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.

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.

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.

Linked to the post-modern historical transformations sociological which raided the developed Western societies since the middle of last century, which consisted mainly in the emergence of what he called Alsosiologion (consumer society a) and (Affluent Society), as it appeared the new social lifestyle is not only characterized by the provision of the accumulation of capital and sparingly in spending, but rather a kind of extravagance and encourage consumption, prompting some to say that consumption is a community postmodern engine, and other labels for this period of economic backgrounds, such as the new capitalism and the system of the new capitalist Alseperntiqi technical and labels purist such as industrial post-society emerged, some a