Let then .

The conjugacy classes for are: .

The conjugacy classes for are: .

Therefore the conjugacy classes for are where is a conjugacy class of and is a conjugacy class of . Note, there are total of conjugacy classes for . Furthermore, , so there are three conjugacy classes that has 1 element, three conjugacy classes that have 2 elements, three conjugacy classes that have 3 elements.

Thus, the class equation is: .