The simple exceptional group , q even, and two-character sets

When q is even the simple exceptional group G 2 ( q ) is a subgroup of PSp 6 ( q ) . We study the action of the group G 2 ( q ) < G 2 ( q 2 ) on points of PG ( 5 , q 2 ) and show that unions of G 2 ( q ) -orbits are two-character sets.