D₅×C₃₂ #64666

order	320
isoclinism	isoclinic class of D₅
automorphism	Aut(G) = C₂²×C₈×AGL(1,𝔽₅) (order 640) · Inn(G) = D₅ · Out(G) = C₂³×C₈
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂

Aliases

D₅×C₃₂

Fitting	C₅×C₃₂ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₃₂

34 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 2 generators on 37 points:

(2,3)(4,5);(1,2,4,5,3)(6,7,8,12,9,13,16,22,10,14,17,23,19,25,28,32,11,15,18,24,20,26,29,33,21,27,30,34,31,35,36,37)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 4);