Dic₆₆₁₁ #40996255

order	26444
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₆₁₁
unambiguous semidirect product	C₁₁⋊Dic₆₀₁

Splittings

derived, Hall	C₁₁×C₆₀₁ ⋊ C₄
Sylow	C₆₀₁ ⋊ Dic₁₁
Sylow	C₁₁ ⋊ Dic₆₀₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₆₁₁
commutator, hypocenter	C₁₁×C₆₀₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₆₀₁	C₂
LCS	G ▷ C₁₁×C₆₀₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 616
transitive degree	μ_t(G) = 26444

A minimal faithful permutation representation — 2 generators on 616 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,616)(18,615)(19,614)(20,613)(21,612)(22,611)(23,610)(24,609)(25,608)(26,607)(27,606)(28,605)(29,604)(30,603)(31,602)(32,601)(33,600)(34,599)(35,598)(36,597)(37,596)(38,595)(39,594)(40,593)(41,592)(42,591)(43,590)(44,589)(45,588)(46,587)(47,586)(48,585)(49,584)(50,583)(51,582)(52,581)(53,580)(54,579)(55,578)(56,577)(57,576)(58,575)(59,574)(60,573)(61,572)(62,571)(63,570)(64,569)(65,568)(66,567)(67,566)(68,565)(69,564)(70,563)(71,562)(72,561)(73,560)(74,559)(75,558)(76,557)(77,556)(78,555)(79,554)(80,553)(81,552)(82,551)(83,550)(84,549)(85,548)(86,547)(87,546)(88,545)(89,544)(90,543)(91,542)(92,541)(93,540)(94,539)(95,538)(96,537)(97,536)(98,535)(99,534)(100,533)(101,532)(102,531)(103,530)(104,529)(105,528)(106,527)(107,526)(108,525)(109,524)(110,523)(111,522)(112,521)(113,520)(114,519)(115,518)(116,517)(117,516)(118,515)(119,514)(120,513)(121,512)(122,511)(123,510)(124,509)(125,508)(126,507)(127,506)(128,505)(129,504)(130,503)(131,502)(132,501)(133,500)(134,499)(135,498)(136,497)(137,496)(138,495)(139,494)(140,493)(141,492)(142,491)(143,490)(144,489)(145,488)(146,487)(147,486)(148,485)(149,484)(150,483)(151,482)(152,481)(153,480)(154,479)(155,478)(156,477)(157,476)(158,475)(159,474)(160,473)(161,472)(162,471)(163,470)(164,469)(165,468)(166,467)(167,466)(168,465)(169,464)(170,463)(171,462)(172,461)(173,460)(174,459)(175,458)(176,457)(177,456)(178,455)(179,454)(180,453)(181,452)(182,451)(183,450)(184,449)(185,448)(186,447)(187,446)(188,445)(189,444)(190,443)(191,442)(192,441)(193,440)(194,439)(195,438)(196,437)(197,436)(198,435)(199,434)(200,433)(201,432)(202,431)(203,430)(204,429)(205,428)(206,427)(207,426)(208,425)(209,424)(210,423)(211,422)(212,421)(213,420)(214,419)(215,418)(216,417)(217,416)(218,415)(219,414)(220,413)(221,412)(222,411)(223,410)(224,409)(225,408)(226,407)(227,406)(228,405)(229,404)(230,403)(231,402)(232,401)(233,400)(234,399)(235,398)(236,397)(237,396)(238,395)(239,394)(240,393)(241,392)(242,391)(243,390)(244,389)(245,388)(246,387)(247,386)(248,385)(249,384)(250,383)(251,382)(252,381)(253,380)(254,379)(255,378)(256,377)(257,376)(258,375)(259,374)(260,373)(261,372)(262,371)(263,370)(264,369)(265,368)(266,367)(267,366)(268,365)(269,364)(270,363)(271,362)(272,361)(273,360)(274,359)(275,358)(276,357)(277,356)(278,355)(279,354)(280,353)(281,352)(282,351)(283,350)(284,349)(285,348)(286,347)(287,346)(288,345)(289,344)(290,343)(291,342)(292,341)(293,340)(294,339)(295,338)(296,337)(297,336)(298,335)(299,334)(300,333)(301,332)(302,331)(303,330)(304,329)(305,328)(306,327)(307,326)(308,325)(309,324)(310,323)(311,322)(312,321)(313,320)(314,319)(315,318)(316,317)

Polycyclic presentation:

2,11,601,2|a^2=d,b^a=b^10,c^a=c^600

Conjugacy classes & character table

6614 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₃₂₂₂
maximal normal subgroup of	Dic₁₃₂₂₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26444, 4);

Dic6611 #40996255