I have the permutations for an equilateral triangular prism

e

(25)

(35)

(23)

(14)

(235)

(253)

(14)(23)

(14)(25)

(14)(35)

(14)(235)

(14)(253)

I am trying to find the conjugacy classes.

I think the answer is:

e

(25)

(35)

(23)

(14)

(235)

(253)

(14)(23)

(14)(25)

(14)(35)

(14)(235)

(14)(253)

I've put gaps to separate each class. So I have six conjugacy classes here. Is this correct?

Thanks