MathCastle
Groups and FieldsEasyGroup Actions

Group Actions · Easy problem

S6S_6 acts on the 33-element subsets of {1,…,6}\{1,\ldots,6\} by σ⋅T={σ(t):t∈T}\sigma\cdot T=\{\sigma(t):t\in T\}. This action is transitive. Find ∣Stab⁡({1,2,3})∣|\operatorname{Stab}(\{1,2,3\})|.