Finite group theory is one of the most delightful areas in mathematics. The ideal aim of finite group theory is to find all finite groups up of groups of order less than or equal to 17 by using the presentation techniques of each group with the help of Lagrange's Theorem.

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In recent times, conjugate gradient method (CG) have been broadly used to solve nonlinear unconstrained minimization problems as a result of fewer storage locations and computational expensive in dealing with large-scale problems. In this work, we present a spectral PRP CG method which derived from the CG search direction without secant condition and utilized some of the benchmark test problem functions with several variables to prove its global convergence properties and satisfies sufficient descent condition, the results are validated by exact line search techniques.