C₂×#674 #3997

order	160
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	Aut(G) = #41×AGL(1,𝔽₅) (order 320) · Inn(G) = AGL(1,𝔽₅) · Out(G) = #41
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₅ ⋊ C₂×C₁₆

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 23 points:

(4,5,6,7)(8,9,10,13,11,14,16,19,12,15,17,20,18,21,22,23);(1,2)(3,4,5,7,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 72);