C₉×D₉ #4167

order	162
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂×C₃×AGL(1,ℤ/9) (order 324) · Inn(G) = D₉ · Out(G) = C₂×C₃²
holomorph	G ⋊ Aut(G) = AGL(1,ℤ/9)×#92265⋊C₂
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₉

Fitting, Sylow	C₉² ⋊ C₂
derived	C₉ ⋊ C₂×C₉

25 conjugacy classes of subgroups.

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(162, 3);