[GAP Forum] Linear representation of G2(q), q even

[Nagy Gábor]

Dear Forum,

It is "well known" that for even prime power q, the exceptional Lie 
group G2(q) has two linear representations of dimension 6, both are 
transitive on the set of non-zero vectors.

Can you suggest me some literature about this construction?

I am escpecially interested in the question if the induced transitive 
representations on the 5-dimensional projective spaces PG(5,q) are 
primitive?

Thank you very much for your help.

Bye,

Gabor