What is Symmetry number?

The symmetry number $\sigma$ of a molecule is the number of distinct orientations of the rigid molecule that are reached by proper rotations and are indistinguishable from the starting one (the order of the rotational subgroup of its point group): 1 for $\ce{HCl}$ and $\ce{CO}$, 2 for $\ce{N2}$, $\ce{CO2}$ and $\ce{H2O}$, 3 for $\ce{NH3}$, 12 for $\ce{CH4}$ and $\ce{C6H6}$.