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A computer program is developed using Microsoft Visual C++ in theWindows environment. This program focuses on two specific finite Abelian groups, which are the group Zn under addition modulo n and the group U(n) under multiplication modulo n, where n is any positive integer less than or equal to 120. Computations of the properties of the two groups get more tedious and time consuming as the value of n increases. Therefore a program that couldassist in the computation would indeed be of great help. This program in C++ is written relating to some properties of Zn and U(n). It enables the user to enter any positive integer n (n · 120) to generate answers to some properties of these two groups. A lattice diagram can be obtained for any groups of Zn and, for groups of U(n) which are cyclic.