Matrices and finite quandles

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.