C₂×#685 #4073

order	160
isoclinism	isoclinic class of Dic₁₀
automorphism	Aut(G) = AGL(1,𝔽₅)×#15947 (order 5120) · Inn(G) = C₂×D₅ · Out(G) = #34736
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

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

132 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 148);