The Klein model of the hyperbolic 3-space is defined as follows
$$\mathbb{H}^3=\{x\in\mathbb{R}^{3,1}:\langle x,x\rangle_{3,1}<0\}/\sim$$
where $x\sim x'$ if and only there exists $\lambda$ such that $x =\lambda x' $, and $\mathbb{R}^{3,1}$ is the (3+1)-Minkowski space.
My question: What is the group of isometries in this case?
Thank You.
