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S8 point group
Abelian, 5(8) irreducible representations
Subgroups: C2, C4

Character table
E S8 C4 (z) (S8)3 C2 (S8)5 (C4)3 (S8)7 linear,
rotations
quadratic
A 1 1 1 1 1 1 1 1 Rz x2+y2, z2
B 1 -1 1 -1 1 -1 1 -1 z
E1 1
1
e
e*
i
-i
-e*
-e
-1
-1
-e
-e*
-i
i
e*
e
x+iy
x-iy
E2 1
1
i
-i
-1
-1
-i
i
1
1
i
-i
-1
-1
-i
i
(x2-y2, xy)
E3 1
1
-e
-e*
i
-i
e*
e
-1
-1
e
e*
-i
i
-e*
-e
Rx+iRy
Rx-iRy
(xz, yz)

Product table
 ABE1E2E3
AABE1E2E3
BBAE3E2E1
E1E1E32A+E2E1+E32B+E2
E2E2E2E1+E32A+2BE1+E3
E3E3E12B+E2E1+E32A+E2

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