I have a question about an irreducible representation of the (full) group $C^*$-algebra of an infinite dihedral group $D_\infty$, denoted by $C^*(D_\infty)$

Ultimately, I'm interested in finding a primitive ideal space of $C^*(D_\infty)$ which is the kernel of irreducible representation of $C^*(D_\infty)$.

But I'm having a hard time finding it.

Should I find pure states on $C^*(D_\infty)$ first since they correspond to irreducible representations of $C^*(D_\infty)$?

Any reference will be appreciated.

Hope there is someone who's familiar with these stuff and thank you in advance.


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