1. The problem statement, all variables and given/known data The question is, "How many conjugates does (1,2,3,4) have in S7? Another similar one -- how many does (1,2,3) have in S5? 3. The attempt at a solution I know that the conjugates are all the elements with the same cycle structure, so for (123) I found there are 20 conjugates by hand listing them (132)...(354) etc. But I was wondering if there's some equation to find this amount- I haven't taken probability but I think there's got to be a statistical way to figure it out!! Thanks a lot.