A₄⋊PSU(3,𝔽₂) #11724700

order	864
isoclinism	isoclinic class of A₄⋊PSU(3,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃² ⋊ Dic₆

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, prime radical, cosocle	A₄×C₃⋊D₃	C₂²
Fitting, socle	C₂²×C₃²	Dic₆
hypocenter	C₃²×A₄	Q₈
LCS	G ▷ A₄×C₃⋊D₃ ▷ C₃²×A₄
UCS	C₁

100 conjugacy classes of subgroups.

μ_t(G) = 36

Polycyclic presentation:

2^3,3^3,2^2|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^2f,f^a=ef,g^a=h,h^a=g,e^b=f^2,f^b=e,e^c=e^2,f^c=f^2,g^d=gh,h^d=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4667);