Suzuki sporadic group Suz
The presentation and the subgroup generators used for the completed enumerations come from page 97 of Praeger and Soicher's book. This presentation is not the presentation given on the ATLAS website. The remaining subgroup generators are words in the ATLAS standard generators.
Subgroup enumerations
The following table summarises the subgroup enumerations represented by the files in the verification directory.
| Subgroup | Subgroup order | Index in \(\mathrm{Suz}\) | Verification |
|---|---|---|---|
| Trivial | \(1\) | \(448,345,497,600\) | |
| \(G_2(4)\) | \(251,596,800\) | \(1,782\) | |
| \(3.U_4(3):2\) | \(19,595,520\) | \(22,880\) | |
| \(U_5(2)\) | \(13,685,760\) | \(32,760\) | |
| \(2^{1+6}.U_4(2)\) | \(3,317,760\) | \(135,135\) | |
| \(3^5:\mathrm{M}_{11}\) | \(1,924,560\) | \(232,960\) | |
| \(\mathrm{J}_2:2\) | \(1,209,600\) | \(370,656\) | |
| \(2^{4+6}:3.A_6\) | \(1,105,920\) | \(405,405\) | |
| \(\mathrm{M}_{12}:2\) | \(190,080\) | \(2,358,720\) | |
| \(L_3(3):2\) | \(11,232\) | \(39,916,800\) | |
| \(L_2(25)\) | \(7,800\) | \(57,480,192\) | |
| \(A_7\) | \(2,520\) | \(177,914,880\) |
Key
| Symbol | Meaning |
|---|---|
| We could verify the index. | |
| We have not yet verified the index. |