C₂×#677 #4048

order	160
isoclinism	isoclinic class of #677
automorphism	Aut(G) = AGL(1,𝔽₅)×#3484 (order 2560) · Inn(G) = D₂₀ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₂×SD₁₆

68 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)(8,9,10,12,11,13,14,15);(1,2)(4,5)(6,7)(9,12)(10,14)(13,15);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 123);