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D3h point group
not Abelian, 6(8) irreducible representations
Subgroups: Cs, C2, C3, D3, C2v, C3v, C3h

Character table
E 2C3 3C'2 σh 2S3 v
linear,
rotations
quadratic
A'1 1 1 1 1 1 1 x2+y2, z2
A'2 1 1 -1 1 1 -1 Rz
E' 2 -1 0 2 -1 0 (x, y) (x2-y2, xy)
A''1 1 1 1 -1 -1 -1
A''2 1 1 -1 -1 -1 1 z
E'' 2 -1 0 -2 1 0 (Rx, Ry) (xz, yz)

Product table
 A'1A'2E'A''1A''2E''
A'1A'1A'2E'A''1A''2E''
A'2A'2A'1E'A''2A''1E''
E'E'E'A'1+A'2+E'E''E''A''1+A''2+E''
A''1A''1A''2E''A'1A'2E'
A''2A''2A''1E''A'2A'1E'
E''E''E''A''1+A''2+E''E'E'A'1+A'2+E'

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