C₃⋊#4628 #10590114

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

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₈	C₃⋊S₄
commutator, hypocenter	C₃×SL(2,𝔽₃)	C₈
Fitting	C₃×#131	D₃
socle	C₂×C₃	A₄⋊C₈
prime radical	C₃×#41⋊C₃	C₄
cosocle	C₃×#131⋊C₃	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₈

76 conjugacy classes of subgroups.

μ_t(G) = 192

Polycyclic presentation:

2^3,3^2,2^3|a^2=b,b^2=c,c^2=h,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, 1996);