[GAP Forum] Defining subgroups of symplectic groups

[James Read]

Hi,

I want to define subgroups of Sp(4,Z) of the form:

G_0\left(N\right) = \left\{ \left( \begin{array}{cccc}

\mathbb{Z} & \mathbb{Z} & \mathbb{Z} & N \mathbb{Z} \\
N \mathbb{Z} & \mathbb{Z} & N \mathbb{Z} & N^2 \mathbb{Z} \\
\mathbb{Z} & \mathbb{Z} & \mathbb{Z} & N \mathbb{Z} \\
\mathbb{Z} & \mathbb{Z} & \mathbb{Z} & \mathbb{Z}

\end{array} \right) \right\} \cap Sp\left(4,\mathbb{Z}\right)

and then find their generators. Is it possible to define such subgroups in GAP? I'm having trouble doing it.. It looks like Sage might offer a little more functionality here, but I couldn't figure out how to do it there either.

Thanks for any help!

James Read