# Is there a method to find the order of a lift of an element of order 2 to the Schur cover?

Let $$G$$ be a finite non-abelian simple group, $$M.G$$ the Schur covering group of $$G$$. Is there a method to find the order of a preimage of an element of order 2 in the natural homomorphism $$\pi: M.G\rightarrow G$$?

We can find the result using the 'Atlas of finite groups' for some finite simple groups, but is there a general method?