Degrees of freedom and mutual coupling are two important factors to determine the ability of direction of arrival (DOA) estimation. Although coprime planar array (CPPA) has less mutual coupling than hourglass array (HA) and ladder array (LA), its positive and negative covariance corresponding lags are discontinuous, resulting in low degrees of freedom. In this study, we propose a generalized and symmetric coprime planar array (GSCA) by employing the symmetric property of the difference co-array. By moving one subarray and introducing a supplementary subarray, we construct a connected virtual uniform rectangular array (URA). Through further optimizing the sensor number, the redundant lags are reduced and the array structure is more general. We show that the degrees of freedom are much higher than those of CPPA, HA and LA. Besides, the mutual coupling is close to CPPA, but less than HA and LA. The superiority of GSCA is verified by simulations.