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C4h point group
Abelian, 6(8) irreducible representations
Subgroups: Cs, Ci, C2, C4, C2h, S4

Character table
E C4(z) C2 (C4)3 i (S4)3 σh S4 linear,
rotations
quadratic
Ag 1 1 1 1 1 1 1 1 Rz x2+y2, z2
Bg 1 -1 1 -1 1 -1 1 -1 x2-y2, xy
Eg 1
1
i
-i
-1
-1
-i
i
1
1
i
-i
-1
-1
-i
i
Rx+iRy
Rx-iRy
(xz, yz)
Au 1 1 1 1 -1 -1 -1 -1 z
Bu 1 -1 1 -1 -1 1 -1 1
Eu 1
1
i
-i
-1
-1
-i
i
-1
-1
-i
i
1
1
i
-i
x+iy
x-iy

Product table
 AgBgEgAuBuEu
AgAgBgEgAuBuEu
BgBgAgEgBuAuEu
EgEgEgAg+Bg+EgEuEuAu+Bu+Eu
AuAuBuEuAgBgEg
BuBuAuEuBgAgEg
EuEuEuAu+Bu+EuEgEgAg+Bg+Eg

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