C₂×D₈₄₅₉ #46799156

order	33836
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₉₁₈
direct product	C₂×D₈₄₅₉
unambiguous semidirect product	(C₂×C₁₁)⋊D₇₆₉
unambiguous semidirect product	(C₂×C₇₆₉)⋊D₁₁

Splittings

Fitting, socle	C₂×C₁₁×C₇₆₉ ⋊ C₂
derived, Hall	C₁₁×C₇₆₉ ⋊ C₂²
Sylow	C₇₆₉ ⋊ C₂×D₁₁
Sylow	C₁₁ ⋊ C₂×D₇₆₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₄₅₉
commutator, cosocle, hypocenter	C₁₁×C₇₆₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁×C₇₆₉	C₂
LCS	G ▷ C₁₁×C₇₆₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 782
transitive degree	μ_t(G) = 16918

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

Conjugacy classes & character table

8462 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33836, 11);

C2×D8459 #46799156