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) = C₂³

Aliases

C₂×D₄₀

Splittings

Fitting	C₂×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₈

76 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)(8,9,13,15,11,14,10,12);(1,2)(4,5)(6,7)(9,12)(10,13)(14,15);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 124);