I have been working with SAGE online, and have made some programs to test some hypothesis about finite groups. However, the pre-defined "named" groups in SAGE are quite limited (basically, the symmetric, dihedral, and alternating groups, plus PSL/PSU/PGU's and a couple sporadics). SAGE evidently interfaces with GAP, so what I would like to do is pull some groups out of GAP's SmallGroups library so that I can run them through my SAGE code.
I am able to create a GAP group in SAGE with
A = gap.SmallGroup(27,4)
Group( [ f1, f2, f3 ] )
I can get its elements using
which are then given to me in symbolic form, e.g.
[ <identity> of ..., f1, f2, f3, f1^2, f1*f2, f1*f3, f2^2, ... etc. ]
I just don't know how to turn these elements into permutations that SAGE can work with. In other words, I want to take the gap.SmallGroup(27,4) and turn it into something of the form
Permutation Group with generators [(2,4,3), (1,3)(2,4), (1,4)(2,3)]
Could anyone show me how to do this?