C₁₆×D₉ #63356

order	288
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂²×C₄×AGL(1,ℤ/9) (order 864) · Inn(G) = D₉ · Out(G) = C₂²×C₃×C₄
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₁₆×D₉

Fitting	C₉×C₁₆ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₆

42 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 2 generators on 25 points:

(2,4)(3,7)(5,8)(6,9);(1,6,4,3,8,5,7,2,9)(10,11,12,15,13,16,18,21,14,17,19,22,20,23,24,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 4);