TITLE: Reference for the triple covering of A_6
QUESTION [19 upvotes]: 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 $\mathfrak{A}_7$?

REPLY [17 votes]: 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. 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.)