The lowest frequency parallel fundamental band nu (5) of CH3SiH3 near 700 cm(-1) has been measured at a resolution of 0.004 cm(-1) with Fourier transform spectroscopy to investigate vibration-torsion-rotation interactions in symmetric tops. The torsional splittings in the spectrum are increased from similar to0.005 cm(-1) to similar to1 cm(-1) by Fermi-type vibration-torsion interactions between the torsional stack (v(6)=0,1,2,...) in the ground vibrational state and the corresponding stack for v(5)=1. Resonant interactions were observed between the states (v(5)=1,v(6)=0) and (v(5)=0,v(6)=5) for the rotational series with (k=+/-1,sigma=-/+1), where sigma labels the torsional sublevels. In this resonance, the two unperturbed states are near opposite limits for torsional motion: (v(5)=0,v(6)=5) involves nearly free rotation, while (v(5)=1,v(6)=0) involves small amplitude torsional oscillation. For the (k=+/-1,sigma=-/+1) rotational series, perturbation-allowed transitions in the high overtone (v(6)=5 <--0) were observed. Over 750 frequencies measured here have been analyzed together with more than 2500 measurements involved in the recent analysis of the lowest-lying degenerate fundamental band nu (12) given by Moazzen-Ahmadi [J. Mol. Spectrosc. 175, 54 (1996)]. A fit to within experimental error was achieved using 41 parameters, an increase of only 4 when the new band is added. The analysis shows that the inclusion of the Fermi-type interactions leads to a considerable simplification of the Hamiltonian for the ground vibrational state. For example, both the second and third terms (V-0,V-6,V-0,V-9) in the Fourier expansion of the hindering potential as well as the torsional flexing term (F-0,F-m) vanish in the ground state. The changes in the leading terms in the torsional Hamiltonian have been quantitatively explained by a contact transformation. The large perturbations produced by the interaction matrix elements off-diagonal by 5 units in v(6) have serious implications for vibrational relaxation in molecules undergoing internal rotation.