D₄×D₉ #3698

order	144
automorphism	Aut(G) = C₂×D₄×AGL(1,ℤ/9) (order 864) · Inn(G) = C₂²×D₉ · Out(G) = C₂²×C₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₄×D₉

Fitting	D₄×C₉ ⋊ C₂
Sylow	C₉ ⋊ C₂×D₄

81 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 36

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(144, 41);