Remember if then we can write and where are cycles so that and are disjoint for . Two elements are said to have the samestructureiff when we write and then and can be relabled so that has the same cycle length as . Two elements are conjugate to eachother if and only if and have the same structure.

If you take then we have a certain number of possibilities:

- is 1-cycle i.e. identity --> there is only one element that has this property
- is a 2-cycle --> there are such elements
- is a 3-cycle --> there are such elements
- is a 4-cycle --> there are such elements
- is a product of two 2-cycles --> there are such elements

As a check confirm that (this happens to be the conjugacy class equation).