- Let
`p = (0 3 4)(1 2)`

. Let`G =`

`. What is the stabilizer of`

`k=0`

? -
`purify(p) = e`

so we would imagine we would have`H = e`

. - But actually, consider orbit(k). We have
`0 <-> id`

,`3 <-> p`

,`4 <-> p^2`

. - If I now consider
`p * orbit(k)`

then I get`p, p^2, p^3`

, where`purify(p) = id`

,`purify(p^2) = id`

,`purify(p^3) = p^3`

. - Thus we find the nontrivial generator
`p^3`

.