The automorphism group of finite p -groups associated to the Macdonald group

Given positive integers p and m, where p is assumed to be an odd prime, we determine the automorphism groups of p-groups J, H, and K of orders p7m, p6m, and p5m, and nilpotency classes 5, 4, and 3, respectively, all of which arise naturally from the Macdonald group 〈x,y|x[x,y]=x1+pmℓ,y[y,x]=y1+pmℓ〉, where ℓ∈Z is relatively prime to p.