A₄⋊D₈₁ #14516454

order	1944
isoclinism	isoclinic class of A₄⋊D₈₁
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	A₄⋊D₈₁
unambiguous semidirect product	C₈₁⋊S₄

Fitting	C₂²×C₈₁ ⋊ D₃
derived	A₄×C₈₁ ⋊ C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄×C₈₁	C₂
Frattini	C₂₇	C₃⋊S₄
Fitting	C₂²×C₈₁	D₃
socle	C₂²×C₃	C₃⋊D₂₇
LCS	G ▷ A₄×C₈₁
UCS	C₁

87 conjugacy classes of subgroups.

μ_t(G) = 324

Polycyclic presentation:

2,3^5,2^2|c^3=d,d^3=e,e^3=f,b^a=b^2,c^a=c^2d^2e^2f^2,d^a=d^2e^2f^2,e^a=e^2f^2,f^a=f^2,g^a=gh,g^b=h,h^b=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 848);