order	216
isoclinism	isoclinic class of Dic₁₈
automorphism	Aut(G) = C₂×D₄×AGL(1,ℤ/9) (order 864) · Inn(G) = C₂×D₉ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

C₃×Dic₁₈

Splittings

C₃×C₉ ⋊ Q₈

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 20 points:

(1,2,3)(4,9,11,10,5,7,6,12,8)(13,20,16,15)(14,19,18,17);(5,7)(6,10)(8,9)(11,12)(13,18,16,14)(15,17,20,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 43);