#46803907

order	34242
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₃×C₄₃₉ ⋊ C₂×C₃
Hall	#30686125 ⋊ C₂
Hall	D₅₇₀₇ ⋊ C₃
Sylow	C₄₃₉ ⋊ D₁₃⋊C₃
Sylow	C₁₃ ⋊ D₄₃₉⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₄₃₉	C₂×C₃
LCS	G ▷ C₁₃×C₄₃₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 452
transitive degree	μ_t(G) = 5707

A minimal faithful permutation representation — 2 generators on 452 points:

(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,27,28,22,23,37)(24,40,41,30,31,54)(25,39,35,33,29,26)(32,59,60,43,44,77)(34,57,58,46,42,51)(36,38,56,48,49,52)(45,82,83,62,63,106)(47,80,81,65,61,74)(50,55,79,67,68,75)(53,95,93,71,72,70)(64,111,112,85,86,141)(66,109,110,88,84,103)(69,78,108,90,91,104)(73,124,125,96,97,99)(76,130,122,100,101,94)(87,146,147,114,115,182)(89,144,145,117,113,138)(92,107,143,119,120,139)(98,159,160,126,127,134)(102,166,164,131,132,129)(105,171,157,135,136,123)(116,187,188,149,150,229)(118,185,186,152,148,179)(121,142,184,154,155,180)(128,200,201,161,162,175)(133,207,208,167,168,170)(137,213,205,172,173,165)(140,218,198,176,177,158)(151,234,235,190,191,282)(153,232,233,193,189,226)(156,183,231,195,196,227)(163,247,248,202,203,222)(169,254,255,209,210,217)(174,261,259,214,215,212)(178,266,252,219,220,206)(181,271,245,223,224,199)(192,287,288,237,238,341)(194,285,286,240,236,279)(197,230,284,242,243,280)(204,300,301,249,250,275)(211,307,308,256,257,270)(216,314,315,262,263,265)(221,320,312,267,268,260)(225,325,305,272,273,253)(228,330,298,276,277,246)(239,346,347,290,291,399)(241,344,345,293,289,338)(244,283,343,295,296,339)(251,358,359,302,303,334)(258,365,366,309,310,329)(264,372,373,316,317,324)(269,377,350,321,322,319)(274,382,370,326,327,313)(278,387,363,331,332,306)(281,391,356,335,336,299)(292,383,384,349,328,426)(294,401,402,351,348,397)(297,342,400,353,354,398)(304,407,408,360,361,394)(311,412,413,367,368,390)(318,417,418,374,375,386)(323,422,404,378,379,381)(333,430,355,388,389,371)(337,432,406,392,393,364)(340,434,405,395,396,357)(352,427,428,403,385,436)(362,437,438,409,410,435)(369,439,440,414,415,433)(376,443,442,419,420,431)(380,447,411,423,424,429)(416,448,449,441,425,451)(421,452,446,444,445,450);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,18,24,32,45,64,87,116,151,192,239,292,350,315,255,201,145,83,108,130,124,109,82,107,140,178,221,269,323,380,425,445,449,438,402,288,343,391,387,382,377,372,365,358,344,287,342,392,335,243,150,189,203,210,215,220,224,227,229,279,334,390,431,441,414,367,309,256,209,167,131,100,68,31,42,52,54,74,99,129,165,206,253,306,364,405,356,298,245,198,157,122,93,58,28,39,27,38,53,73,98,128,163,204,251,304,362,411,418,366,301,233,147,184,218,213,207,200,185,146,183,228,278,333,291,348,361,368,375,379,384,389,393,396,398,399,436,447,443,439,437,427,383,326,272,223,155,86,113,127,132,136,139,141,179,222,270,324,381,403,351,293,240,193,152,117,88,65,46,33,17,21,26,36,50,69,92,121,156,197,244,297,355,370,312,259,208,160,110,60,79,95,80,59,78,105,137,174,216,264,318,376,421,446,440,408,345,235,284,330,325,320,314,307,300,285,234,283,340,395,296,191,236,250,257,263,268,273,277,280,282,338,394,433,450,444,419,374,316,262,214,172,135,91,44,61,72,75,77,103,134,170,212,260,313,371,353,295,242,195,154,119,90,67,48,35,20,19,25,34,47,66,89,118,153,194,241,294,352,404,373,308,248,186,112,143,171,166,159,144,111,142,181,225,274,328,385,410,415,420,424,428,347,400,434,432,430,426,422,417,412,407,401,346,388,331,276,196,115,148,162,168,173,177,180,182,226,275,329,386,429,409,360,302,249,202,161,126,96,71,49,23,29,37,51,70,94,123,158,199,246,299,357,406,363,305,252,205,164,125,81,41,56,57,40,55,76,102,133,169,211,258,311,369,416,442,413,359,286,188,231,271,266,261,254,247,232,187,230,281,337,354,238,289,303,310,317,322,327,332,336,339,341,397,435,451,452,448,423,378,321,267,219,176,120,63,84,97,101,104,106,138,175,217,265,319,349,290,237,190,149,114,85,62,43,30,22,16)

Polycyclic presentation:

2,3,13,439|c^a=c^12,d^a=d^438,c^b=c^3,d^b=d^171

Conjugacy classes & character table

957 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34242, 24);