I'm looking for a small strongly regular graph whose automorphism group is not vertex-transitive.


[This answer](https://mathoverflow.net/a/115598/75171/) to a different question shows that the Chang graphs on 28 vertices are such graphs. Is there an example on less vertices?


Thanks for all replies.



Smallest strongly regular graph whose automorphism group is not vertex transitive?
There is no smaller example.


Various places, including Andries Brouwer's list of parameters and existence for small SRGS (<http://www.win.tue.nl/~aeb/graphs/srg/srgtab.html>) show that there are only a handful of parameter sets to check.


Those with fewer than 25 vertices can almost be checked by hand as they fall into a few families (Paley graphs) or are well-known individual graphs (e.g Clebsch graph). 


For the parameter set $(25, 12, 5, 6)$ there are exactly $15$ graphs and they have automorphism groups of orders $1$ (twice), $2$ (four times), $3$ (twice), $6$ (four times), $72$ (twice) and $600$.


