Hi there,

I had this question on an exam today and I'm not sure how to do it.

"Let G =

x

. List all the Sylow 2-subgroups of G, and all the Sylow 3-subgroups of G, giving reasons that your lists are complete"

I found that G has order 36, and so I determined that

= 1, 3 or 9 and that

= 1 or 4 (where

denotes the number of Sylow i-subgroups) but from there I couldn't do much. By brute force I managed to find one subgroup of order 4 and one of order 9, so in the end I just put that

= 1 and

= 1.

Can anyone verify, or correct this?

Many thanks