The Clifford group $\mathcal{C}\_n$ is a matrix group on $\mathbb{C}^{2^n}$ generated by tensor products of the following matrices:
$$
P = \begin{pmatrix} 1 & 0 \\\\ 0 & i\end{pmatrix}
\quad
H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\\\ 1 & -1\end{pmatrix}
\quad
\wedge\\! X = \begin{pmatrix}1 & 0 & 0 & 0 \\\\ 0 & 1 & 0 & 0 \\\\ 0 & 0 & 0 & 1 \\\\ 0 & 0 & 1 & 0\end{pmatrix}
$$
For my purposes I take equality up to a complex unit, i.e., if $A = e^{i\alpha}B$ then $A = B$.


My question is: 



> 
> is there an abstract presentation of this group by generators and relations?
> 
> 
> 


Or the easier version: 



> 
> is there a presentation of $\mathcal{C}\_2$ or $\mathcal{C}\_3$ by generators and relations?
> 
> 
> 


I don't care which set of generators is used, although it would be nice if the generators were those given above.



Presentation of the Clifford group by generators and relations?
In the time since the question was asked this paper appeared which does exactly what I want:


[Generators and relations for n-qubit Clifford operators](http://arxiv.org/abs/1310.6813)


