A Pair of Families of Non-isomorphic Group Association Schemes with the same Parameters

We show that for the split and non-split extensions ofFq2bySL (2, q) (q = 2e,e ≥ 3), the group association schemes have the same parameters but are not isomorphic. For the split and non-split extensions ofFq2by the standard Borel subgroup of SL(2,q ) (q = 2e, e ≥ 3), the group association schemes are shown to be isomorphic.