We are studying representation theory and we were asked to find the unirreps (unitary irreducible representations) for a group

given that

,

a prime.

We have the theorem that states that the number of unirreps is equal to the number of conjugacy classes of the group

.

There are five cases, three of which are abelian and therefore trivial. The other two groups, which we figured out in class, are:

1.) Let

. Then

2.)

How do I go about finding the conjugacy classes of these groups, or is there a better way to find the number of unirreps for each group?