C₂×#168 #680

order	80
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×D₄×AGL(1,𝔽₅) (order 320) · Inn(G) = D₅ · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₅ ⋊ C₂×C₈

22 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 9);