  The isomorphism problem for centrally nilpotent loops can be tackled by
methods of cohomology. We develop tools based on cohomology and linear algebra
that either lend themselves to direct count of the isomorphism classes (notably
in the case of nilpotent loops of order $2q$, $q$ a prime), or lead to
efficient classification computer programs. This allows us to enumerate all
nilpotent loops of order less than $24$.
