This is probably not the most efficient way, but here's one way you can do it:
gap> G := PSL(2,25);; gap> A := AutomorphismGroup(G);; gap> M := SubgroupsOfIndexTwo(A);; M will be a list of the three groups you want; you can access these as M[1], M[2], and M[3]. Basically, G is PSL(2,25) and its automorphism group is PGammaL(2,25), which is defined as the semidirect product of PGL(2,25) and the Galois group of the field of 25 elements over the field of 5 elements. The quotient PGammaL(2,25)/PSL(2,25) has order 4 and is a Klein four-group. The three subgroups of order two and index two in there correspond to the three groups of index two in PGammaL(2,25). One of these will be PGL(2,25), the other will be the semidirect product of PSL(2,25) with the Galois group, and there will be a third one. Unfortunately, as far as I can make out, the SubgroupsOfIndexTwo takes a few minutes to run for groups of this size, so you will need to be patient. Vipul * Quoting sadegh salehi who at 2011-11-30 06:25:40+0000 (Wed) wrote > Hello dear GAP Forum members, > > By the Atlas of finite groups, we know that the simple group PSL(2,9)has > three cyclicautomorphic extensions: S6 (Symmetric group of degree 6), > PGL(2,9) and the 'Mathieu' group M(10). > Also we note that M(10) is non-split extension of PSL(2,9). So it can not > be Created by the semidirect product. > Is there any way to access the automorphic extension of PSL(2,25) or > PSL(2,49) , PSL(3,4), ... in Gap? > I will be appreciate for any suggestion. > > With Best Regards. > Seyed Sadegh Salehi Amiri. > Department of Mathematics, Islamic Azad University, Babol Branch, Iran. > salehi...@yahoo.com > salehi...@baboliau.ac.ir > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
