The local graph of this graph is the point graph of $\mathrm{GQ}(2,4)$. The second subconstituent of this graph is the $\mathrm{NO}_6^-(2)$ graph.
Number of vertices: | $64$ |
Diameter: | $2$ |
Intersection array: | $\{27,16;1,12\}$ |
Spectrum: | $27^1 3^{36} (-5)^{27}$ |
Automorphism group: | $2^6:(\mathrm{O}^-(6,2):2) \cong 2^6:\mathrm{GO}^-(6,2)$ |
Distance-transitive: | Yes |
Primitive |