Conway group Co1
The presentations and subgroup generators used in these enumerations come from Section 4.34, pages 121–122, of Praeger and Soicher's book. The presentations define either \(2.\mathrm{Co}_1\) or \(2\times\mathrm{Co}_1\); quotienting by the displayed central involution gives \(\mathrm{Co}_1\).
Subgroup enumerations
The following table lists every subgroup enumeration recorded in the Co1 verification directory.
| Subgroup | Subgroup order | Index in \(\mathrm{Co}_1\) | Verification |
|---|---|---|---|
| Trivial | \(1\) | \(4,157,776,806,543,360,000\) | |
| \(\mathrm{Co}_2\) | \(42,305,421,312,000\) | \(98,280\) | |
| \(3.\mathrm{Suz}:2\) | \(2,690,072,985,600\) | \(1,545,600\) | |
| \(2^{11}:\mathrm{M}_{24}\) | \(501,397,585,920\) | \(8,292,375\) | |
| \(\mathrm{Co}_3\) | \(495,766,656,000\) | \(8,386,560\) |
Key
| Symbol | Meaning |
|---|---|
| We could verify the index. | |
| The computation would require an impractical amount of memory, so we were unable to verify the index. |