order	160
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂²×C₄×AGL(1,𝔽₅) (order 320) · Inn(G) = D₅ · Out(G) = C₂³×C₄
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

D₅×C₁₆

Splittings

Fitting	C₅×C₁₆ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₁₆

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

(2,3)(4,5);(1,2,4,5,3)(6,7,8,11,9,12,14,17,10,13,15,18,16,19,20,21)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 4);