#13097239

order	1584
isoclinism	isoclinic class of C₁₁⋊PSU(3,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊PSU(3,𝔽₂)
commutator	C₁₁×C₃⋊D₃	C₂×C₄
Fitting, socle	C₂×C₃²×C₁₁	Q₈
prime radical, cosocle	C₂×C₁₁×C₃⋊D₃	C₂²
hypocenter	C₃²×C₁₁	C₄⋊C₄
LCS	G ▷ C₁₁×C₃⋊D₃ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂

62 conjugacy classes of subgroups.

μ_t(G) = 264

Polycyclic presentation:

2^4,3^2,11|a^2=c,b^2=cd,b^a=bcd,e^a=f,f^a=e^2,g^a=g^10,e^b=ef,f^b=ef^2,e^c=e^2,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 403);