The general linear group GL(n,F) is important for all topics in algebra because it is a concrete group the dimension of it is n2. Determined the kernel of its determinant map (from this group to its fiels except the zero element) of dimension n2 – 1 which is the non Abelian normal subgroup the special linear group SL(n,F), by the first isomorphism theorem we gain that GL(n,F)/ SL(n,F)  F\{0} . In this work we take it of degree 2 over the field pk where p is prime odd number and k is even number, the group operation for each is the matrix multiplication.