I have tried to use GO(-1,6,2) but encountered

gap> matGroup := GeneralOrthogonalGroup(-1,6,2);
gap> InvariantQuadraticForm(matGroup);
rec(
matrix := [ <an immutable GF2 vector of length 6>, <an immutable GF2
vector of length 6>, <an immutable GF2 vector of length 6>,
<an immutable GF2 vector of length 6>,
<an immutable GF2 vector of length 6>,
<an immutable GF2 vector of length 6> ] )

However when I choose q=3 or 5 I get the quadratic form which gives the
group, and then I can do all kinds of computations. How do I generate the
group when q is even?
Thanks,

shaoyu

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