There are two known $\mathrm{GQ}(7,7)$s, namely $\mathrm{O_5}(7)$ and $\mathrm{Sp}_4(7)$. Each one is the dual of the other.
| Number of vertices: | $400$ |
| Diameter: | $2$ |
| Intersection array: | $\{56,49;1,8\}$ |
| Spectrum: | $56^1 6^{224} (-8)^{175}$ |
| Automorphism group: | $\mathrm{PS_p}(4,7):2$ |
| Distance-transitive: | Yes |
| Primitive |