order	160
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	Aut(G) = C₄×#442 (order 256) · Inn(G) = D₈ · Out(G) = C₄²
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₁

Aliases

C₅×SD₃₂

Subgroups

	subgroup	G/H
center, socle	C₂×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₅
prime radical	C₅×D₈	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ G

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 62);