Dear Anvite + Forum, You could calculate a Sylow 43-subgroup, and then find its normalizer in PSL(2,7^3). The normalizer properly contains a Sylow 2-subgroup.
Best wishes, Derek On Sun, Feb 07, 2021 at 02:56:10PM +0700, Anvita wrote: > Dear Forum, > > I need to construct a proper subgroup of PSL( 2, 7^3 ) that contains a > Sylow 2-subgroup. > According to the manual, IntermediateGroup returns `fail' if the subgroup > is maximal. > But the Sylow 2-subgroup is not maximal in this case. > Thank you in advance for any clarification. > > Anvita > > ===== > gap> L := PSL(2,7^3); > <permutation group of size 20176632 with 2 generators> > gap> > gap> S := SylowSubgroup (L,2); > <permutation group of size 8 with 3 generators> > gap> > gap> U := IntermediateGroup(L,S); > fail > ===== > _______________________________________________ > Forum mailing list > Forum@gap-system.org > https://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
