Question

find the number of elements of order 6 in S4​

Answer 1

Answer:

But since S4 is nothing but group of all permutations on 4 distinct symbols, so using 4 symbols we can't create 6-cycle. First case is thus cancel out. For the second case, if we choose any 3-cycle then we are left with 1 symbols using which we can't create any 2-cycle. Hence no element of order 6 is there in S4.

Answer 2

Answer

Find the number of elements of order two in the symmetric group S4 of all permutations of the four symbols {1,2,3,4}.