There exist precisely four rank-3 strongly regular graphs on 361 vertices. They are $H(2,19)$, the Paley graph $P_{361}$, the Peisert graph on 361 vertices, and the graph below which is the unique rank-3 $\mathrm{SRG}(361,144,59,56)$.
| Number of vertices: | $361$ |
| Diameter: | $2$ |
| Intersection array: | $\{144,84;1,56\}$ |
| Spectrum: | $144^1 11^{144} (-8)^{216}$ |
| Automorphism group: | $19^2:\left(9 \times \mathrm{GL}_2(3)\right)$ |
| Distance-transitive: | Yes |
| Primitive |