Group Theory is a beautiful area of mathematics that systematizes and formalizes mathematical study of symmetry.
Symmetry concepts have many applications in various scientific disciplines such as in biology and chemistry. In physics, it should be emphasized that group theory is primarily valuable for analyzing the effects of known geometrical symmetry on some systems. In this research, we focus on 2-generator p-groups of nilpotency class two of order 32, where p=2 and 3. Specific groups that are isomorphic to each of the group in this classification will first be determined. By choosing those that are symmetry, their
application in
crystallography, particularly in infrared and Raman spectra activities, will be explored.