How to use class equation for determining the center of $S_4$
$$|G|=|Z(G)|+\sum_x [G:C_G(x)]$$ So I guess I need to find $$|G|-\sum_x [G:C_G(x)]=|Z(G)|$$
and $C_G(x)$ is the set of all group elements that commute with $x$. This seems like I would need to use brute force, and that would take a very long time, since each elements has numerous elements in it's centralizer. How do I work this out?