Finite quandles with n elements can be represented as n×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.
Homology, Homotopy and Applications, Vol. 7 (2005), No. 1, pp.197-208.