MathCastle
Groups and FieldsMediumGroup Actions

Group Actions · Medium problem

The alternating group A4A_4 (order 1212) acts on the set of all 22-element subsets of {1,2,3,4}\{1,2,3,4\} by permuting the elements: σ⋅{a,b}={σ(a),σ(b)}\sigma\cdot\{a,b\}=\{\sigma(a),\sigma(b)\}. How many orbits does this action have?