order	160
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) = C₂²×C₄×#120 (order 512) · Inn(G) = C₂³ · Out(G) = C₂⁴×C₄
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₅×C₂²⋊Q₈
unambiguous semidirect product	C₂²⋊(C₅×Q₈)

Subgroups

	subgroup	G/H
center, socle	C₂²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₅
prime radical	C₂³×C₅	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

74 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 183);