I was wondering how can I obtain the three dimensional representation of the Dihedral group of order 6, [itex]D_3[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

If this group has the elements: [itex]D_3 = \left \{ e,c,c^2,b,bc,bc^2 \right \}[/itex]

Where [itex]c[/itex] corresponds to rotation by [itex]120^o[/itex] on the xy plane (so about z-axis) and [itex]b[/itex] to reflections of the [itex]x[/itex] axis, I don't see how [itex]z[/itex] would change at all... so when I try to obtain it I'm getting the known 2-dimensional representation of [itex]D_3[/itex] together with an extra [itex]1[/itex] on the diagonal corresponding to the transformations [itex]z \rightarrow z'=z[/itex]...

Any help?

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# 3 Dimensional Representation of D3

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