The knot group of a knot $K$ is the fundamental group of $\mathbb R^3 \smallsetminus K$; that is, the set of possibly self-crossing closed paths (starting and ending at any single point in space) which you can take through real-space which are not equivalent to each other if you forbid passing through the locus of the knot; and where you can compose the paths in the natural way. For instance, the knot group of the un-knot is just $\mathbb Z$, corresponding to the number of times that a path winds about a cycle in space.
We can consider similar questions for links ("knots" having more than one closed loop) as for knots of a single component: given a link, we can consider the group of closed paths in space which avoids crossing either of the two components.
I have a friend who has a tattoo of a knot (more precisely, a link of two components) in the shape of a maple leaf; we were curious what properties it had. A presentation of the link is given below. How would one obtain a presentation of the link group? Does the link group of this particular link correspond to any relatively nice group?