C₂×#713 #4146

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

Fitting	C₂×C₅×Q₈ ⋊ 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)(8,10,11,14)(9,12,13,15);(8,9,11,13)(10,15,14,12);(4,5)(6,7)(10,14)(12,15);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 221);