[GAP Forum] Finding the maximal subgroup of S_n such that a subpace V of R^n is invariant

[Bulutoglu Dursun A Civ AFIT/ENC]

Let V be an m dimensional subspace of R^n. Let S_n act on R^n and on V
by permuting the coordinates of each vector in R^n. Thus S_n acts on R^n
regularly.
	I was wondering whether there is any tool in GAP that I could
use to find the maximal subgroup G of S_n such that V remains invariant
under this action.  Obviously one can fix a basis for V and compute the
symmetry group of the matrix formed by putting these basis vectors into
a matrix. This symmetry group would be a subgroup of of G but I would
like to be able to compute G or some subgroup of G that has as many
elements of G as possible.

Dursun.