Let $S_n$ denotes symmetric group of $n$ symbols. What is the maximal odd order of permutation in $S_n$?
In other words, what is the value of $\max\{\text{ord }\sigma : \sigma\in S_n, \text{ord }\sigma \text{is odd} \} $ where $\text{ord }\sigma$ denotes smallest positive integer $m$ which satisfies $\sigma ^m = \text{id}$ ?