C₂×C₃×Dic₉ #6218

order	216
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂×D₄×AGL(1,ℤ/9) (order 864) · Inn(G) = D₉ · Out(G) = C₂×C₃×D₄
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×Dic₉

derived	C₉ ⋊ C₂×C₃×C₄
Sylow	C₃×C₉ ⋊ C₂×C₄

58 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(216, 55);