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Find the primitive ideal space, the center, a continuous field of $C^*(Z_2*Z_2)$.

Here, $C^*(Z_2*Z_2)$ is the full group $C^*$-algebra.

I know the definitions of all of them, but I'm having hard time to apply those to the problem.

So for example, the primitive ideal is the kernel of an irreducible presentation of an algebra. But I do not know what to do next from here. How do I know whether there is an infinite number of irred. representations of the given algebra or not?

So I will definitely appreciate your help.

Thank you.

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