 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-3/8d/b/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

There are four main diagonals and the action is transitive, so the stabilizer of one has order

\frac{48}{4} = 12.

For the diagonal spanned by

(1, 1, 1)

, the stabilizing signed permutation matrices are

P

and

- P

with

P

G_{d} ≅ C_{2} \times S_{3} .

The action is not faithful: both

I

and the central inversion

- I

fix every main diagonal setwise. In fact its kernel is exactly

{I, - I}

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