order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂²×AGL(1,𝔽₅)×#120 (order 2560) · Inn(G) = C₂×D₅ · Out(G) = C₂²×C₄×D₄
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₁₀

Splittings

C₅ ⋊ C₄×Q₈

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 89);