This document is provided by the Chemical Portal www.webqc.org

Ih point group
not Abelian, 10(32) irreducible representations

Character table
E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σ linear,
rotations
quadratic
Ag 1 1 1 1 1 1 1 1 1 1 x2+y2+z2
T1g 3 -2cos(4π/5) -2cos(2π/5) 0 -1 3 -2cos(2π/5) -2cos(4π/5) 0 -1 (Rx, Ry, Rz)
T2g 3 -2cos(2π/5) -2cos(4π/5) 0 -1 3 -2cos(4π/5) -2cos(2π/5) 0 -1
Gg 4 -1 -1 1 0 4 -1 -1 1 0
Hg 5 0 0 -1 1 5 0 0 -1 1 [2z2-x2-y2, x2-y2, xy, xz, yz]
Au 1 1 1 1 1 -1 -1 -1 -1 -1
T1u 3 -2cos(4π/5) -2cos(2π/5) 0 -1 -3 2cos(2π/5) 2cos(4π/5) 0 1 (x, y, z)
T2u 3 -2cos(2π/5) -2cos(4π/5) 0 -1 -3 2cos(4π/5) 2cos(2π/5) 0 1
Gu 4 -1 -1 1 0 -4 1 1 -1 0
Hu 5 0 0 -1 1 -5 0 0 1 -1

Product table
 AgT1gT2gGgHgAuT1uT2uGuHu
AgAgT1gT2gGgHgAuT1uT2uGuHu
T1gT1gAg+T1g+HgGg+HgT2g+Gg+HgT1g+T2g+Gg+HgT1uAu+T1u+HuGu+HuT2u+Gu+HuT1u+T2u+Gu+Hu
T2gT2gGg+HgAg+T2g+HgT1g+Gg+HgT1g+T2g+Gg+HgT2uGu+HuAu+T2u+HuT1u+Gu+HuT1u+T2u+Gu+Hu
GgGgT2g+Gg+HgT1g+Gg+HgAg+T1g+T2g+Gg+HgT1g+T2g+Gg+2HgGuT2u+Gu+HuT1u+Gu+HuAu+T1u+T2u+Gu+HuT1u+T2u+Gu+2Hu
HgHgT1g+T2g+Gg+HgT1g+T2g+Gg+HgT1g+T2g+Gg+2HgAg+T1g+T2g+2Gg+2HgHuT1u+T2u+Gu+HuT1u+T2u+Gu+HuT1u+T2u+Gu+2HuAu+T1u+T2u+2Gu+2Hu
AuAuT1uT2uGuHuAgT1gT2gGgHg
T1uT1uAu+T1u+HuGu+HuT2u+Gu+HuT1u+T2u+Gu+HuT1gAg+T1g+HgGg+HgT2g+Gg+HgT1g+T2g+Gg+Hg
T2uT2uGu+HuAu+T2u+HuT1u+Gu+HuT1u+T2u+Gu+HuT2gGg+HgAg+T2g+HgT1g+Gg+HgT1g+T2g+Gg+Hg
GuGuT2u+Gu+HuT1u+Gu+HuAu+T1u+T2u+Gu+HuT1u+T2u+Gu+2HuGgT2g+Gg+HgT1g+Gg+HgAg+T1g+T2g+Gg+HgT1g+T2g+Gg+2Hg
HuHuT1u+T2u+Gu+HuT1u+T2u+Gu+HuT1u+T2u+Gu+2HuAu+T1u+T2u+2Gu+2HuHgT1g+T2g+Gg+HgT1g+T2g+Gg+HgT1g+T2g+Gg+2HgAg+T1g+T2g+2Gg+2Hg

You may print and redistribute verbatim copies of this document.