Motivated by the recent proposal by Potter et al. [Phys. Rev. X 6, 031026 (2016)] concerning possible thermoelectric signatures of Dirac composite fermions, we perform a systematic experimental study of thermoelectric transport of an ultrahigh-mobility GaAs/AlxGa1−xAs two-dimensional electron system at filling factor v=1/2. We demonstrate that the thermopower Sxx and Nernst Sxy are symmetric and antisymmetric with respect to B=0 T, respectively. The measured properties of thermopower Sxx at v=1/2 are consistent with previous experimental results. The Nernst signals Sxy of v=1/2, which have not been reported previously, are nonzero and show a power-law relation with temperature in the phonon-drag dominant region. In the electron-diffusion dominant region, the Nernst signals Sxy of v=1/2 are found to be significantly smaller than the linear temperature dependent values predicted by Potter et al., and decreasing with temperature faster than linear dependence.