A₄⋊#622 #11724157

order	864
isoclinism	isoclinic class of A₄⋊#157
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃²×A₄ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄⋊#157
commutator, hypocenter	C₃²×A₄	C₈
Fitting, socle	C₂³×C₃²	Dic₃
prime radical	C₂×C₃²×A₄	C₄
cosocle	A₄×C₃⋊Dic₃	C₂
LCS	G ▷ C₃²×A₄
UCS	C₁ ◁ C₂

106 conjugacy classes of subgroups.

μ_t(G) = 72

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4124);