C₂×#689 #4089

order	160
isoclinism	isoclinic class of #686
automorphism	Aut(G) = AGL(1,𝔽₅)×#3484 (order 2560) · Inn(G) = C₂²⋊D₅ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₅ ⋊ C₂×Q₁₆

60 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 3 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 164);