Probably an elementary question, but I don't get it, so:
From wikipedia: "The Sylow p-subgroups of the symmetric group of degree $p$ are just the cyclic subgroups genereated by $p$-cycles. There are $(p-1)!/(p-1) = (p-2)!$ such subgroups."
I get that there are $(p-1)!$ $p$-cycles and that there are $(p-1)$ different elements of order $p$ in G, the"supgroup", of the Sylow p-subgroups.
But I don't understand why # of subgroups = $\frac{\# of-p-cycles}{\#of-generators-of-G}$