Hi.
There is no unique faithful linear representation for a arbitrary finite
group in general. (For arbitrary groups there is in general not a single
faithful linear representation)
I guess the only canonical choice is the regular representation, i.e.
the group of permutation matrices that corresponds to the permutation
action of G on itself via left-translation (or right-translation if you
choose to act from the right). Therefore your way should be the easiest
one to implement. Caveat: In general this procedure does not give you a
faithful representation of smallest possible degree, i.e. it might be
possible to find a "better" embedding in the sense that the matrices
have smaller dimension. I don't think that there is some good way to do
that besides the brute-force-way: Look through all characters of the
group and check which are faithful. Then find a representation for this
character (which is itself a nontrivial problem).
Johannes Hahn.
Am 21.11.2011 14:36, schrieb Robert Heffernan:
Hi,
Given a group G in GAP (eg. a group from the Small Groups library) is
there an easy way to get the group as a subgroup of a linear group?
I guess I could run IsomorphismPermGroup(G) and then get permutation
matrices for the generators. Is there a better way to do it than
this? A browse through the documentation didn't turn up anything
obvious.
Thank you,
Bob Heffernan
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