map from spin to special orthogonal in Magma [closed]

Question

Let $G:=\operatorname{Spin}(7,5)$. How to construct in Magma the map $G \rightarrow G/Z(G) $ where $Z(G)$ is the center. I get this from Magma:

 > G:=Spin(7,5);
 > c:=Center(G);
 > Q:=quo(G|c);

 >> Q:=quo(G|c);
       ^
 User error: bad syntax
 > Q:=G/c;

 >> Q:=G/c;
   ^
 Runtime error in '/': index of subgroup is too large

I can construct a map from $G$ to $\operatorname{Omega}$. But is there a direct way to map to SO?

Answer 1

> G:=Spin(7,5);
> Q, phi := RadicalQuotient(G);
> Q : Minimal;
GrpPerm: Q, Degree 19656, Order 2^9 * 3^4 * 5^9 * 7 * 13 * 31
> ChiefFactors(Q);
    G
    |  B(3, 5)                    = O(7, 5)
    1

This works because in this example the centre of the group is equal to its solvable radical. There is no general efficient method for finding a nice representation of $G/Z(G)$.

You can use $\mathtt{IsIsomorphic}$ to find an isomorphism between $Q$ and the matrix group $\Omega(7,5)$.