Let $\mathbf { S }$ denote the group of all those permutations of the English alphabet that fix the letters T,E,N,D,U,L,K,A and R. Other letters may or may not be fixed. Show that $\mathbf { S }$ has elements $\sigma , \tau$ of order 36 and 39 respectively, but does not have any element of order 37 or 38.