Dear Forum members:
Does GAP have the means to compute real
irreducible components, say for a group of reasonably
small order and representation degree (eg. a subgroup of order 128
in S_16)? (Maybe that doesn't qualify as reasonable).
I realize that the "matrix"
package can handle my group over a finite field, and
this has been of some use. Still, I want real representations,
or more accurately, representations over some finite extension
of the rationals.
I suppose this ultimately means finding common
eigenvectors for the generators of some algebra. However,
I am really only seeking to understand a few examples, so
that I definitely want to avoid writing my own program to cope
with such things.

Thanks for your help,
Barry Monson.