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 $600$.