SU(3,𝔽₂)⋊C₉ #14517898

order	1944
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, socle, hypercenter	C₃²	PSU(3,𝔽₂)⋊C₃
commutator, hypocenter	SU(3,𝔽₂)	C₉
Fitting	C₃×H(3,𝔽₃)	SL(2,𝔽₃)
prime radical	C₃×#272	A₄
cosocle	C₃×SU(3,𝔽₂)	C₃
LCS	G ▷ SU(3,𝔽₂)
UCS	C₁ ◁ C₃²

73 conjugacy classes of subgroups.

μ_t(G) = 243

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2292);