C₃⋊D₃ #47

order	18
isoclinism	isoclinic class of C₃⋊D₃
automorphism	Aut(G) = AGL(2,𝔽₃) (order 432) · Inn(G) = G · Out(G) = S₄
holomorph	G ⋊ Aut(G) = #72210382
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃

Aliases

C₃⋊D₃

C₃² ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²	C₂
LCS	G ▷ C₃²
UCS	C₁

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 6
transitive degree	μ_t(G) = 9

A minimal faithful permutation representation — 3 generators on 6 points:

(2,3)(5,6);(4,5,6);(1,2,3)

2,3^2|b^a=b^2,c^a=c^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18, 4);