C₅×#124 #4110

order	160
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) = C₄×#23900 (order 1024) · Inn(G) = C₂³ · Out(G) = C₂²×C₄×D₄
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₅	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₅
prime radical	C₂×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ G

76 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 185);