Cycle Notation/Examples/Permutations in S8

Examples of Cycle Notation
Consider the permutations in $S_8$, presented in two-row notation as:

These can be expressed in cycle notation as:

We have that:

$\pi$ is of order $\lcm {4, 3} = 12$, and is of odd parity

$\rho$ is of order $2$, and is of even parity

$\pi \rho$ and $\rho \pi$ are both of order $\lcm {4, 2} = 4$, and are of odd parity

$\pi^2 \rho$ is of order $\lcm {6, 2} = 6$, and is of even parity.