O'Nan group O'N
The presentation and the generators for \(L_3(7):2\) come from Section 4.23, page 101, of Praeger and Soicher's book. The tidied relations are justified in Soicher's paper, which also gives the generators for the other two subgroups. This presentation is not the presentation given on the ATLAS website.
Subgroup enumerations
The following table summarises the subgroup enumerations represented by the files in the verification directory.
| Subgroup | Subgroup order | Index in \(\mathrm{O'N}\) | Verification |
|---|---|---|---|
| \(L_3(7):2\) | \(3,753,792\) | \(122,760\) | |
| \(4.L_3(4):2\) | \(161,280\) | \(2,857,239\) | |
| \((3^2:4 \times A_6).2\) | \(25,920\) | \(17,778,376\) |
Key
| Symbol | Meaning |
|---|---|
| We could verify the claimed index. | |
| The computation terminated with a different index, so we could not verify the claim. |