Notations for high symmetry points in the 1st Brillouin zone

I am trying to understand how I should interpret the letters like Г,K,M,T etc., that are usually there in the electronic band structure diagrams.

So, let's assume we have graphene with its hexagonal structure. Then we make a Fourier transform of real space and obtain another hexagonal structure in reciprocal space, with a single hexagonal cell representing the 1st Brillouin zone. And there are letters "K" in the corners, "Г" in the center, M between two corners and other letters. And they are called the points of high symmetry.

So how does it work? For example, we have 6-fold rotational symmetry. How does this kind of symmetry convert into one point in the Brillouin zone? And how do we know where exactly the point is: in the center or in the corner or somewhere else? And how are letters chosen initially? Why is it the letter "K" is in the corner and "Г" is in the center? I assume these came from the group theory... So can I find some easy explanation of the notation without dipping into the theory itself?

Thanks!