Conway group Co2
On this page, we provide links to verifications that the generators of maximal subgroups of the Conway group Co2 from the ATLAS generate subgroups of the correct index.
| Subgroup | Subgroup order | Index in Co2 | Verification |
|---|---|---|---|
| \(U_6(2):2\) | \(18,393,661,440\) | \(2,300\) | |
| \(2^{10}:\mathrm{M}_{22}:2\) | \(908,328,960\) | \(46,575\) | |
| \(\mathrm{McL}\) | \(898,128,000\) | \(47,104\) | |
| \(2^{1+8}.S_6(2)\) | \(743,178,240\) | \(56,925\) | |
| \(\mathrm{HS}:2\) | \(88,704,000\) | \(476,928\) | |
| \((2^4 \times 2^{1+6}).A_8\) | \(41,287,680\) | \(1,024,650\) | |
| \(U_4(3):D_8\) | \(26,127,360\) | \(1,619,200\) | |
| \(2^{4+10}.(S_5 \times S_3)\) | \(11,796,480\) | \(3,586,275\) | |
| \(\mathrm{M}_{23}\) | \(10,200,960\) | \(4,147,200\) | |
| \(3^{1+4}.2^{1+4}.S_5\) | \(933,120\) | \(45,337,600\) | |
| \(5^{1+2}:4S_4\) | \(12,000\) | \(3,525,451,776\) |
Key
| Symbol | Meaning |
|---|---|
| We could verify the index. | |
| The computation did not terminate, so we were unable to verify the index. | |
| We have not yet attempted the computation. |