A cwatset of order n can be represented by a transitive subgroup of Sn. Previous work has shown that each conjugacy class of representation groups corresponds to an isomorphism class of cwatsets. We present a technique for determining whether a particular transitive subgroup of Sn can appear as the representation group for a cwatset of order n. Using this method, we provide a full classification of cwatset isomorphism classes through order 23.
Goodwin, Ben and Lin, Dennis, "Classification of Cwatsets Through Order 23" (2000). Mathematical Sciences Technical Reports (MSTR). 100.