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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.