We present experimental data on the electric permanent dipole moments d(v',J') and lambda splittings (q factors) in the quasidegenerate (3) 1pi(e/f) state of the NaCs molecule over a wide range of the vibrational (v') and rotational (J') quantum numbers by using the combination of dc Stark mixing and electric radio frequency-optical double resonance methods. Within the experimental (3) 1pi state v' ranged from v' = 0 to 34, q values exhibited a pronounced decrease from 7.91x10(-6) to 0.47x10(-6) cm(-1), while absolute value(d) values varied between 8.0 and 5.0 D. Experimental evaluation yielded small d values about 1 D for D2 1pi state v' < 3 levels. The experiment is supported by ab initio electronic structure calculations performed for the (1-3) 1pi states of NaCs by means of the many-body multipartitioning perturbation theory of potential energy curves, permanent dipole, and angular coupling matrix elements for the lowest singlet states. The predicted d values reproduce their experimental counterparts within the measurement errors while theoretical q factors reproduce the measured v' dependence being, however, systematically overestimated by ca. 1x10(-6) cm(-1). The present NaCs data are compared with those of the NaK and NaRb molecules.