Product of disjoint cycles in Abstract Algebra I've got some permutations:
$\left( \begin{smallmatrix}
  1 & 2 & 3 & 4 & 5 & 6 \\
 3 & 5 & 4 & 1 & 6 & 2 \end{smallmatrix} \right) $ and $\left( \begin{smallmatrix} 1 & 2 & 3 & 4 & 5 & 6 \\ 3 & 2 & 1 & 5 & 4 & 6 \end{smallmatrix} \right)$
I've found the cycles to be: $(1,3,4)(2,5,6)(1,3)(2)(4,5)(6)$ but now I want to decompose this into product of disjoint cycles.
I have no idea how to do that. After I do that, I want to write them as a product of transposition. I've searched high and low for a good explanation on how to do this but none seems to help.

This is a decomposition into product of disjoint cycles and into product of transpositions
$$\left( \begin{smallmatrix}
  1 & 2 & 3 & 4 & 5 & 6 \\
 3 & 5 & 4 & 1 & 6 & 2 \end{smallmatrix} \right)=(1\ 3\ 4)(2\ 5\ 6)=(1\ 4)(1\ 3)(2\ 6)(2\ 5) $$
Can you do the same for the second permutation?
