Group of order p^3 and its represenations

Suppose we have G a non-abelian group of order p^3 for prime p. I'm interested in finding all irreducible representations of G.

I can compute the number of conjugacy classes - it is
p^2 - p+1, hence we have p^2 - p + 1 irreducible representations. It is also not difficult to check that due to the fact that G is non-abelian, Z(G) = Z_p = G', hence |G/G'| = p^2 and we have p^2 irreducible representations of G of degree 1.
I want to find the other p-1 representations - it seems to me that those are all representations of degree p, but i don't know how to construct them / prove that it is so.

I would be grateful for any of you ideas.

Thanks.
.

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