McLaughlin group McL
The presentation and subgroup identifications used in these enumerations come from presentation (11.1) in Đoković's paper. This presentation is not the presentation given on the ATLAS website.
Subgroup enumerations
The following table lists every subgroup enumeration that we attempted with this presentation.
| Subgroup | Subgroup order | Index in \(\mathrm{McL}\) | Verification |
|---|---|---|---|
| Trivial | \(1\) | \(898,128,000\) | |
| \(\mathrm{M}_{22}\) | \(443,520\) | \(2,025\) | |
| \(\mathrm{M}_{21} \cong L_3(4)\) | \(20,160\) | \(44,550\) | |
| \(S_6\) | \(720\) | \(1,247,400\) | |
| \(2^4:S_4\) | \(384\) | \(2,338,875\) | |
| \(3^2:D_8\) | \(72\) | \(12,474,000\) | |
| \((D_8 * D_8):2\) | \(64\) | \(14,033,250\) | |
| \(2 \times S_4\) | \(48\) | \(18,711,000\) | |
| \(S_4\) | \(24\) | \(37,422,000\) |