The H-orbits corresponding to , , have been dealt with above. We now discuss the remaining forms individually. The stabilizer of is a connected 3-dimensional group with a 2-dimensional unipotent radical. Thus, is a single H-orbit of size .

For there are two orbits. An element representing the second coset is given by . The number of elements in the orbit corresponding to the identity is . The number of elements in the orbit corresponding to the other orbit is . This follows as the values of and which satisfy the relations are , and with . There is one orbit for containing where the denominator is the order of .

There are two orbits for . The second is given by . The number in the first is . The number in the second is . This follows as the elements in S acting in the appropriate manner are given by and the relations , .

The remaining forms are in 3 variables. There are three orbits for as in the case of three variables. The contribution of the identity is . The contributions from the involution and the 3-cycle are and , respectively.

The remaining forms and each have just one orbit, of sizes and , respectively.