Character Table for Point Group C92v

Character table for the C_92v point group

C92v E 2 C92 2 C46 2 C92^3 2 C23 2 C92^5 2 C46^3 2 C92^7 2 C23^2 2 C92^9 2 C46^5 2 C92^11 2 C23^3 2 C92^13 2 C46^7 2 C92^15 2 C23^4 2 C92^17 2 C46^9 2 C92^19 2 C23^5 2 C92^21 2 C46^11 2 C4 2 C23^6 2 C92^25 2 C46^13 2 C92^27 2 C23^7 2 C92^29 2 C46^15 2 C92^31 2 C23^8 2 C92^33 2 C46^17 2 C92^35 2 C23^9 2 C92^37 2 C46^19 2 C92^39 2 C23^10 2 C92^41 2 C46^21 2 C92^43 2 C23^11 2 C92^45 C2 46 sv 46 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ..T ....T ......T ........T ..........T ............T A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1 2.00000 1.99534 1.98137 1.95817 1.92583 1.88452 1.83442 1.77577 1.70884 1.63394 1.55142 1.46167 1.36511 1.26218 1.15336 1.03917 0.92013 0.79680 0.66976 0.53959 0.40691 0.27233 0.13648 0.00000 -0.13648 -0.27233 -0.40691 -0.53959 -0.66976 -0.79680 -0.92013 -1.03917 -1.15336 -1.26218 -1.36511 -1.46167 -1.55142 -1.63394 -1.70884 -1.77577 -1.83442 -1.88452 -1.92583 -1.95817 -1.98137 -1.99534 -2.00000 0.00000 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.98137 1.92583 1.83442 1.70884 1.55142 1.36511 1.15336 0.92013 0.66976 0.40691 0.13648 -0.13648 -0.40691 -0.66976 -0.92013 -1.15336 -1.36511 -1.55142 -1.70884 -1.83442 -1.92583 -1.98137 -2.00000 -1.98137 -1.92583 -1.83442 -1.70884 -1.55142 -1.36511 -1.15336 -0.92013 -0.66976 -0.40691 -0.13648 0.13648 0.40691 0.66976 0.92013 1.15336 1.36511 1.55142 1.70884 1.83442 1.92583 1.98137 2.00000 0.00000 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.95817 1.83442 1.63394 1.36511 1.03917 0.66976 0.27233 -0.13648 -0.53959 -0.92013 -1.26218 -1.55142 -1.77577 -1.92583 -1.99534 -1.98137 -1.88452 -1.70884 -1.46167 -1.15336 -0.79680 -0.40691 0.00000 0.40691 0.79680 1.15336 1.46167 1.70884 1.88452 1.98137 1.99534 1.92583 1.77577 1.55142 1.26218 0.92013 0.53959 0.13648 -0.27233 -0.66976 -1.03917 -1.36511 -1.63394 -1.83442 -1.95817 -2.00000 0.00000 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 1.92583 1.70884 1.36511 0.92013 0.40691 -0.13648 -0.66976 -1.15336 -1.55142 -1.83442 -1.98137 -1.98137 -1.83442 -1.55142 -1.15336 -0.66976 -0.13648 0.40691 0.92013 1.36511 1.70884 1.92583 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.88452 1.55142 1.03917 0.40691 -0.27233 -0.92013 -1.46167 -1.83442 -1.99534 -1.92583 -1.63394 -1.15336 -0.53959 0.13648 0.79680 1.36511 1.77577 1.98137 1.95817 1.70884 1.26218 0.66976 0.00000 -0.66976 -1.26218 -1.70884 -1.95817 -1.98137 -1.77577 -1.36511 -0.79680 -0.13648 0.53959 1.15336 1.63394 1.92583 1.99534 1.83442 1.46167 0.92013 0.27233 -0.40691 -1.03917 -1.55142 -1.88452 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.83442 1.36511 0.66976 -0.13648 -0.92013 -1.55142 -1.92583 -1.98137 -1.70884 -1.15336 -0.40691 0.40691 1.15336 1.70884 1.98137 1.92583 1.55142 0.92013 0.13648 -0.66976 -1.36511 -1.83442 -2.00000 -1.83442 -1.36511 -0.66976 0.13648 0.92013 1.55142 1.92583 1.98137 1.70884 1.15336 0.40691 -0.40691 -1.15336 -1.70884 -1.98137 -1.92583 -1.55142 -0.92013 -0.13648 0.66976 1.36511 1.83442 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.77577 1.15336 0.27233 -0.66976 -1.46167 -1.92583 -1.95817 -1.55142 -0.79680 0.13648 1.03917 1.70884 1.99534 1.83442 1.26218 0.40691 -0.53959 -1.36511 -1.88452 -1.98137 -1.63394 -0.92013 0.00000 0.92013 1.63394 1.98137 1.88452 1.36511 0.53959 -0.40691 -1.26218 -1.83442 -1.99534 -1.70884 -1.03917 -0.13648 0.79680 1.55142 1.95817 1.92583 1.46167 0.66976 -0.27233 -1.15336 -1.77577 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 1.70884 0.92013 -0.13648 -1.15336 -1.83442 -1.98137 -1.55142 -0.66976 0.40691 1.36511 1.92583 1.92583 1.36511 0.40691 -0.66976 -1.55142 -1.98137 -1.83442 -1.15336 -0.13648 0.92013 1.70884 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.63394 0.66976 -0.53959 -1.55142 -1.99534 -1.70884 -0.79680 0.40691 1.46167 1.98137 1.77577 0.92013 -0.27233 -1.36511 -1.95817 -1.83442 -1.03917 0.13648 1.26218 1.92583 1.88452 1.15336 0.00000 -1.15336 -1.88452 -1.92583 -1.26218 -0.13648 1.03917 1.83442 1.95817 1.36511 0.27233 -0.92013 -1.77577 -1.98137 -1.46167 -0.40691 0.79680 1.70884 1.99534 1.55142 0.53959 -0.66976 -1.63394 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.55142 0.40691 -0.92013 -1.83442 -1.92583 -1.15336 0.13648 1.36511 1.98137 1.70884 0.66976 -0.66976 -1.70884 -1.98137 -1.36511 -0.13648 1.15336 1.92583 1.83442 0.92013 -0.40691 -1.55142 -2.00000 -1.55142 -0.40691 0.92013 1.83442 1.92583 1.15336 -0.13648 -1.36511 -1.98137 -1.70884 -0.66976 0.66976 1.70884 1.98137 1.36511 0.13648 -1.15336 -1.92583 -1.83442 -0.92013 0.40691 1.55142 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.46167 0.13648 -1.26218 -1.98137 -1.63394 -0.40691 1.03917 1.92583 1.77577 0.66976 -0.79680 -1.83442 -1.88452 -0.92013 0.53959 1.70884 1.95817 1.15336 -0.27233 -1.55142 -1.99534 -1.36511 0.00000 1.36511 1.99534 1.55142 0.27233 -1.15336 -1.95817 -1.70884 -0.53959 0.92013 1.88452 1.83442 0.79680 -0.66976 -1.77577 -1.92583 -1.03917 0.40691 1.63394 1.98137 1.26218 -0.13648 -1.46167 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 1.36511 -0.13648 -1.55142 -1.98137 -1.15336 0.40691 1.70884 1.92583 0.92013 -0.66976 -1.83442 -1.83442 -0.66976 0.92013 1.92583 1.70884 0.40691 -1.15336 -1.98137 -1.55142 -0.13648 1.36511 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.26218 -0.40691 -1.77577 -1.83442 -0.53959 1.15336 1.99534 1.36511 -0.27233 -1.70884 -1.88452 -0.66976 1.03917 1.98137 1.46167 -0.13648 -1.63394 -1.92583 -0.79680 0.92013 1.95817 1.55142 0.00000 -1.55142 -1.95817 -0.92013 0.79680 1.92583 1.63394 0.13648 -1.46167 -1.98137 -1.03917 0.66976 1.88452 1.70884 0.27233 -1.36511 -1.99534 -1.15336 0.53959 1.83442 1.77577 0.40691 -1.26218 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.15336 -0.66976 -1.92583 -1.55142 0.13648 1.70884 1.83442 0.40691 -1.36511 -1.98137 -0.92013 0.92013 1.98137 1.36511 -0.40691 -1.83442 -1.70884 -0.13648 1.55142 1.92583 0.66976 -1.15336 -2.00000 -1.15336 0.66976 1.92583 1.55142 -0.13648 -1.70884 -1.83442 -0.40691 1.36511 1.98137 0.92013 -0.92013 -1.98137 -1.36511 0.40691 1.83442 1.70884 0.13648 -1.55142 -1.92583 -0.66976 1.15336 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 1.03917 -0.92013 -1.99534 -1.15336 0.79680 1.98137 1.26218 -0.66976 -1.95817 -1.36511 0.53959 1.92583 1.46167 -0.40691 -1.88452 -1.55142 0.27233 1.83442 1.63394 -0.13648 -1.77577 -1.70884 0.00000 1.70884 1.77577 0.13648 -1.63394 -1.83442 -0.27233 1.55142 1.88452 0.40691 -1.46167 -1.92583 -0.53959 1.36511 1.95817 0.66976 -1.26218 -1.98137 -0.79680 1.15336 1.99534 0.92013 -1.03917 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.92013 -1.15336 -1.98137 -0.66976 1.36511 1.92583 0.40691 -1.55142 -1.83442 -0.13648 1.70884 1.70884 -0.13648 -1.83442 -1.55142 0.40691 1.92583 1.36511 -0.66976 -1.98137 -1.15336 0.92013 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17 2.00000 0.79680 -1.36511 -1.88452 -0.13648 1.77577 1.55142 -0.53959 -1.98137 -1.03917 1.15336 1.95817 0.40691 -1.63394 -1.70884 0.27233 1.92583 1.26218 -0.92013 -1.99534 -0.66976 1.46167 1.83442 0.00000 -1.83442 -1.46167 0.66976 1.99534 0.92013 -1.26218 -1.92583 -0.27233 1.70884 1.63394 -0.40691 -1.95817 -1.15336 1.03917 1.98137 0.53959 -1.55142 -1.77577 0.13648 1.88452 1.36511 -0.79680 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 0.66976 -1.55142 -1.70884 0.40691 1.98137 0.92013 -1.36511 -1.83442 0.13648 1.92583 1.15336 -1.15336 -1.92583 -0.13648 1.83442 1.36511 -0.92013 -1.98137 -0.40691 1.70884 1.55142 -0.66976 -2.00000 -0.66976 1.55142 1.70884 -0.40691 -1.98137 -0.92013 1.36511 1.83442 -0.13648 -1.92583 -1.15336 1.15336 1.92583 0.13648 -1.83442 -1.36511 0.92013 1.98137 0.40691 -1.70884 -1.55142 0.66976 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 0.53959 -1.70884 -1.46167 0.92013 1.95817 0.13648 -1.88452 -1.15336 1.26218 1.83442 -0.27233 -1.98137 -0.79680 1.55142 1.63394 -0.66976 -1.99534 -0.40691 1.77577 1.36511 -1.03917 -1.92583 0.00000 1.92583 1.03917 -1.36511 -1.77577 0.40691 1.99534 0.66976 -1.63394 -1.55142 0.79680 1.98137 0.27233 -1.83442 -1.26218 1.15336 1.88452 -0.13648 -1.95817 -0.92013 1.46167 1.70884 -0.53959 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.40691 -1.83442 -1.15336 1.36511 1.70884 -0.66976 -1.98137 -0.13648 1.92583 0.92013 -1.55142 -1.55142 0.92013 1.92583 -0.13648 -1.98137 -0.66976 1.70884 1.36511 -1.15336 -1.83442 0.40691 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21 2.00000 0.27233 -1.92583 -0.79680 1.70884 1.26218 -1.36511 -1.63394 0.92013 1.88452 -0.40691 -1.99534 -0.13648 1.95817 0.66976 -1.77577 -1.15336 1.46167 1.55142 -1.03917 -1.83442 0.53959 1.98137 0.00000 -1.98137 -0.53959 1.83442 1.03917 -1.55142 -1.46167 1.15336 1.77577 -0.66976 -1.95817 0.13648 1.99534 0.40691 -1.88452 -0.92013 1.63394 1.36511 -1.26218 -1.70884 0.79680 1.92583 -0.27233 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22 2.00000 0.13648 -1.98137 -0.40691 1.92583 0.66976 -1.83442 -0.92013 1.70884 1.15336 -1.55142 -1.36511 1.36511 1.55142 -1.15336 -1.70884 0.92013 1.83442 -0.66976 -1.92583 0.40691 1.98137 -0.13648 -2.00000 -0.13648 1.98137 0.40691 -1.92583 -0.66976 1.83442 0.92013 -1.70884 -1.15336 1.55142 1.36511 -1.36511 -1.55142 1.15336 1.70884 -0.92013 -1.83442 0.66976 1.92583 -0.40691 -1.98137 0.13648 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 -0.13648 -1.98137 0.40691 1.92583 -0.66976 -1.83442 0.92013 1.70884 -1.15336 -1.55142 1.36511 1.36511 -1.55142 -1.15336 1.70884 0.92013 -1.83442 -0.66976 1.92583 0.40691 -1.98137 -0.13648 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E25 2.00000 -0.27233 -1.92583 0.79680 1.70884 -1.26218 -1.36511 1.63394 0.92013 -1.88452 -0.40691 1.99534 -0.13648 -1.95817 0.66976 1.77577 -1.15336 -1.46167 1.55142 1.03917 -1.83442 -0.53959 1.98137 0.00000 -1.98137 0.53959 1.83442 -1.03917 -1.55142 1.46167 1.15336 -1.77577 -0.66976 1.95817 0.13648 -1.99534 0.40691 1.88452 -0.92013 -1.63394 1.36511 1.26218 -1.70884 -0.79680 1.92583 0.27233 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26 2.00000 -0.40691 -1.83442 1.15336 1.36511 -1.70884 -0.66976 1.98137 -0.13648 -1.92583 0.92013 1.55142 -1.55142 -0.92013 1.92583 0.13648 -1.98137 0.66976 1.70884 -1.36511 -1.15336 1.83442 0.40691 -2.00000 0.40691 1.83442 -1.15336 -1.36511 1.70884 0.66976 -1.98137 0.13648 1.92583 -0.92013 -1.55142 1.55142 0.92013 -1.92583 -0.13648 1.98137 -0.66976 -1.70884 1.36511 1.15336 -1.83442 -0.40691 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27 2.00000 -0.53959 -1.70884 1.46167 0.92013 -1.95817 0.13648 1.88452 -1.15336 -1.26218 1.83442 0.27233 -1.98137 0.79680 1.55142 -1.63394 -0.66976 1.99534 -0.40691 -1.77577 1.36511 1.03917 -1.92583 0.00000 1.92583 -1.03917 -1.36511 1.77577 0.40691 -1.99534 0.66976 1.63394 -1.55142 -0.79680 1.98137 -0.27233 -1.83442 1.26218 1.15336 -1.88452 -0.13648 1.95817 -0.92013 -1.46167 1.70884 0.53959 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 -0.66976 -1.55142 1.70884 0.40691 -1.98137 0.92013 1.36511 -1.83442 -0.13648 1.92583 -1.15336 -1.15336 1.92583 -0.13648 -1.83442 1.36511 0.92013 -1.98137 0.40691 1.70884 -1.55142 -0.66976 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29 2.00000 -0.79680 -1.36511 1.88452 -0.13648 -1.77577 1.55142 0.53959 -1.98137 1.03917 1.15336 -1.95817 0.40691 1.63394 -1.70884 -0.27233 1.92583 -1.26218 -0.92013 1.99534 -0.66976 -1.46167 1.83442 0.00000 -1.83442 1.46167 0.66976 -1.99534 0.92013 1.26218 -1.92583 0.27233 1.70884 -1.63394 -0.40691 1.95817 -1.15336 -1.03917 1.98137 -0.53959 -1.55142 1.77577 0.13648 -1.88452 1.36511 0.79680 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30 2.00000 -0.92013 -1.15336 1.98137 -0.66976 -1.36511 1.92583 -0.40691 -1.55142 1.83442 -0.13648 -1.70884 1.70884 0.13648 -1.83442 1.55142 0.40691 -1.92583 1.36511 0.66976 -1.98137 1.15336 0.92013 -2.00000 0.92013 1.15336 -1.98137 0.66976 1.36511 -1.92583 0.40691 1.55142 -1.83442 0.13648 1.70884 -1.70884 -0.13648 1.83442 -1.55142 -0.40691 1.92583 -1.36511 -0.66976 1.98137 -1.15336 -0.92013 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E31 2.00000 -1.03917 -0.92013 1.99534 -1.15336 -0.79680 1.98137 -1.26218 -0.66976 1.95817 -1.36511 -0.53959 1.92583 -1.46167 -0.40691 1.88452 -1.55142 -0.27233 1.83442 -1.63394 -0.13648 1.77577 -1.70884 0.00000 1.70884 -1.77577 0.13648 1.63394 -1.83442 0.27233 1.55142 -1.88452 0.40691 1.46167 -1.92583 0.53959 1.36511 -1.95817 0.66976 1.26218 -1.98137 0.79680 1.15336 -1.99534 0.92013 1.03917 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 2.00000 -1.15336 -0.66976 1.92583 -1.55142 -0.13648 1.70884 -1.83442 0.40691 1.36511 -1.98137 0.92013 0.92013 -1.98137 1.36511 0.40691 -1.83442 1.70884 -0.13648 -1.55142 1.92583 -0.66976 -1.15336 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E33 2.00000 -1.26218 -0.40691 1.77577 -1.83442 0.53959 1.15336 -1.99534 1.36511 0.27233 -1.70884 1.88452 -0.66976 -1.03917 1.98137 -1.46167 -0.13648 1.63394 -1.92583 0.79680 0.92013 -1.95817 1.55142 0.00000 -1.55142 1.95817 -0.92013 -0.79680 1.92583 -1.63394 0.13648 1.46167 -1.98137 1.03917 0.66976 -1.88452 1.70884 -0.27233 -1.36511 1.99534 -1.15336 -0.53959 1.83442 -1.77577 0.40691 1.26218 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E34 2.00000 -1.36511 -0.13648 1.55142 -1.98137 1.15336 0.40691 -1.70884 1.92583 -0.92013 -0.66976 1.83442 -1.83442 0.66976 0.92013 -1.92583 1.70884 -0.40691 -1.15336 1.98137 -1.55142 0.13648 1.36511 -2.00000 1.36511 0.13648 -1.55142 1.98137 -1.15336 -0.40691 1.70884 -1.92583 0.92013 0.66976 -1.83442 1.83442 -0.66976 -0.92013 1.92583 -1.70884 0.40691 1.15336 -1.98137 1.55142 -0.13648 -1.36511 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E35 2.00000 -1.46167 0.13648 1.26218 -1.98137 1.63394 -0.40691 -1.03917 1.92583 -1.77577 0.66976 0.79680 -1.83442 1.88452 -0.92013 -0.53959 1.70884 -1.95817 1.15336 0.27233 -1.55142 1.99534 -1.36511 0.00000 1.36511 -1.99534 1.55142 -0.27233 -1.15336 1.95817 -1.70884 0.53959 0.92013 -1.88452 1.83442 -0.79680 -0.66976 1.77577 -1.92583 1.03917 0.40691 -1.63394 1.98137 -1.26218 -0.13648 1.46167 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E36 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 2.00000 -1.55142 0.40691 0.92013 -1.83442 1.92583 -1.15336 -0.13648 1.36511 -1.98137 1.70884 -0.66976 -0.66976 1.70884 -1.98137 1.36511 -0.13648 -1.15336 1.92583 -1.83442 0.92013 0.40691 -1.55142 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E37 2.00000 -1.63394 0.66976 0.53959 -1.55142 1.99534 -1.70884 0.79680 0.40691 -1.46167 1.98137 -1.77577 0.92013 0.27233 -1.36511 1.95817 -1.83442 1.03917 0.13648 -1.26218 1.92583 -1.88452 1.15336 0.00000 -1.15336 1.88452 -1.92583 1.26218 -0.13648 -1.03917 1.83442 -1.95817 1.36511 -0.27233 -0.92013 1.77577 -1.98137 1.46167 -0.40691 -0.79680 1.70884 -1.99534 1.55142 -0.53959 -0.66976 1.63394 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E38 2.00000 -1.70884 0.92013 0.13648 -1.15336 1.83442 -1.98137 1.55142 -0.66976 -0.40691 1.36511 -1.92583 1.92583 -1.36511 0.40691 0.66976 -1.55142 1.98137 -1.83442 1.15336 -0.13648 -0.92013 1.70884 -2.00000 1.70884 -0.92013 -0.13648 1.15336 -1.83442 1.98137 -1.55142 0.66976 0.40691 -1.36511 1.92583 -1.92583 1.36511 -0.40691 -0.66976 1.55142 -1.98137 1.83442 -1.15336 0.13648 0.92013 -1.70884 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E39 2.00000 -1.77577 1.15336 -0.27233 -0.66976 1.46167 -1.92583 1.95817 -1.55142 0.79680 0.13648 -1.03917 1.70884 -1.99534 1.83442 -1.26218 0.40691 0.53959 -1.36511 1.88452 -1.98137 1.63394 -0.92013 0.00000 0.92013 -1.63394 1.98137 -1.88452 1.36511 -0.53959 -0.40691 1.26218 -1.83442 1.99534 -1.70884 1.03917 -0.13648 -0.79680 1.55142 -1.95817 1.92583 -1.46167 0.66976 0.27233 -1.15336 1.77577 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E40 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 2.00000 -1.83442 1.36511 -0.66976 -0.13648 0.92013 -1.55142 1.92583 -1.98137 1.70884 -1.15336 0.40691 0.40691 -1.15336 1.70884 -1.98137 1.92583 -1.55142 0.92013 -0.13648 -0.66976 1.36511 -1.83442 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E41 2.00000 -1.88452 1.55142 -1.03917 0.40691 0.27233 -0.92013 1.46167 -1.83442 1.99534 -1.92583 1.63394 -1.15336 0.53959 0.13648 -0.79680 1.36511 -1.77577 1.98137 -1.95817 1.70884 -1.26218 0.66976 0.00000 -0.66976 1.26218 -1.70884 1.95817 -1.98137 1.77577 -1.36511 0.79680 -0.13648 -0.53959 1.15336 -1.63394 1.92583 -1.99534 1.83442 -1.46167 0.92013 -0.27233 -0.40691 1.03917 -1.55142 1.88452 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E42 2.00000 -1.92583 1.70884 -1.36511 0.92013 -0.40691 -0.13648 0.66976 -1.15336 1.55142 -1.83442 1.98137 -1.98137 1.83442 -1.55142 1.15336 -0.66976 0.13648 0.40691 -0.92013 1.36511 -1.70884 1.92583 -2.00000 1.92583 -1.70884 1.36511 -0.92013 0.40691 0.13648 -0.66976 1.15336 -1.55142 1.83442 -1.98137 1.98137 -1.83442 1.55142 -1.15336 0.66976 -0.13648 -0.40691 0.92013 -1.36511 1.70884 -1.92583 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E43 2.00000 -1.95817 1.83442 -1.63394 1.36511 -1.03917 0.66976 -0.27233 -0.13648 0.53959 -0.92013 1.26218 -1.55142 1.77577 -1.92583 1.99534 -1.98137 1.88452 -1.70884 1.46167 -1.15336 0.79680 -0.40691 0.00000 0.40691 -0.79680 1.15336 -1.46167 1.70884 -1.88452 1.98137 -1.99534 1.92583 -1.77577 1.55142 -1.26218 0.92013 -0.53959 0.13648 0.27233 -0.66976 1.03917 -1.36511 1.63394 -1.83442 1.95817 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E44 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 -1.98137 1.92583 -1.83442 1.70884 -1.55142 1.36511 -1.15336 0.92013 -0.66976 0.40691 -0.13648 -0.13648 0.40691 -0.66976 0.92013 -1.15336 1.36511 -1.55142 1.70884 -1.83442 1.92583 -1.98137 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E45 2.00000 -1.99534 1.98137 -1.95817 1.92583 -1.88452 1.83442 -1.77577 1.70884 -1.63394 1.55142 -1.46167 1.36511 -1.26218 1.15336 -1.03917 0.92013 -0.79680 0.66976 -0.53959 0.40691 -0.27233 0.13648 0.00000 -0.13648 0.27233 -0.40691 0.53959 -0.66976 0.79680 -0.92013 1.03917 -1.15336 1.26218 -1.36511 1.46167 -1.55142 1.63394 -1.70884 1.77577 -1.83442 1.88452 -1.92583 1.95817 -1.98137 1.99534 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995337538381 = 2*cos(2*π/92) = 2*cos(π/46) 1.981371892073 = 2*cos(4*π/92) = 2*cos(π/23) 1.958168175365 = 2*cos(6*π/92) = 2*cos(3*π/46) 1.925834574696 = 2*cos(8*π/92) = 2*cos(2*π/23) 1.884521844238 = 2*cos(10*π/92) = 2*cos(5*π/46) 1.834422603011 = 2*cos(12*π/92) = 2*cos(3*π/23) 1.775770436805 = 2*cos(14*π/92) = 2*cos(7*π/46) 1.708838809093 = 2*cos(16*π/92) = 2*cos(4*π/23) 1.633939786021 = 2*cos(18*π/92) = 2*cos(9*π/46) 1.551422581409 = 2*cos(20*π/92) = 2*cos(5*π/23) 1.461671928556 = 2*cos(22*π/92) = 2*cos(11*π/46) 1.365106286437 = 2*cos(24*π/92) = 2*cos(6*π/23) 1.262175888652 = 2*cos(26*π/92) = 2*cos(13*π/46) 1.153360644230 = 2*cos(28*π/92) = 2*cos(7*π/23) 1.039167900071 = 2*cos(30*π/92) = 2*cos(15*π/46) 0.920130075462 = 2*cos(32*π/92) = 2*cos(8*π/23) 0.796802179692 = 2*cos(34*π/92) = 2*cos(17*π/46) 0.669759224342 = 2*cos(36*π/92) = 2*cos(9*π/23) 0.539593542314 = 2*cos(38*π/92) = 2*cos(19*π/46) 0.406912026105 = 2*cos(40*π/92) = 2*cos(10*π/23) 0.272333298192 = 2*cos(42*π/92) = 2*cos(21*π/46) 0.136484826729 = 2*cos(44*π/92) = 2*cos(11*π/23) Symmetry of Rotations and Cartesian products A1 p+d+f+g+h+i z, z², z³, z⁴, z⁵, z⁶ A2 R R_z E1 R+p+d+f+g+h+i {x, y}, {R_x, R_y}, {xz, yz}, {xz², yz²}, {xz³, yz³}, {xz⁴, yz⁴}, {xz⁵, yz⁵} E2 d+f+g+h+i {x²–y², xy}, {z(x²–y²), xyz}, {z²(x²–y²), xyz²}, {z³(x²–y²), xyz³}, {z⁴(x²–y²), xyz⁴} E3 f+g+h+i {x(x²–3y²), y(3x²–y²)}, {xz(x²–3y²), yz(3x²–y²)}, {xz²(x²–3y²), yz²(3x²–y²)}, {xz³(x²–3y²), yz³(3x²–y²)} E4 g+h+i {(x²–y²)²–2x²y², xy(x²–y²)}, {z((x²–y²)²–4x²y²), xyz(x²–y²)}, {z²((x²–y²)²–4x²y²), xyz²(x²–y²)} E5 h+i {x(x²–(5+2√5)y²)(x²–(5–2√5)y²), y(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)}, {xz(x²–(5+2√5)y²)(x²–(5–2√5)y²), yz(y²–(5+2√5)x²)(y²–(5–2√5)x²)(y²–(5–2√5)x²)} E6 i {x²(x²–3y²)²–y²(3x²–y²)², xy(x²–3y²)(3x²–y²)} Notes: α The order of the C_92v point group is 184, and the order of the principal axis is 92. β There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σ_v contains both the xz and the yz planes. γ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. δ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less). For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the C_92v point group was created by Gernot Katzer.

For other groups and some explanations, see the Main Page.

	C_91v
C₉₂	C_92v	C_92h D₉₂ D_92h D_92d S₉₂
	C_93v

Character table for the C92v point group

Character table for the C_92v point group