# P-Sylow subgroup

1. Nov 22, 2009

### cmj1988

1. The problem statement, all variables and given/known data
S4xZ/5

Find the number of p-Sylow subgroups for p=2, 3, and 5

3. The attempt at a solution

S4 is no problem. There I can use some binomial coefficients and count stuff. I was wondering how to tackle any Z/n.

2-Sylow

First we find 2-sylow subgroups of S4. $$\frac{\binom{4}{2}*2!}{2}$$ or 3.

Now I'm stuck, are the 2-Sylow subgroups of Z/5 just elements of order 2. I don't think there are any.