[Haskell-beginners] Expressing the idea of a group in Haskell

[Christian]

Hello Haskell-Experts!
I was trying to express the notion of a (mathematical) group
in Haskell, using type classes, as an exercise.
If I am not mistaken, a group can be for example the Reals together with
the multiplication operation and "1" as the neutral element.
Or, the Reals with addition and "0".
my first idea was to write something like

 class Group a where
   ...

_but_, I thought, I need to parameterise, so to speak, not only using the
type "a", but also the group operation. 
How could I do that in Haskell? Is that even possible?

Thanks in advance!
Christian