How embeding the direct product of permutational groups in $S_n$ using the Magma?

Question

I would like embedding the direct product $Sym(\{1,2,3\} ) \times Sym(\{4,5,6\}) \times Sym(\{7,8\})$ in $Sym(8)$ using the software Magma. Anyone can help me?

Answer 1

You need to use subgroup coercion (g!!h) to make those other symmetric groups be viewed as subgroups of the larger symmetric group.

> g:=Sym(8);
> a:=Sym({1,2,3}); b:=Sym({4,5,6}); c:=Sym({7,8});
> sub< g | g!!a, g!!b, g!!c >;