For instance, W 2 (1) = C 2 and W 2 (2) = D 8, the dihedral group of order 8, and so a Sylow 2-subgroup of the symmetric group of degree 7 is generated by { (1,3)(2,4), (1,2), (3,4), (5,6) } and is isomorphic to D 8 × C 2.