C₁₁⋊GL(2,𝔽₃) #10587221

order	528
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊S₄
commutator, cosocle, hypocenter	C₁₁×SL(2,𝔽₃)	C₂
Fitting	Q₈×C₁₁	D₃
socle	C₂×C₁₁	S₄
LCS	G ▷ C₁₁×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

μ_t(G) = 88

Polycyclic presentation:

2,3,11,2^3|d^2=f,e^2=f,b^a=b^2,c^a=c^10,d^a=e,e^a=d,d^b=ef,e^b=de,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 91);