Exercise
Let G be the group S3. Consider the conjugation representation C : G -> Sym({e, a, b, c, y, z}), where
How many choices of invariant subsets are there in G?
1
2
4
8
No.
The empty and the full set already make two.
No, the empty, the full set and {e} already make three.
No.
Determine the minimal invariant subsets first.
Yes. There are three minimal invariant subsets:
- {e}
- {a, b, c}
- {y, z}