C₂²⋊Dic₅ #690

order	80
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = AGL(1,𝔽₅)×#120 (order 640) · Inn(G) = C₂×D₅ · Out(G) = C₄×D₄
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₂²⋊Dic₅

C₅ ⋊ C₂²⋊C₄

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 2 generators on 13 points:

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

Polycyclic presentation:

2^4,5|a^2=c,b^a=bd,e^a=e^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 19);