order	160
isoclinism	isoclinic class of #677
automorphism	Aut(G) = AGL(1,𝔽₅)×#23882 (order 5120) · Inn(G) = D₂₀ · Out(G) = C₄×#120
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₂×Dic₂₀

Splittings

C₅ ⋊ C₂×Q₁₆

60 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 126);