A census of small Schurian association schemes

Abstract

Using the classification of transitive groups of degree $n$, for $2⩽n⩽48$, we classify the Schurian association schemes of order $n$, and as a consequence, the transitive groups of degree $n$ 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 $n$, for $2⩽n⩽48$. The results of this classification are made available as a supplementary database.

arXiv commentThe author is supported by the Australian Research Council Discovery Grant DP200101951. This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia