Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${ heta}$:G -> G given by ${ heta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{ heta}>$ which is the split extension of the group G by the cyclic group $<{ heta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{ heta}>$.