C₃⋊(SL(2,𝔽₃)⋊C₈) #10590110

order	576
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊(SL(2,𝔽₃)⋊C₈)
unambiguous semidirect product	SL(2,𝔽₃)⋊(C₃⋊C₈)

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	C₃⋊S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₈
Fitting	C₃×C₄×Q₈	D₃
socle	C₂²×C₃	SL(2,ℤ/4)
prime radical	C₂×C₃×SL(2,𝔽₃)	C₄
cosocle	C₃×C₄×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₄

114 conjugacy classes of subgroups.

μ_t(G) = 192

Polycyclic presentation:

2^3,3^2,2^3|a^2=b,b^2=c,f^2=h,g^2=h,d^a=d^2,e^a=e^2,f^a=gh,g^a=fh,f^d=g,g^d=fgh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 1992);