Calculator
Example data table
| n | Permutation | Centralizer size |
|---|---|---|
| 4 | (1 2)(3 4) | 8 |
| 4 | (1 2 3 4) | 4 |
| 4 | identity | 24 |
These values follow the cycle-type formula shown below.
Formula used
In the symmetric group Sn, the centralizer of a permutation σ is the set of permutations that commute with it: C(σ) = { τ ∈ Sn : τσ = στ }.
Write σ as disjoint cycles. If it has mi cycles of length i, then the centralizer size is:
|C(σ)| = ∏i ( imi · mi! ).
This tool computes the cycle counts, applies the formula exactly (big integers), and can brute-force verify it for n ≤ 8.
How to use
- Enter n, or leave it blank to infer from your input.
- Choose a format or keep auto-detect.
- Enter a permutation in one-line form (e.g., 2 1 3 4) or cycles (e.g., (1 2 3)(4 5)).
- Click Calculate to see results above the form.
- Use Download CSV or Download PDF for reporting.