C₁₁⋊SL(2,ℤ/4) #10587222

order	528
isoclinism	isoclinic class of C₁₁⋊S₄
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	C₁₁⋊SL(2,ℤ/4)
unambiguous semidirect product	A₄⋊Dic₁₁

derived	C₁₁×A₄ ⋊ C₄
Sylow	C₁₁ ⋊ SL(2,ℤ/4)

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊S₄
commutator, hypocenter	C₁₁×A₄	C₄
Fitting, socle	C₂³×C₁₁	D₃
prime radical, cosocle	C₂×C₁₁×A₄	C₂
LCS	G ▷ C₁₁×A₄
UCS	C₁ ◁ C₂

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 132

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(528, 92);