C₂×C₄×Dic₅ #4068

order	160
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = AGL(1,𝔽₅)×#144366 (order 10240) · Inn(G) = D₅ · Out(G) = C₂×#144366
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₄×Dic₅

C₅ ⋊ C₂×C₄²

108 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 3 generators on 15 points:

(1,2)(3,4,5,6)(12,13)(14,15);(7,8,9,10)(11,12,14,15,13);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 143);