There exist precisely ten rank-3 strongly regular graphs on 2401 vertices. They are $H(2,49)$, the Paley graph $P_{2401}$, the Peisert graph on 2401 vertices, the Van Lint-Schrijver graph on 2401 vertices, the $\mathrm{VO}_4^-(7)$ graph, the $\mathrm{VO}_4^+(7)$ graph, and the four graphs below.
Number of vertices: | $2401$ |
Diameter: | $2$ |
Intersection array: | $\{240,180;1,20\}$ |
Spectrum: | $240^1 44^{240} (-5)^{2160}$ |
Automorphism group: | $7^4:6.\mathrm{O}(5,3)$ |
Distance-transitive: | Yes |
Primitive |
Number of vertices: | $2401$ |
Diameter: | $2$ |
Intersection array: | $\{480,360;1,90\}$ |
Spectrum: | $480^1 39^{480} (-10)^{1920}$ |
Automorphism group: | $7^4:6.\left(2^4:\mathrm{S}_5\right)$ |
Distance-transitive: | Yes |
Primitive |
Number of vertices: | $2401$ |
Diameter: | $2$ |
Intersection array: | $\{720,490;1,210\}$ |
Spectrum: | $720^1 34^{720} (-15)^{1680}$ |
Automorphism group: | $7^4:6.\mathrm{S}_7$ |
Distance-transitive: | Yes |
Primitive |
Number of vertices: | $2401$ |
Diameter: | $2$ |
Intersection array: | $\{960,570;1,380\}$ |
Spectrum: | $960^1 29^{960} (-20)^{1440}$ |
Automorphism group: | $7^4:48.\mathrm{S}_5$ |
Distance-transitive: | Yes |
Primitive |