If different D12 × D12-orbits are collected under the action of a bigger group to a bigger orbit, then it is possible to determine permuting elements between the D12 × D12-normal forms of these orbits by opening a pop-up window.
If the D12 × D12-orbit of a tone row f coincides with its orbit under a bigger group, then for all additional generators h of the bigger group it is possible to determine elements g∈ D12 × D12 so that g*f=h*f by opening a pop-up window.
The output consists of a big table. The first column contains the number of the D12 × D12-orbit, the second column the stabilizer type of this orbit. The third column displays the Aff 1(Z12) × D12-orbit. Usually it consists of two D12 × D12-orbits, the one from the first column and an additional orbit whose number is written in the third column. If this number is smaller than the number in the first column, then this new orbit contains the normal form of the Aff 1(Z12) × D12-orbit. In this case its number will be printed in bold face. If the first column contains the normal form of the Aff 1(Z12) × D12-orbit, then in the fourth column the stabilizer type of this orbit is indicated. The next two columns describe the D12 × Aff 1(Z12)-orbit in a similar way. The following two columns describe the Aff 1(Z12) × Aff 1(Z12)-orbit which consists of the D12 × D12-orbit from the first column and up to three further D12 × D12-orbits. The following four columns describe the 𝔄12- and 𝔇12-orbits in a similar way.