Abstraction algebraic structures have been heavily transformed by computational techniques in many mathematical systems. Through a more pragmatic process, methods can gain a deeper understanding of more abstract mathematically based systems through their application together as the group theories that formed their basis. In this paper, we investigate how we can grow that knowledge outside the domain of classical math in such a way that the theoretical frameworks can be transformed into computational modelling. All of the central algorithms for coset enumeration such as the Todd-Coxeter way, permutation groups using Schreier-Sims algorithm and solvable groups using the polycyclic presentations are prominent in this transformation. All of these methods to deal with large and complex group structures are able to solve the problem of analysis manually. Thus, through calculation, we will be able to increase the output in accuracy and speed, so that interaction of computational methods as well as algebra has turned heads in a million different directions. The projects might be something like cryptography, where the structures of large groups support secure communication systems or coding theory for reliable transmission in chemistry or physics. This way of thinking illustrates the adaptability of mathematics can create a wider view and applications.