C₃⋊#10620032 #14519156

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₉	C₃⋊PSU(3,𝔽₂)
commutator, prime radical, cosocle	C₃×#272	C₂²×C₃
Frattini	C₃	C₃×C₃⋊PSU(3,𝔽₂)
Fitting	C₃×#737	Q₈
socle	C₃²	C₃×PSU(3,𝔽₂)
hypocenter	C₃×H(3,𝔽₃)	C₃×Q₈
LCS	G ▷ C₃×#272 ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₉

112 conjugacy classes of subgroups.

μ_t(G) = 108

Polycyclic presentation:

2^2,3,2,3^4|a^2=d,b^2=d,c^3=h^2,b^a=bd,e^a=fh^2,f^a=e^2,g^a=g^2,e^b=ef^2,f^b=e^2f^2h,e^d=e^2h^2,f^d=f^2h,f^e=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3550);