  We examine the ramification groups of finite Galois extensions over complete
discrete valuation fields of equal characteristic $p>0$. Brylinski (1983)
calculated the ramification groups in the case where the Galois groups are
abelian. We extend the results of Brylinski to some non-abelian cases where the
Galois groups are of order $\leq p^{p+1}$ and of maximal nilpotency class.
