I would like to ask for a reference (book, paper ...) for the following nice construction, which I have found as an exercise in some notes of a course by R. Borcherds. For $n=6$ or $7$ (and only in that case), the alternating group $\mathfrak{A}\_n$ has a nontrivial central extension by $\mathbb{Z}/3$. The construction in the case $n=6$ is as follows.


Define an *oval* in $\mathbb{P}^2(\mathbb{F}\_4)$ as a set of 6 points which are in general position (i.e. no 3 of them are collinear). It is easy to show that any projective frame of $\mathbb{P}^2(\mathbb{F}\_4)$ is contained in a unique oval, and from this that the stabilizer of an oval in $PGL\_3(\mathbb{F}\_4)$ is isomorphic to $\mathfrak{A}\_6$. The inverse image of this $\mathfrak{A}\_6$ in $SL\_3(\mathbb{F}\_4)$ provides the nontrivial extension by $\mathbb{Z}/3$. 


Does anyone know a reference for this? and/or an analogous construction for $\mathfrak{A}\_7$? 



Reference for the triple covering of A_6
The oval construction for $3\cdot A\_6$ can be found on p.110 of



> 
> *Symmetric Generation of Groups With Applications to Many of the Sporadic Finite
>  Simple Groups* by Robert Curtis.
> 
> 
> 


An e-version is [here](http://f3.tiera.ru/2/M_Mathematics/MA_Algebra/MAtg_Group%20theory/Curtis%20R.T.%20Symmetric%20generation%20of%20groups%20%28CUP,%202007%29%28ISBN%20052185721X%29%28O%29%28331s%29_MAtg_.pdf). In fact Curtis does better: he constructs $3\cdot A\_6\cdot 2^2$.


If you read on to p.112 and beyond you will also find a construction of $3\cdot A\_7$, as you requested.


(It seems like the e-version is freely available on the web. But if you can't get it, contact me and I'll email it to you.)


