Group theory character table is a very useful tool to know important information about molecular activities and their spectra but suffers different defects such as the physical meaning of ω, the entire levels of degenerate states and the atomic motion through molecular vibration. On the way to define the infrared spectra, Raman spectra and natural frequency of molecules; it is important to split degenerate states and determine the motion of each atom through molecular vibration. While symmetry can be seen as the most basic and important concept in physics, the higher n-fold rotation axis Cn symmetry element can be represented as a full or partial symmetric rotation axis and governs other symmetry elements in the molecule through the vibrational motion. Symmetry states and Omega-table which hold all possible symmetry states of the molecule will solve the character table defects. Selection rules judge some of the symmetry states to be forbidden. Omega-table illustrates the relation between symmetry elements in the molecule through its translation, rotation and vibration processes and separates the degenerate states as well as can be reduced to point group character table. Based on omega-table, the description of the atomic motion of NH3 molecule or any other molecules through vibration was so clear according to ω mathematical value and its physical meaning.