  We study certain unitary CM fields whose Galois closure has Galois group
$\operatorname{PSL}_2(\mathbb{F}_q) \times \mathbb{Z}/2\mathbb{Z}$. After
investigating the CM types of these fields, we turn towards Colmez's
conjectural formula on the Faltings heights of CM abelian varieties. We
explicitly calculate the class functions appearing in the statement of the
conjecture and then apply refinements of the recently proven average version to
establish Colmez's conjecture in this case.
