Vibrational spectra of the methyl groups in mono-methylamine (MMA), dimethylamine (DMA), and trimethylamine (TMA) monomers and their clusters were measured in three experimental set-ups to capture their complex spectral features as a result of bend/umbrella-stretch Fermi resonance (FR). Multiple bands were observed between 2800 and 3000 cm^-1 corresponding to the methyl groups for MMA and DMA. On the other hand, the corresponding spectrum of TMA is relatively simple, exhibiting only four prominent bands in the same frequency window, even though TMA has a larger number of methyl groups. The discrete variable representation (DVR) based ab initio anharmonic algorithm with potential energy surface (PES) at CCSD/aug-cc-pVDZ quality is able to capture all the experimentally observed spectral features across all three amines, and the constructed vibrational Hamiltonian was used to analyze the couplings that give rise to the observed FR patterns. It was observed that the vibrational coupling among CH stretch modes on different methyl groups is weak (less than 2 cm^-1) and stronger vibrational coupling is found to localize within a methyl group. In MMA and DMA, the complex feature between 2850 and 2950 cm^-1 is a consequence of closely packed overtone states that gain intensities by mixing with the stretching modes. The simplification of the spectral pattern of TMA can be understood by the red-shift of the symmetric CH₃ stretching modes by about 80 cm_-1 relative to MMA, which causes the symmetric CH₃ stretch to shift outside the FR window.