  Magnetic torque measurements have been performed on a KOs$_2$O$_6$ single
crystal in magnetic fields up to 35.3 T and at temperatures down to 0.6 K. The
upper critical field is determined to be $\sim$30 T. De Haas-van Alphen
oscillations are observed. A large mass enhancement of (1+$\lambda$) = $m^* /
m_{band}$ = 7.6 is found. It is suggested that, for the large upper critical
field to be reconciled with Pauli paramagnetic limiting, the observed mass
enhancement must be of electron-phonon origin for the most part.
