GU(3,𝔽₂) #10620014

order	648
automorphism	?
homology	Abelianization (H₁) = C₃ · Schur multiplier (H₂) = C₁

Aliases

GU(3,𝔽₂)

Fitting	H(3,𝔽₃) ⋊ SL(2,𝔽₃)
derived	SU(3,𝔽₂) ⋊ C₃

	subgroup	G/H
center, Frattini, socle, hypercenter	C₃	PSU(3,𝔽₂)⋊C₃
commutator, cosocle, hypocenter	SU(3,𝔽₂)	C₃
Fitting	H(3,𝔽₃)	SL(2,𝔽₃)
LCS	G ▷ SU(3,𝔽₂)
UCS	C₁ ◁ C₃

41 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 27

Polycyclic presentation:

3,2^3,3^3|b^2=d,c^2=d,b^a=c,c^a=bcd,e^a=fg^2,f^a=e^2f^2g,c^b=cd,e^b=ef,f^b=ef^2g,e^c=fg^2,f^c=e^2,e^d=e^2g^2,f^d=f^2g,f^e=fg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(648, 533);