Held group He
On this page, we provide links to verifications that the generators of maximal subgroups of the Held group He from the ATLAS generate subgroups of the correct index.
| Subgroup | Subgroup order | Index in He | Verification |
|---|---|---|---|
| \(S_4(4):2\) | \(1,958,400\) | \(2,058\) | |
| \(2^2.L_3(4).S_3\) | \(483,840\) | \(8,330\) | |
| \(2^6:3.S_6\) | \(138,240\) | \(29,155\) | |
| \(2^6:3.S_6\) | \(138,240\) | \(29,155\) | |
| \(2^{1+6}.L_3(2)\) | \(21,504\) | \(187,425\) | |
| \(7^2:2.L_2(7)\) | \(16,464\) | \(244,800\) | |
| \(3.S_7\) | \(15,120\) | \(266,560\) | |
| \(7^{1+2}:(3 \times S_3)\) | \(6,174\) | \(652,800\) | |
| \(S_4 \times L_3(2)\) | \(4,032\) | \(999,600\) | |
| \(7:3 \times L_3(2)\) | \(3,528\) | \(1,142,400\) | |
| \(5^2:4A_4\) | \(1,200\) | \(3,358,656\) |