Conway group Co3
The presentation and subgroup identifications used in these enumerations come from presentation (13.1) in Đoković's paper. This presentation is not the presentation given on the ATLAS website.
Subgroup enumerations
The following table lists every subgroup enumeration recorded for presentation (13.1).
| Subgroup | Subgroup order | Index in \(\mathrm{Co}_3\) | Verification |
|---|---|---|---|
| Trivial | \(1\) | \(495,766,656,000\) | |
| \(\mathrm{McL}:2\) | \(1,796,256,000\) | \(276\) | |
| \(U_4(3):2\) | \(6,531,840\) | \(75,900\) | |
| \(2.S_6(2)\) | \(2,903,040\) | \(170,775\) | |
| \(U_4(2):2 \cong S_4(3):2\) | \(51,840\) | \(9,563,400\) | |
| \(U_3(3):2\) | \(12,096\) | \(40,986,000\) | |
| \(3^3:(2 \times S_4)\) | \(1,296\) | \(382,536,000\) |
Key
| Symbol | Meaning |
|---|---|
| We could verify the index. | |
| The computation did not terminate, so we were unable to verify the index. | |
| We have not attempted the computation. |