Q₈×D₉ #3700

order	144
automorphism	Aut(G) = C₂×S₄×AGL(1,ℤ/9) (order 2592) · Inn(G) = C₂²×D₉ · Out(G) = C₂×C₃×D₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×D₉

Fitting	Q₈×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×Q₈

57 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)(10,12,13,17)(11,14,15,16);(10,11,13,15)(12,16,17,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 43);