The Octahedral Group

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^^ Greetings everyone. I am very sorry for bothering everyone, however I do hope this is alrighty that I perhaps ask for some advice regarding the octahedral group (the group of rotational symmetries of a cube (of order 24)). ^^ I believe that I am blessed with a happy little assignment concerning applications of representation theory in virology and I believe I am finding great difficulty with this. ^^This is a very fun assignment I believe.

I believe that there exists five conjugacy classes of the octahedral group. These are the identity class, the class of 3-fold rotations (by 2Pi/3) containing eight elements, the class of 4-fold rotations (containing 6 elements), the class of 2-fold rotations (containing 6 elements) and also a class of additional 2-fold rotations (containing 3 elements). ^^ I believe that I understand very much the axes associated to the first four classes, however I am very confused which axis is associated with the final class.

(I believe that I must consider the quotient group O/D2, where O is the above octahedral group and D2 is the dihedral group of order 4 - I believe that the dihedral group contains the identity and the final class that I listed, however I am very sorry if I am incorrect.)

I am very sorry for bothering everyone and you need not answer.

^^ Yaye thankee ruveyn.