Elements with different formats in S4 correspond to different yoke classes. Note that (1)=( 1)(2)(3)(4), (1 2 3)=( 1 2 3)(4) and so on, so the format of elements in S4 is as follows.
( 1) 4, ( 1) 1 (3) 1, ( 1) 2 (2) 1, (2) 2, (4) 6558.
( 1)^4={( 1)(2)(3)(4)},
(2)^2={( 1 2)(3 4),( 1 3)(2 4),( 1 4)(2 3)}。