SD₁₆×D₉ #63475

order	288
automorphism	Aut(G) = C₂²×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = D₄×D₉ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

SD₁₆×D₉

Fitting	C₉×SD₁₆ ⋊ C₂
Sylow	C₉ ⋊ C₂×SD₁₆

102 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 123);