A census of small Schurian association schemes

Abstract

Using the classification of transitive groups of degree [Formula: see text], for [Formula: see text], we classify the Schurian association schemes of order [Formula: see text], and as a consequence, the transitive groups of degree [Formula: see text] that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree [Formula: see text], for [Formula: see text]. The results of this classification are made available as a supplementary database.