C₂×D₄×D₅ #4142

order	160
automorphism	Aut(G) = AGL(1,𝔽₅)×#23900 (order 5120) · Inn(G) = C₂²×D₅ · Out(G) = C₂×D₄²
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₄×D₅

Fitting	C₂×C₅×D₄ ⋊ C₂
Sylow	C₅ ⋊ C₂²×D₄

236 conjugacy classes of subgroups.

minimal degree	μ(G) = 11
transitive degree	μ_t(G) = 40

A minimal faithful permutation representation — 4 generators on 11 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 217);