recall the dihedral group of order 6, in fact every non abelian group of order 6 is isomorphic. So
I am looking for a mechanism to find a decomposition of symmetric groups. For finitely generated abelian group G, there is a mechanism to decompose G such that G is isomorphic to a direct sum of cyclic groups.
For symmetric groups, it seems a bit complex for me to find it.
For example,
(1) is it possible for to be decomposed as a direct product of groups?
In more general cases, is there any mechanism to decompose as a direct product of groups?
(2) is there any mechanism to find an isomorphic group of a direct product of symmetric groups? Let's say,
Any isomorphic group of above G?