order	160
automorphism	Aut(G) = C₂²×D₄×AGL(1,𝔽₅) (order 640) · Inn(G) = C₂²×D₅ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

D₅×M₁₆

Splittings

Fitting	C₅×M₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×M₁₆

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 127);