This article presents a study of special material properties of the single crystalline material Ca3TaGa3Si2O14 (CTGS = Catangasite). The comparatively highly ordered crystal structure and acceptable piezoelectric strength make it a candidate for microacoustic applications under extreme conditions. Obviously, low-loss dynamic behavior is typical for this crystal which consequently enables high-temperature use. As a particular challenge, the behavior at gigahertz frequencies is investigated here. For that, High overtone Bulk Acoustic wave Resonator (HBAR) type measurements in the range of 1-6 GHz are performed. The selection of five distinctive propagation directions for exclusively pure or quasi-longitudinal modes enables to derive the dynamic viscosities from the quality factors of HBAR results. The observed frequency dependences exhibit Akhiezer behavior as the predominant loss mechanism in the cases examined.