  Finite quandles with n elements can be represented as n-by-n matrices. We
show how to use these matrices to distinguish all isomorphism classes of finite
quandles for a given cardinality n, as well as how to compute the automorphism
group of each finite quandle. As an application, we classify finite quandles
with up to 5 elements and compute the automorphism group for each quandle.
