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

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