We present an analysis of the binary and physical parameters of a unique pulsating white dwarf with a main-sequence companion, SDSS J1136+0409, observed for more than 77 d during the first pointing of the extended Kepler mission: K2 Campaign 1. Using new ground-based spectroscopy, we show that this post-common-envelope binary has an orbital period of 6.89760103(60) hr, which is also seen in the photometry as a result of Doppler beaming and ellipsoidal variations of the secondary. We spectroscopically refine the temperature of the white dwarf to 12330(260) K and its mass to 0.601(36) Msun. We detect seven independent pulsation modes in the K2 light curve. A preliminary asteroseismic solution is in reasonable agreement with the spectroscopic atmospheric parameters. Three of the pulsation modes are clearly rotationally split multiplets, which we use to demonstrate that the white dwarf is not synchronously rotating with the orbital period but has a rotation period of 2.49(53) hr. This is faster than any known isolated white dwarf, but slower than almost all white dwarfs measured in non-magnetic cataclysmic variables, the likely future state of this binary.
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