Dic₆₄₅₇ #38788890

order	25828
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₄₅₇
unambiguous semidirect product	C₁₁⋊Dic₅₈₇
unambiguous semidirect product	C₅₈₇⋊Dic₁₁

Splittings

derived, Hall	C₁₁×C₅₈₇ ⋊ C₄
Sylow	C₅₈₇ ⋊ Dic₁₁
Sylow	C₁₁ ⋊ Dic₅₈₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₄₅₇
commutator, hypocenter	C₁₁×C₅₈₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₅₈₇	C₂
LCS	G ▷ C₁₁×C₅₈₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 602
transitive degree	μ_t(G) = 25828

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

Polycyclic presentation:

2,11,587,2|a^2=d,b^a=b^10,c^a=c^586

Conjugacy classes & character table

6460 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₂₉₁₄
maximal normal subgroup of	Dic₁₂₉₁₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25828, 4);

Dic6457 #38788890