So I am supposed to calculate the amount of 2-,3- and 5-Sylow subgroups in $S_5$ and I already calculated that the amount for 3 and 5 are 10 and 6. So can I use this to drag myself over the finish line and imply that there really are 15 Sylow 2-subgroups or do I need to come up with a completely new proof again? We didn't do much on the symmetric and dihedral groups so I am struggling a little bit to figure out how to get a proof for Sylow 2-subgroups.
2026-03-28 11:34:07.1774697647
Calculating amount of Sylow 2-subgroups in $S_5$ by using the amounts of 3- and 5- subgroups?
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