Result for the group SL(2,172)

Abstract

The set of all (n×n) non-singular matrices over the field F this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension n over the field F, denoted by GL(n,F). The determinant of these matrices is a homomorphism from GL(n,F) into F* and the kernel of this homomorphism was the special linear group and denoted by SL(n,F). Thus SL(n,F) is the subgroup of GL(n,F) which contains all matrices of determinant one. The rational valued characters of the rational representations written as a linear combination of the induced characters for the groups SL(2,17^2 ) discuss in this work and find the Artin indicator for this group after study the rational valued characters of the rational representations and the induced characters.