C₈×D₉ #3662

order	144
isoclinism	isoclinic class of D₉
automorphism	Aut(G) = C₂³×AGL(1,ℤ/9) (order 432) · Inn(G) = D₉ · Out(G) = C₂³×C₃
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₈×D₉

Fitting	C₈×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₈

33 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 5);