A particular procedure has been followed in [1] to construct the conjugacy classes of the split extension p 2 : G L2(p). The object of this paper is to develop a general m ethod for constructing the conjugacy classes of p 2 : GL2(p), where p 2 is an elem entary Abelian p-group of order p 2. This procedure can be used to construct the conjugacy classes of the split extension p n : k where k is any finite group. A brief descrip- tion of the character table of p 2 : GL2 (p) is also given, the character table of p 2 : GL2(p) plays a big role in the construction of the character table of the m axim al subgroup pl+2 : GL2(p) of the projeçtive symplectic group PSP4(p) p-prim e [4], where pi+2 is the extra special group of order p 3, this is because (pl+2 : GL2(p)) / Z (p1+2) ~ p 2 : GL2(p) where Z (p1+2) is the çenter of p l+ 2 in p i+ 2 : GL2(p). These character tables are of great im portance to the docum entation program me of finite simple groups [3].