Solution: To find the number of elements conjugate to the given permutation $(1234567)$ in $S_{7}$, we can determine the conjugacy class to which it belongs. In general, two permutations in the symmetric group $S_n$ are conjugate if and only if they have the same cycle structure. Therefore, $g\in S_7$ will be conjugate to $(1234567)$ if and only if $g = \left( a_1 a_2 a_3 a_4 a_5 a_6 a_7 \right) $, where $a_i \in \{ 1,2,3,\dots,7 \} $. That is, we need to determine how many $7$-cycles are there in $S_7$. In general, the number of $k$-cycles in $S_n$ is given by \[ m = (k-1)! \dbinom{n}{k} = \dfrac {n!} {k (n-k)!} \] Therefore, the number of $7$-cycle in $S_7$ will be \[ \text{ Number of $7$-cycles in $S_7$ } = (7-1)! \dbinom{7}{7} = 6!. \]