
2sylow subgroups of S6
Can someone suggest some method to find 2sylow subgroups of S6. From what I know  we first find 2sylow subgroups of S8 and then find an isomorphism from S6 into S8. Then our desired subgroup is (S6 /\ xQx') where Q is 2sylow subgroup of S8. This method requires us to find x, which may not be easy. IS there an alternative method?

Solution
The link has good detailed description on 2sylow subgroups:
http://sps.nus.edu.sg/~kokyiksi/roddyurops.pdf
However, for S6 we can directly get the 2sylow subgroup.
Consider, S4. The 2sylow subgroup in this group has order 2^3 = 8 and is given as:
P = {(1)(2)(3)(4), (1 2), (3 4), (1 2)(3 4), (1 3)(2 4), (1 4)(2 3), (1 4 2 3), (1 3 2 4)}.
Since S6 has 6 characters {1, 2, 3, 4, 5, 6}. Consider:
Q = AP. Where A = ((5 6)).
Clearly, Q is of order 2^4 = 16 and is the required 2sylow subgroup.