C₂²×Dic₅ #714

order	80
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = AGL(1,𝔽₅)×#5934 (order 3840) · Inn(G) = D₅ · Out(G) = C₂×#5934
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₂²×Dic₅

C₅ ⋊ C₂²×C₄

54 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 43);