[GAP Forum] Double cosets of orthogonal groups (rather than permutation groups)

[Katie Morrison]

I am trying to compute double cosets within the orthogonal group with
similitudes (which I am taking to be the set of matrices that satisfy
MM^T=\lambda *I where I is the identity and \lambda is a non-zero scalar).
I have obtained the orthogonal group with similitudes by starting with
GO(n,q), conjugating it by an appropriate change of basis matrix to get the
matrices that preserve the standard dot product rather than the bilinear
form that GAP uses, and then taking the normalizer of this group in
GL(n,q).  Using this construction of the orthogonal group with similitudes,
I would like to then find double cosets of certain subgroups of this, but as
far as I know GAP only has the double-cosets function implemented for
permutation groups.  Is there an efficient way that I can use these built-in
GAP functions to determine if two matrices are in the same double-coset
and/or enumerate a list of double-coset representatives?  Thanks in advance
for any help with this.

Katie Morrison