C₂×#686 #4077

order	160
isoclinism	isoclinic class of #686
automorphism	Aut(G) = AGL(1,𝔽₅)×#3484 (order 2560) · Inn(G) = C₂²⋊D₅ · Out(G) = C₂×C₄×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂×C₅×D₄ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₈

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 152);