### Generating all elements of $SL_2(\mathbb{F}_q)$
What is the fastest way to create a set with all elements of $SL_2(\mathbb{F}_q)$ for $q$ some prime power of size about $50$? One way to do it is to find a representative for each conjugacy class and then use the ConjugacyClass method, but this seems inefficient. Is there a better way?