Abstract: I plan on highlighting some of the important open problems left in finite group theory (namely, the Higman PORC Conjecture) and then shifting tack to discuss faithful permutation representations (long name, but it just means "injective homomorphisms G->S_n). For a finite group G, let d(G) be the smallest n such that there is an injection G->S_n, and let alpha(G)=d(G)/#G, a rational number between 0 and 1. I will discuss some of the key properties of alpha, with an emphasis on p-groups, and display an intuitive algorithm to calculate alpha for any group. This leads naturally to the PORC-alpha conjecture, a stronger conjecture than the Higman PORC conjecture and yet somehow an easier one. If I still have time, I will discuss some other features of alpha, such as averages and limit points. This talk is based mostly on my own undergraduate work, which means that almost everything is trivial. If you know what a group action is, you are more than prepared for this talk.