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D4d point group
not Abelian, 7(10) irreducible representations
Subgroups: Cs, C2, C4, D2, D4, C2v, C4v, S8

Character table
E 2S8 2C4 2(S8)3 C2 4C'2 d linear,
rotations
quadratic
A1 1 1 1 1 1 1 1 x2+y2, z2
A2 1 1 1 1 1 -1 -1 Rz
B1 1 -1 1 -1 1 1 -1
B2 1 -1 1 -1 1 -1 1 z
E1 2 (2)1/2 0 -(2)1/2 -2 0 0 (x, y)
E2 2 0 -2 0 2 0 0 (x2-y2, xy)
E3 2 -(2)1/2 0 (2)1/2 -2 0 0 (Rx, Ry) (xz, yz)

Product table
 A1A2B1B2E1E2E3
A1A1A2B1B2E1E2E3
A2A2A1B2B1E1E2E3
B1B1B2A1A2E3E2E1
B2B2B1A2A1E3E2E1
E1E1E1E3E3A1+A2+E2E1+E3B1+B2+E2
E2E2E2E2E2E1+E3A1+A2+B1+B2E1+E3
E3E3E3E1E1B1+B2+E2E1+E3A1+A2+E2

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