On the geometry of the exceptional group \(G_2(q)\), \(q\) even (Q1009002)

The authors study some geometry of the exceptional group \(G_{2}(q)\), \(q\) even, in terms of symplectic geometric configurations in the projective space \(PG(5,q)\). Using the spin representation of \(Sp_{6}(q)\), they obtain an alternative description of the Split Cayley hexagon \(H(q)\) related to \(G_{2}(q)\). They also give another geometric proof of the maximality of \(G_{2}(q)\), q even, in \(PSp_{6}(q)\).