M₁₆×D₉ #63468

order	288
automorphism	Aut(G) = C₂²×D₄×AGL(1,ℤ/9) (order 1728) · Inn(G) = C₂²×D₉ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

M₁₆×D₉

Fitting	C₉×M₁₆ ⋊ C₂
Sylow	C₉ ⋊ C₂×M₁₆

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 116);