Summary of Group Operations
With x, y, and z different blocks R, G, and B we have:
- (xyz)(xyz)=(xzy)
- (xyz)(xzy)=
- (xyz)(xy)=(xz)
- (xy)(xyz)=(yz)
- (xy)(xy)=
- (xy)(xz)=(xzy)
In the form of a Cayley table:
| * | e | a | b | c | d | f |
|---|---|---|---|---|---|---|
| e | e | a | b | c | d | f |
| a | a | e | d | f | b | c |
| b | b | f | e | d | c | a |
| c | c | d | f | e | a | b |
| d | d | c | a | b | f | e |
| f | f | b | c | a | e | d |
Note that non-equal non-identity elements only commute if they are each other's inverse. Therefore the group is centerless.
Read more about this topic: Dihedral Group Of Order 6
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