A₄⋊AGL(1,𝔽₉) #11724696

order	864
isoclinism	isoclinic class of A₄⋊AGL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₂

Aliases

Fitting, socle	C₂²×C₃² ⋊ C₃⋊C₈
derived	C₃²×A₄ ⋊ C₈

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	C₃²×A₄	C₈
Fitting, socle	C₂²×C₃²	C₃⋊C₈
prime radical	A₄×C₃⋊D₃	C₄
cosocle	A₄×#157	C₂
LCS	G ▷ C₃²×A₄
UCS	C₁

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 36

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4663);