[GAP Forum] size of permutation groups

[Allan Adler]

I'm using Gap 3 on a PC running RH 7.1 Linux. Using it, I took a couple
of permutations on a little over 100 objects and had no trouble, after
waiting long enough, getting Gap 3 to confirm that they generated the
entire symmetric group. I tried the same thing with some permutations
on several hundred objects and, after 5 hours of waiting for Gap 3 to
compute the order of the group, I gave up and stopped the program.

What I'd like to know is the following:
(1) How large can n be for me to do stuff like this with the symmetric
    group on n objects and expect the program to run to completion?
(2) It is frustrating to wait a long time for a program to run and
    to have no idea how far it is getting. Is there some way to get
    the program to tell me a little about its progress while it is
    figuring out the order of the group generated by the given permutations?
    One other advantage of such feedback is that it might tell me something
    that might let me find a proof that I get the full symmetric group.

I have nothing against Gap 4, I just haven't installed it yet. One reason
I'm not in a hurry is that Gap 3 is doing a good job so far. Another is
that I'm not absolutely sure that the programs that run on Gap 3 will
also run on Gap 4, and I'm not prepared to rewrite them at the  moment.
But I'll get to it.

Anyway, people here probably don't want to support Gap 3 any more, so
it's perfectly all right with me if you pretend that I said I was using
Gap 4 and answer the questions for Gap 4 instead.
-- 
Ignorantly,
Allan Adler <ara at zurich.csail.mit.edu>
* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.