order	80
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = AGL(1,𝔽₅)×B(4,𝔽₂) (order 1280) · Inn(G) = C₂×D₅ · Out(G) = #525
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₂₀

Splittings

Fitting	C₂×C₄×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 11 points:

(3,4,5,6)(7,8,10,11,9);(1,2)(4,6)(8,9)(10,11);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 37);