C₅×#121 #4107

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) = C₂³

Aliases

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

94 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)(6,8)(9,10,11,12,13);(5,6,7,8);(2,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 182);