C₂×#709 #4141

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = AGL(1,𝔽₅)×#23900 (order 5120) · Inn(G) = C₂×D₅ · Out(G) = #34655
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₄×C₅ ⋊ C₂
Sylow	C₅ ⋊ C₂×#41

164 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 216);