order	72
isoclinism	isoclinic class of C₃⋊D₃
automorphism	Aut(G) = D₄×AGL(2,𝔽₃) (order 3456) · Inn(G) = C₃⋊D₃ · Out(G) = D₄×S₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊Dic₃
unambiguous semidirect product	(C₂×C₃)⋊Dic₃

Splittings

C₃² ⋊ C₂×C₄

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 12 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(72, 34);