Class Of Permutations

I am creating a class of permutations. The problem is that there are many ways to describe what a permutation does. for example.

Dim aPerm As New clsPermutation
Dim bPerm As New clsPermutation
aPerm.DoesTranspose(2,3) : Rem aPerm.Action({a,b,c}) = {a,c,b}
MsgBox (aPerm Is aPerm.Inverse)

I want the message box to return True. But since aPerm and aPerm.Inverse are different instances of clsPermutaion, it returns False. (.Inverse is a read-only property that returns a clsPermutation.). What I would like to do is have a collection, myPermutations. When I specify the action that aPerm does, I would like

1) if nothing in myPermutations does the same thing as aPerm, then add aPerm to myPermutations.

2) if something (xPerm) does the same thing as aPerm, then

Set aPerm=xPerm
so that "xPerm Is aPerm" returns True.
The problem I have is that in the class module,.....................