C₂×Q₈×D₅ #4145

order	160
automorphism	Aut(G) = AGL(1,𝔽₅)×#11713200 (order 15360) · Inn(G) = C₂²×D₅ · Out(G) = C₂×D₄×S₄
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

C₂×Q₈×D₅

Fitting	C₂×C₅×Q₈ ⋊ C₂
Sylow	C₅ ⋊ C₂²×Q₈

156 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)(4,5)(6,7);(3,4,6,7,5)(8,10,11,15)(9,12,13,14);(8,9,11,13)(10,14,15,12);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 220);