This paper represents some small finite groups as groups of transformations of a compact surface of small genus. In particular, we start with a designated pair of regions of this surface and each region is labeled with the group element, which transforms the designated region into it. This gives a portrait of that finite group. These surfaces and the regions corresponding to the group elements are shown in this paper. William Burnside first gave a simple example of such a portrait in his 1911 book, Theory of Groups of Finite Order.