Order of Product of Disjoint Permutations/Examples/Permutations in S9

Example of Order of Product of Disjoint Permutations
Consider the permutation given in cycle notation as
 * $\rho = \begin{pmatrix} 1 & 2 & 3 & 4 \end{pmatrix} \begin{pmatrix} 5 & 6 & 7 \end{pmatrix} \begin{pmatrix} 8 & 9 \end{pmatrix}$

Its order is given by:
 * $\order \rho = 12$

Proof
$\rho$ is the product of $3$ disjoint permutations, of orders $4$, $3$ and $2$.

From Order of Product of Disjoint Permutations:
 * $\order \rho = \lcm \set {4, 3, 2} = 12$