Note that the $2^{11}.\mathrm{M}_{24}$ encountered for the valency 276 graph is not isomorphic to the $2^{11}.\mathrm{M}_{24}$ encountered for the valency 759 and valency 1288 graphs.
This graph is the unique rank-3 strongly regular graph with parameters $(2048,276,44,36)$. The first subconstituent of this graph is the Johnson graph $\mathrm{J}(24,2)$.
| Number of vertices: | $2048$ |
| Diameter: | $2$ |
| Intersection array: | $\{276,231;1,36\}$ |
| Spectrum: | $276^1 20^{759} (-12)^{1288}$ |
| Automorphism group: | $2^{11}.\mathrm{M}_{24}$ |
| Distance-transitive: | Yes |
| Primitive |
This graph is the unique rank-3 strongly regular graph with parameters $(2048,759,310,264)$. The second subconstituent of this graph is the complement of the Dodecad graph. The complement of this graph is the graph with valency 1288 that is given below.
| Number of vertices: | $2048$ |
| Diameter: | $2$ |
| Intersection array: | $\{759,448;1,264\}$ |
| Spectrum: | $759^1 55^{276} (-9)^{1771}$ |
| Automorphism group: | $2^{11}.\mathrm{M}_{24}$ |
| Distance-transitive: | Yes |
| Primitive |
This graph is the unique rank-3 strongly regular graph with parameters $(2048,1288,792,840)$. The first subconstituent of this graph is the Dodecad graph. This graph is the complement of the graph with valency 759 that was given above.
| Number of vertices: | $2048$ |
| Diameter: | $2$ |
| Intersection array: | $\{1288,495;1,840\}$ |
| Spectrum: | $1288^1 8^{1771} (-56)^{276}$ |
| Automorphism group: | $2^{11}.\mathrm{M}_{24}$ |
| Distance-transitive: | Yes |
| Primitive |