C₃×D₄₀₃₉ #37564555

order	24234
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₄₀₃₉

Splittings

Fitting, socle, Hall	C₃×C₇×C₅₇₇ ⋊ C₂
derived, Hall	C₇×C₅₇₇ ⋊ C₂×C₃
Hall	C₃×C₅₇₇ ⋊ D₇
Sylow	C₅₇₇ ⋊ C₃×D₇
Hall	C₃×C₇ ⋊ D₅₇₇
Sylow	C₇ ⋊ C₃×D₅₇₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₄₀₃₉
commutator, cosocle, hypocenter	C₇×C₅₇₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₅₇₇	C₂
LCS	G ▷ C₇×C₅₇₇
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 587
transitive degree	μ_t(G) = 12117

A minimal faithful permutation representation — 2 generators on 587 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);(5,10)(6,9)(7,8)(12,587)(13,586)(14,585)(15,584)(16,583)(17,582)(18,581)(19,580)(20,579)(21,578)(22,577)(23,576)(24,575)(25,574)(26,573)(27,572)(28,571)(29,570)(30,569)(31,568)(32,567)(33,566)(34,565)(35,564)(36,563)(37,562)(38,561)(39,560)(40,559)(41,558)(42,557)(43,556)(44,555)(45,554)(46,553)(47,552)(48,551)(49,550)(50,549)(51,548)(52,547)(53,546)(54,545)(55,544)(56,543)(57,542)(58,541)(59,540)(60,539)(61,538)(62,537)(63,536)(64,535)(65,534)(66,533)(67,532)(68,531)(69,530)(70,529)(71,528)(72,527)(73,526)(74,525)(75,524)(76,523)(77,522)(78,521)(79,520)(80,519)(81,518)(82,517)(83,516)(84,515)(85,514)(86,513)(87,512)(88,511)(89,510)(90,509)(91,508)(92,507)(93,506)(94,505)(95,504)(96,503)(97,502)(98,501)(99,500)(100,499)(101,498)(102,497)(103,496)(104,495)(105,494)(106,493)(107,492)(108,491)(109,490)(110,489)(111,488)(112,487)(113,486)(114,485)(115,484)(116,483)(117,482)(118,481)(119,480)(120,479)(121,478)(122,477)(123,476)(124,475)(125,474)(126,473)(127,472)(128,471)(129,470)(130,469)(131,468)(132,467)(133,466)(134,465)(135,464)(136,463)(137,462)(138,461)(139,460)(140,459)(141,458)(142,457)(143,456)(144,455)(145,454)(146,453)(147,452)(148,451)(149,450)(150,449)(151,448)(152,447)(153,446)(154,445)(155,444)(156,443)(157,442)(158,441)(159,440)(160,439)(161,438)(162,437)(163,436)(164,435)(165,434)(166,433)(167,432)(168,431)(169,430)(170,429)(171,428)(172,427)(173,426)(174,425)(175,424)(176,423)(177,422)(178,421)(179,420)(180,419)(181,418)(182,417)(183,416)(184,415)(185,414)(186,413)(187,412)(188,411)(189,410)(190,409)(191,408)(192,407)(193,406)(194,405)(195,404)(196,403)(197,402)(198,401)(199,400)(200,399)(201,398)(202,397)(203,396)(204,395)(205,394)(206,393)(207,392)(208,391)(209,390)(210,389)(211,388)(212,387)(213,386)(214,385)(215,384)(216,383)(217,382)(218,381)(219,380)(220,379)(221,378)(222,377)(223,376)(224,375)(225,374)(226,373)(227,372)(228,371)(229,370)(230,369)(231,368)(232,367)(233,366)(234,365)(235,364)(236,363)(237,362)(238,361)(239,360)(240,359)(241,358)(242,357)(243,356)(244,355)(245,354)(246,353)(247,352)(248,351)(249,350)(250,349)(251,348)(252,347)(253,346)(254,345)(255,344)(256,343)(257,342)(258,341)(259,340)(260,339)(261,338)(262,337)(263,336)(264,335)(265,334)(266,333)(267,332)(268,331)(269,330)(270,329)(271,328)(272,327)(273,326)(274,325)(275,324)(276,323)(277,322)(278,321)(279,320)(280,319)(281,318)(282,317)(283,316)(284,315)(285,314)(286,313)(287,312)(288,311)(289,310)(290,309)(291,308)(292,307)(293,306)(294,305)(295,304)(296,303)(297,302)(298,301)(299,300)

Conjugacy classes & character table

6063 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24234, 8);

C3×D4039 #37564555