[GAP Forum] request

[dmitrii.pasechnik at cs.ox.ac.uk]

On Thu, Jul 04, 2019 at 01:42:54AM +0430, zohreh sayanjali wrote:
> Dear GAP Forum,
>  I have two groups of orders  $   2^5.3^2.5.7   $ and  $  2^4.3^2.5.7  $. I
> need to calculate  the number of  Sylow  7-subgroup of these groups by Gap.
> I would really appreciate it if you help me to find it.

One can compute the normalizer H in G (where G is one of your groups)
of the subgroup generated by an element
of order 7; then |G|/|H| is the number of Sylow 7-subgroups. See
https://www.gap-system.org/Manuals/doc/ref/chap39.html#X87B5370C7DFD401D

HTH
Dima