A factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. In this paper, the factor groups K(SL(2,121)) and K(SL(2,169)) computed for each group from the character table of rational representations.

For any group G, we define G/H (read” G mod H”) to be the set of left cosets of H in G and this set forms a group under the operation (a)(bH) = abH. The character table of rational representations study to gain the K( SL(2,81)) and K( SL(2, 729)) in this work.

The group for the multiplication of closets is the set G|N of all closets of N in G, if G is a group and N is a normal subgroup of G. The term “G by N factor group” describes this set. In the quotient group G|N, N is the identity element. In this paper, we procure K(SL(2,125)) and K(SL(2,3125)) from the character table of rational representations for each group.

The effective application of the method of measuring and evaluating performance according to the Balanced  Scorecard the need for an information system a comprehensive and integrated for internal and external environment, Which requires the need to develop accounting information system in general and cost management information systems to suit the particular requirements of the environment in terms of the development of modern methods of measurement to include the use of some methods that have proven effective in measuring and evaluating performance.

The research problem in need of management to develop methods of measuring and evaluating performance through the use of both financial measures and non