C₃²×GL(2,𝔽₃) #88967

order	432
isoclinism	isoclinic class of #226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

Fitting	C₃²×Q₈ ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂×C₃²

	subgroup	G/H
center, socle, hypercenter	C₂×C₃²	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂×C₃²
Frattini	C₂	C₃²×S₄
Fitting	C₃²×Q₈	D₃
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃²

120 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 14 points:

(1,2,8,3,4,7,6,5)(12,13,14);(2,5,8)(3,6,7)(9,10,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 614);