D₅×#41 #4148

order	160
automorphism	Aut(G) = C₂²×AGL(1,𝔽₅)×S₄ (order 1920) · Inn(G) = C₂²×D₅ · Out(G) = C₂³×D₃
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₅×#41 ⋊ C₂
Sylow	C₅ ⋊ C₂×#41

164 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 4 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(160, 223);