GroupStabilizer[group, {p1, ..., pn}]
returns the subgroup of elements of group that move none of the points , ..., .

GroupStabilizer[group, {p1, ..., pn}, f]
returns the stabilizer subgroup under the action given by the function f.


  • The output is a subgroup of group defined by generators, but possibly using different generators.
  • The stabilizer group is also known as the little group or isotropy group.
  • The stabilizer of a list of points is a subgroup of the setwise stabilizer of the same list of points.
  • For permutation groups, the default group action is taken to be PermutationReplace.
New in 8 | Last modified in 9
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