This graph is the bipartite double of the coset graph of the binary Golay code.
| Number of vertices: | $4096$ |
| Diameter: | $7$ |
| Intersection array: | $\{23,22,21,20,3,2,1;1,2,3,20,21,22,23\}$ |
| Spectrum: | $23^1 9^{253} 7^{506} 1^{1288} (-1)^{1288} (-7)^{506} (-9)^{253} (-23)^1$ |
| Automorphism group: | $(2^{11}.\mathrm{M}_{23}) \times 2$ |
| Distance-transitive: | Yes |
| Bipartite, Anipodal |