BUILT-IN MATHEMATICA SYMBOL
GroupOrbits
GroupOrbits[group, {p1, ...}]
returns the orbits of the points 
under the action of the elements of group.
GroupOrbits[group, {p1, ...}, f]
finds the orbits under the group action given by a function f.
- Two points belong to the same orbit under group if there is an element g in group such that the image of one point under g is the other point.
- If a point p is fixed by all elements in group then it forms an orbit {p}.
- GroupOrbits[group] gives all orbits in the natural domain of action of group.
- Orbits are given as sorted lists.
- For permutation groups, the default group action is taken to be PermutationReplace.
Take a permutation group:
Orbit of point 3:
| Out[2]= |  |
Point 7 belongs to the same orbit:
| Out[3]= |  |
Point 4 belongs to a different orbit:
| Out[4]= |  |
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