# Conjugacy classes

## Homework Statement

Given (1,2,3)(4,5,6) in S_6, compute all the elements in the centralizers.

## Homework Equations

Well I know that cycle structure is preserved. Etc. I just want to know if there is a less brute force way to compute all 18 instead of going:

(1,2,3)(4,5,6)(1,2,3)(4,5,6)(1,2,3)(4,5,6)=(1,2,3)(4,5,6)
(2,3,1)(4,5,6)(1,2,3)(4,5,6)(2,3,1)(4,5,6)=(2,3,1)(4)(5)(6)
etc.
Also, for some reason I haven't been able to get all 18