D₉×C₂₇ #92169

order	486
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂×C₉×AGL(1,ℤ/9) (order 972) · Inn(G) = D₉ · Out(G) = C₂×C₃×C₉
homology	Abelianization (H₁) = C₂×C₂₇ · Schur multiplier (H₂) = C₁

Aliases

D₉×C₂₇

Fitting, Sylow	C₉×C₂₇ ⋊ C₂
derived	C₉ ⋊ C₂×C₂₇

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 54

A minimal faithful permutation representation — 2 generators on 36 points:

(2,4)(3,7)(5,8)(6,9)(10,11,14,12,15,20,17,22,27,13,16,21,18,23,28,25,30,33,19,24,29,26,31,34,32,35,36);(1,6,4,3,8,5,7,2,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 14);