D₁₁₄₄₁ #37504282

order	22882
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₄₄₁
unambiguous semidirect product	C₁₇⋊D₆₇₃
unambiguous semidirect product	C₆₇₃⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₁₇×C₆₇₃ ⋊ C₂
Sylow	C₆₇₃ ⋊ D₁₇
Sylow	C₁₇ ⋊ D₆₇₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₆₇₃	C₂
LCS	G ▷ C₁₇×C₆₇₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 690
transitive degree	μ_t(G) = 11441

A minimal faithful permutation representation — 2 generators on 690 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,690)(20,689)(21,688)(22,687)(23,686)(24,685)(25,684)(26,683)(27,682)(28,681)(29,680)(30,679)(31,678)(32,677)(33,676)(34,675)(35,674)(36,673)(37,672)(38,671)(39,670)(40,669)(41,668)(42,667)(43,666)(44,665)(45,664)(46,663)(47,662)(48,661)(49,660)(50,659)(51,658)(52,657)(53,656)(54,655)(55,654)(56,653)(57,652)(58,651)(59,650)(60,649)(61,648)(62,647)(63,646)(64,645)(65,644)(66,643)(67,642)(68,641)(69,640)(70,639)(71,638)(72,637)(73,636)(74,635)(75,634)(76,633)(77,632)(78,631)(79,630)(80,629)(81,628)(82,627)(83,626)(84,625)(85,624)(86,623)(87,622)(88,621)(89,620)(90,619)(91,618)(92,617)(93,616)(94,615)(95,614)(96,613)(97,612)(98,611)(99,610)(100,609)(101,608)(102,607)(103,606)(104,605)(105,604)(106,603)(107,602)(108,601)(109,600)(110,599)(111,598)(112,597)(113,596)(114,595)(115,594)(116,593)(117,592)(118,591)(119,590)(120,589)(121,588)(122,587)(123,586)(124,585)(125,584)(126,583)(127,582)(128,581)(129,580)(130,579)(131,578)(132,577)(133,576)(134,575)(135,574)(136,573)(137,572)(138,571)(139,570)(140,569)(141,568)(142,567)(143,566)(144,565)(145,564)(146,563)(147,562)(148,561)(149,560)(150,559)(151,558)(152,557)(153,556)(154,555)(155,554)(156,553)(157,552)(158,551)(159,550)(160,549)(161,548)(162,547)(163,546)(164,545)(165,544)(166,543)(167,542)(168,541)(169,540)(170,539)(171,538)(172,537)(173,536)(174,535)(175,534)(176,533)(177,532)(178,531)(179,530)(180,529)(181,528)(182,527)(183,526)(184,525)(185,524)(186,523)(187,522)(188,521)(189,520)(190,519)(191,518)(192,517)(193,516)(194,515)(195,514)(196,513)(197,512)(198,511)(199,510)(200,509)(201,508)(202,507)(203,506)(204,505)(205,504)(206,503)(207,502)(208,501)(209,500)(210,499)(211,498)(212,497)(213,496)(214,495)(215,494)(216,493)(217,492)(218,491)(219,490)(220,489)(221,488)(222,487)(223,486)(224,485)(225,484)(226,483)(227,482)(228,481)(229,480)(230,479)(231,478)(232,477)(233,476)(234,475)(235,474)(236,473)(237,472)(238,471)(239,470)(240,469)(241,468)(242,467)(243,466)(244,465)(245,464)(246,463)(247,462)(248,461)(249,460)(250,459)(251,458)(252,457)(253,456)(254,455)(255,454)(256,453)(257,452)(258,451)(259,450)(260,449)(261,448)(262,447)(263,446)(264,445)(265,444)(266,443)(267,442)(268,441)(269,440)(270,439)(271,438)(272,437)(273,436)(274,435)(275,434)(276,433)(277,432)(278,431)(279,430)(280,429)(281,428)(282,427)(283,426)(284,425)(285,424)(286,423)(287,422)(288,421)(289,420)(290,419)(291,418)(292,417)(293,416)(294,415)(295,414)(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,407)(303,406)(304,405)(305,404)(306,403)(307,402)(308,401)(309,400)(310,399)(311,398)(312,397)(313,396)(314,395)(315,394)(316,393)(317,392)(318,391)(319,390)(320,389)(321,388)(322,387)(323,386)(324,385)(325,384)(326,383)(327,382)(328,381)(329,380)(330,379)(331,378)(332,377)(333,376)(334,375)(335,374)(336,373)(337,372)(338,371)(339,370)(340,369)(341,368)(342,367)(343,366)(344,365)(345,364)(346,363)(347,362)(348,361)(349,360)(350,359)(351,358)(352,357)(353,356)(354,355)

Polycyclic presentation:

2,17,673|b^a=b^16,c^a=c^672

Conjugacy classes & character table

5722 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22882, 3);

D11441 #37504282