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Background: When I divide a hexagon in six triangles the group $D_6$ works on the triangles. The cycle index of the group action would be in this case $$p(x_1,x_2,x_3,x_6)=\frac{1}{12}(x_1^6 + 3x_1^2x_2^2 + 4x_2^3+2x_3^2+2x_6)$$

Question: How does CycleIndex work in GAP? The doc in GAP notes that CycleIndex is undocumented, but the function exists.

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    Perhaps the GAP forum could provide a better/faster response: forum@gap-system.org2012-02-28
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    There are GAP experts here, they answered me before, this forum supports LaTeX and I can easily document all my questions in one system. We should ask all the GAP guys to come here, instead of sending people away.2012-02-28
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    The GAP guys are of course welcome here, but this question is completely off-topic here.2012-02-28
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    CycleIndex is documented in GAP 4.5. The implementation is in lib/oprt.gi and is the naive by the definition implementation, summing over the conjugacy classes.2012-02-29
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    Thanks, time to install GAP 4.5 right now.2012-02-29
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    The code can also be seen using `Print(CycleIndex,"\n");`2012-09-19
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    @DouglasS.Stones: `PageSource(CycleIndex);` will show you the file with the source code, so you will be able to see the comments in the code, too (if there are any). Note that the argument must be a function, so for operations etc. one has to use `ApplicableMethod` first.2013-04-22

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