We shall demonstrate how to derive the compatibility relation between G and D. The reader should repeat the calculation for the remaining compatibility relations.

First we need to find the operations of G which are also symmetry operations in the group of D . From Table 2. 13 we find the following correspondence:

Operation in G	Corresponding Operation in D
{E}	{E}
{C2}	{C24}
{s}	{md}
{s'}	{md'}

By definition on page 45, two representations are compatible if they have the same characters for the corresponding classes according to the above table. Based on this definition clearly G₁ is compatible with D₁ while G₂ is compatible with D₂.

For G₃ the characters for the above 4 classes are:

	{E}	{C2}	{s}	{s'}
G3	2	2	0	0

From Table 2.14 we see that the characters of D₁+D₂ are exactly the same for the corresponding classes:

	{E}	{C24}	{md}	{md'}
D1+D2	2	2	0	0

It should be a straight forward exercise to show the remaining compatibility relations between Gand D.