We demonstrate a variety of precessional responses of the magnetization to ultrafast optical excitation in nanolayers of Galfenol (Fe,Ga), which is a ferromagnetic material with large saturation magnetization and enhanced magnetostriction. The particular properties of Galfenol, including cubic magnetic anisotropy and weak damping, allow us to detect up to 6 magnon modes in a 120-nm layer, and a single mode with effective damping ${alpha}_{eff}$ = 0.005 and frequency up to 100 GHz in a 4-nm layer. This is the highest frequency observed to date in time-resolved experiments with metallic ferromagnets. We predict that detection of magnetization precession approaching THz frequencies should be possible with Galfenol nanolayers.