order	80
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	Aut(G) = C₂×C₄×D₄ (order 64) · Inn(G) = D₄ · Out(G) = C₂×C₄
holomorph	G ⋊ Aut(G) = AGL(1,𝔽₅)×#61110
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×SD₁₆

Subgroups

	subgroup	G/H
center, socle	C₂×C₅	D₄
commutator, Frattini, cosocle	C₄	C₂²×C₅
prime radical	C₅×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ G

20 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(80, 26);