,609)(231,608)(232,607)(233,606)(234,605)(235,604)(236,603)(237,602)(238,601)(239,600)(240,599)(241,598)(242,597)(243,596)(244,595)(245,594)(246,593)(247,592)(248,591)(249,590)(250,589)(251,588)(252,587)(253,586)(254,585)(255,584)(256,583)(257,582)(258,581)(259,580)(260,579)(261,578)(262,577)(263,576)(264,575)(265,574)(266,573)(267,572)(268,571)(269,570)(270,569)(271,568)(272,567)(273,566)(274,565)(275,564)(276,563)(277,562)(278,561)(279,560)(280,559)(281,558)(282,557)(283,556)(284,555)(285,554)(286,553)(287,552)(288,551)(289,550)(290,549)(291,548)(292,547)(293,546)(294,545)(295,544)(296,543)(297,542)(298,541)(299,540)(300,539)(301,538)(302,537)(303,536)(304,535)(305,534)(306,533)(307,532)(308,531)(309,530)(310,529)(311,528)(312,527)(313,526)(314,525)(315,524)(316,523)(317,522)(318,521)(319,520)(320,519)(321,518)(322,517)(323,516)(324,515)(325,514)(326,513)(327,512)(328,511)(329,510)(330,509)(331,508)(332,507)(333,506)(334,505)(335,504)(336,503)(337,502)(338,501)(339,500)(340,499)(341,498)(342,497)(343,496)(344,495)(345,494)(346,493)(347,492)(348,491)(349,490)(350,489)(351,488)(352,487)(353,486)(354,485)(355,484)(356,483)(357,482)(358,481)(359,480)(360,479)(361,478)(362,477)(363,476)(364,475)(365,474)(366,473)(367,472)(368,471)(369,470)(370,469)(371,468)(372,467)(373,466)(374,465)(375,464)(376,463)(377,462)(378,461)(379,460)(380,459)(381,458)(382,457)(383,456)(384,455)(385,454)(386,453)(387,452)(388,451)(389,450)(390,449)(391,448)(392,447)(393,446)(394,445)(395,444)(396,443)(397,442)(398,441)(399,440)(400,439)(401,438)(402,437)(403,436)(404,435)(405,434)(406,433)(407,432)(408,431)(409,430)(410,429)(411,428)(412,427)(413,426)(414,425)(415,424)(416,423)(417,422)(418,421)(419,420)
Polycyclic presentation:
2^2,829|a^2=b,c^a=c^828
Conjugacy classes & character table
832 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3316, 1);
Finite Group Databasebeta