[GAP Forum] An overgroup of Sylow in PSL( 2, 7^3 )

[Derek Holt]

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
> =====
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