Feasibility of counting Hoffman-Singleton graph cycles?

Question

I know that counting all distinct simple cycles in an arbitrary graph has exponential time complexity, but what does that really mean in terms of trying to compute the number of cycles in say the Hoffman Singleton Graph? (50 vertices, 175 edges, 7-regular) Say I implement a basic algorithm in Java (the one language I've recently learned to code in) and run this program on my run-of-the-mill laptop, could I compute it letting my computer run straight for a couple of days?