Let H = {β ∈ S5 | β(1) = 1} and K = {β ∈ S5 | β(2) = 2}. Prove that H is isomorphic to K. 

This problem has been posted on here before but the only response to it is the hint:

H is conjugated to K by the transposition (1,2).

I still don't understand it. Does this mean β(1 2) = (1 2)?