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D4 point group
not Abelian, 5(6) irreducible representations
Subgroups: C2, C4, D2

Character table
E 2C4 (z) C2 (z) 2C'2 2C''2
linear functions,
rotations
quadratic
functions
A1 1 1 1 1 1 x2+y2, z2
A2 1 1 1 -1 -1 z, Rz
B1 1 -1 1 1 -1 x2-y2
B2 1 -1 1 -1 1 xy
E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)

Product table
 A1A2B1B2E
A1A1A2B1B2E
A2A2A1B2B1E
B1B1B2A1A2E
B2B2B1A2A1E
EEEEEA1+A2+B1+B2

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