C₂×#676 #4046

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = C₂×AGL(1,𝔽₅)×#120 (order 1280) · Inn(G) = C₂×D₅ · Out(G) = C₂²×#41
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Fitting	C₂×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₂×M₁₆

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 121);