Q₈×D₅ #712

order	80
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×S₄ (order 960) · Inn(G) = C₂²×D₅ · Out(G) = C₂²×D₃
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₈×D₅

Fitting	C₅×Q₈ ⋊ C₂
Sylow	C₅ ⋊ C₂×Q₈

38 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 41);