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) = C₂²

Aliases

direct product	C₂×Dic₁₀
unambiguous semidirect product	(C₂×C₅)⋊Q₈

Splittings

C₅ ⋊ C₂×Q₈

38 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 35);