Obtating the Fermi Coupling Constant from expeced muon decay

I recently performed a lab where we found the expected muon lifetime as $tau = 2.02$ microseconds. I am now supposed to use this value to obtain the Fermi Coupling Constant $G_F$, by using the equation:
$$tau= frac{192pi^2hbar^7}{G_F^2m^5c^4}$$
I was wondering if someone could take a look at my solution and tell me if this makes sense. I started by arranging the equation as follows:
$$G_F=sqrt{frac{1}{tau}frac{192pi^2hbar^7}{m^5c^4}}$$
This is where I start having a problem. I tried calculating $G_F$ by simply plugging in SI units into the previous equation, but this gives me $G_F = 1.5times10^{-62} ;kg;m^7;s^{-1}$.

This is my first time every hearing about the Fermi Coupling Constant or doing anything particle physics related so I’m not really sure if this makes any sense. But to me those units do not really make any sense. When I did some googling I noticed that Fermi Coupling Constant is always given as $G_F/(chbar)^3$, why is that?