Dear GAP Forum,

Thanks for all who have answered my question on semidirect products, especially
Thomas Breuer.
He gave three ways to obtain the group I was looking for, and I've questions
about the two last ones.

Thomas Breuer wrote:

In the example mentioned,
I suspect the desired action of G on H is the natural
symplectic one.
There are several ways to construct the group in question.

2. An alternative is to use the library of perfect groups in GAP.

That's a good method, but how do you know that the group in question is perfect?

Thomas Breuer wrote:

3. A third possibility is the construction of the semidirect
product as a group of 4 by 4 matrices over the field with
5 elements.

I can't see why this construction gives the group in question.Can you say a bit
more or give some references about that?

Best regards,

Olivier Cormier.