The frequency output of the Permanent Magnet Generator is related to the pole count of the exciter - compared to the motor it is feeding.
If the motor line frequency is 50 Hz, then the exciter has 3x the pole count of the synchronous machine (i.e. 2-pole synch with 6-pole exciter design, or 4-pole synch and 12-pole exciter, etc.)
If the motor line frequency is 60 Hz, the exciter has 2.5x the pole count of the synchronous machine (i.e. 4-pole synch with 10-pole exciter, 8-pole synch with 20-pole exciter, etc.)
The purpose of the high frequency operation is three-fold. First, higher frequency generally means more output for a given volume. Second, the higher frequency delivers a "smoother" waveform and thus reduces DC ripple - translating in turn to a reduced torque pulsation effect in the motor operation. And third, there has to be some minimum frequency capability to show up as an AC waveform from very slow speeds so that the rectification portion of the exciter has something to work with. This necessitates much higher frequencies for the exciter output than the typical motor line frequencies.
Lastly - the generator can generate high frequencies from a small package because the nature and size of the "permanent magnet" poles delivers far more poles-per-inch-of-periphery than more traditional electromagnetic pole approaches. They are also "always on"; this means there is effectively the capability of producing field current for the synchronous machine right from zero speed - which in turn will result in a smaller variable frequency drive (VFD), since the starting performance is no longer restricted to "inductive" effects from the amortisseur (damper) cage winding.
High frequency generators (higher than 50Hz, 60Hz) are mostly used in aviation where the generators are driven by high speed gas turbines. High speed generators have much less weight than low speed generators of the same output power since that the generator power is directly proportional to its volume multiplied by its rotating speed. The less weight of the generator is an important advantage for aviation.