Dic₇₂₄₁ #44394240

order	28964
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₇₂₄₁

Splittings

derived, Hall	C₁₃×C₅₅₇ ⋊ C₄
Sylow	C₅₅₇ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ Dic₅₅₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₇₂₄₁
commutator, hypocenter	C₁₃×C₅₅₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₃×C₅₅₇	C₂
LCS	G ▷ C₁₃×C₅₅₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 574
transitive degree	μ_t(G) = 28964

A minimal faithful permutation representation — 2 generators on 574 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,574)(20,573)(21,572)(22,571)(23,570)(24,569)(25,568)(26,567)(27,566)(28,565)(29,564)(30,563)(31,562)(32,561)(33,560)(34,559)(35,558)(36,557)(37,556)(38,555)(39,554)(40,553)(41,552)(42,551)(43,550)(44,549)(45,548)(46,547)(47,546)(48,545)(49,544)(50,543)(51,542)(52,541)(53,540)(54,539)(55,538)(56,537)(57,536)(58,535)(59,534)(60,533)(61,532)(62,531)(63,530)(64,529)(65,528)(66,527)(67,526)(68,525)(69,524)(70,523)(71,522)(72,521)(73,520)(74,519)(75,518)(76,517)(77,516)(78,515)(79,514)(80,513)(81,512)(82,511)(83,510)(84,509)(85,508)(86,507)(87,506)(88,505)(89,504)(90,503)(91,502)(92,501)(93,500)(94,499)(95,498)(96,497)(97,496)(98,495)(99,494)(100,493)(101,492)(102,491)(103,490)(104,489)(105,488)(106,487)(107,486)(108,485)(109,484)(110,483)(111,482)(112,481)(113,480)(114,479)(115,478)(116,477)(117,476)(118,475)(119,474)(120,473)(121,472)(122,471)(123,470)(124,469)(125,468)(126,467)(127,466)(128,465)(129,464)(130,463)(131,462)(132,461)(133,460)(134,459)(135,458)(136,457)(137,456)(138,455)(139,454)(140,453)(141,452)(142,451)(143,450)(144,449)(145,448)(146,447)(147,446)(148,445)(149,444)(150,443)(151,442)(152,441)(153,440)(154,439)(155,438)(156,437)(157,436)(158,435)(159,434)(160,433)(161,432)(162,431)(163,430)(164,429)(165,428)(166,427)(167,426)(168,425)(169,424)(170,423)(171,422)(172,421)(173,420)(174,419)(175,418)(176,417)(177,416)(178,415)(179,414)(180,413)(181,412)(182,411)(183,410)(184,409)(185,408)(186,407)(187,406)(188,405)(189,404)(190,403)(191,402)(192,401)(193,400)(194,399)(195,398)(196,397)(197,396)(198,395)(199,394)(200,393)(201,392)(202,391)(203,390)(204,389)(205,388)(206,387)(207,386)(208,385)(209,384)(210,383)(211,382)(212,381)(213,380)(214,379)(215,378)(216,377)(217,376)(218,375)(219,374)(220,373)(221,372)(222,371)(223,370)(224,369)(225,368)(226,367)(227,366)(228,365)(229,364)(230,363)(231,362)(232,361)(233,360)(234,359)(235,358)(236,357)(237,356)(238,355)(239,354)(240,353)(241,352)(242,351)(243,350)(244,349)(245,348)(246,347)(247,346)(248,345)(249,344)(250,343)(251,342)(252,341)(253,340)(254,339)(255,338)(256,337)(257,336)(258,335)(259,334)(260,333)(261,332)(262,331)(263,330)(264,329)(265,328)(266,327)(267,326)(268,325)(269,324)(270,323)(271,322)(272,321)(273,320)(274,319)(275,318)(276,317)(277,316)(278,315)(279,314)(280,313)(281,312)(282,311)(283,310)(284,309)(285,308)(286,307)(287,306)(288,305)(289,304)(290,303)(291,302)(292,301)(293,300)(294,299)(295,298)(296,297)

Polycyclic presentation:

2,13,557,2|a^2=d,b^a=b^12,c^a=c^556

Conjugacy classes & character table

7244 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₄₄₈₂
maximal normal subgroup of	Dic₁₄₄₈₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28964, 4);

Dic7241 #44394240