| Number of vertices: | $512$ |
| Diameter: | $3$ |
| Intersection array: | $\{21,20,16;1,2,12\}$ |
| Spectrum: | $21^1 5^{210} (-3)^{280} (-11)^{21}$ |
| Automorphism group: | $2^9.\mathrm{P} \Gamma \mathrm{L}(3,4) \cong 2^9 : (\mathrm{PSL}(3,4) : S_3)$ |
| Distance-transitive: | Yes |
| Primitive |