[r-t] irregular leadheads

[King, Peter R]

> There are n! rows on n bells and, in total, (n-1)! lead
> heads which form the permutation group S_(n-1).  So we now
> need to know how many elements of S_(n-1) are n-1 cycles.
> As they are n-1 cycles, we can write down the place bell
> order for each of them starting from some arbitrary choice
> of bells (say the tenor).  We then find that there are
> (n-2)! possible place bell orders each of which corresponds
> to a valid (n-1)-cycle lead head.  So there's the answer:
> (n-2)!.
> 

That's what I thought and is true for n-1 prime but for Royal (for
example) there are only 6 regular lheads (and presumably each family of
irregular ones has only 6 members) to avoid the cycles of 3. Or am I
wrong?