MathCastle
Groups and FieldsMediumGroup Actions

Group Actions · Medium problem

S6S_6 acts on ordered triples (a,b,c)(a,b,c) of distinct elements from {1,…,6}\{1,\ldots,6\} by σ⋅(a,b,c)=(σ(a),σ(b),σ(c))\sigma\cdot(a,b,c)=(\sigma(a),\sigma(b),\sigma(c)). This action is transitive. Find ∣Stab⁡((1,2,3))∣|\operatorname{Stab}((1,2,3))|.