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Apr 2, 2014 at 22:30 comment added Binzhou Xia @DerekHolt Thank you! I've edited the question and focus on three almost simple families now.
Apr 2, 2014 at 22:26 history edited Binzhou Xia CC BY-SA 3.0
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Apr 2, 2014 at 6:26 comment added Derek Holt Of course there are known results. For example the sizes of the orbits of the $2$-point stabilizer of ${\rm PSL}(n,q)$ are $1,1,q-1,(q^n-1)/(q-1)-(q+1)$, and it would be possible to write formulae for all of the infinite families (although the affine examples are less straightforward). I think you need say more precisely what you want to know.
Apr 1, 2014 at 21:23 history asked Binzhou Xia CC BY-SA 3.0