I'm reading some notes concerning Sylow subgroups of S4:
Since #S4 = 24 = 3 . 2^3 from Sylow's Theorems we know there are either 1 or 4 Sylow 3-subgroups and either 1 or 3 Sylow 2-subgroups.
The question I have regards how we narrow this down:
My notes argue that since S4 has 9 elements...