Classification problems are a central feature in finite group theory. Most first year graduate algebra students have seen the classification of many groups of small order, including the proof that a non-abelian simple group of order 60 is isomorphic to the alternating group of degree 5. In these talks, we will consider a non-abelian simple group of order 168 and will use elementary methods together with a little projective geometry, to show that such a group is isomorphic to the group of invertible 3x3 matrices of the field of two elements.