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.