C₂×#672 #3943

order	160
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂×#41×AGL(1,𝔽₅) (order 640) · Inn(G) = D₅ · Out(G) = C₂²×#41
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₅ ⋊ C₂×C₁₆

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2)(4,5)(6,7)(8,9,10,13,11,14,16,19,12,15,17,20,18,21,22,23);(1,2)(3,4,6,7,5)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 18);