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**poirot** question: Find the order of the folowing elements of s15 and determine which pairs are conjugate.

i) (1 2 4 8)(3 6 12)(5 10 15)

ii) (1 2)(4 8)(3 12 11)(5 13 7)

iii) (1 7 9)(11 12 13)(5 10 8 6)

I have found the orders using lcm i) 12, ii) 6, iii) 12.

To be conjugate, elements need to have same order so only i) and iii) are possibilities.

I tried using ii) as 'g' in a=gbg^-1 but it didn't work. I don't think it expects to trawl through s15 looking for a g so is there an easy way to determine conjugacy?