D₅×D₈ #4056

order	160
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×AGL(1,ℤ/8) (order 1280) · Inn(G) = D₄×D₅ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₅×D₈

Fitting	C₅×D₈ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 131);