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.
