How many conjugacy classes are there in Symmetric group 4.?
I’m going to guess 4, because the conjugacy class is defined as the orbit of the set of elements that conjugate to each other… obviously a permutation which permutes the same number of elements can be commuted to by some other permutation of the same number of elements … so the number of different conjugacy classes should just be the number of different permutation sizes? Correct?
it’s the number of partitions of 4, which map to the length of cycles in the conjugacy class.
for each partition, i’ll list a member of the conjugacy class.
4 (1234)
31 (123)
22 (12)(34)
211 (12)
1111 () = e
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