Character Table for Point Group D46d

Character table for the D_46d point group

D46d E 2 S92 2 C46 2 S92^3 2 C23 2 S92^5 2 C46^3 2 S92^7 2 C23^2 2 S92^9 2 C46^5 2 S92^11 2 C23^3 2 S92^13 2 C46^7 2 S92^15 2 C23^4 2 S92^17 2 C46^9 2 S92^19 2 C23^5 2 S92^21 2 C46^11 2 S4 2 C23^6 2 S92^25 2 C46^13 2 S92^27 2 C23^7 2 S92^29 2 C46^15 2 S92^31 2 C23^8 2 S92^33 2 C46^17 2 S92^35 2 C23^9 2 S92^37 2 C46^19 2 S92^39 2 C23^10 2 S92^41 2 C46^21 2 S92^43 2 C23^11 2 S92^45 C2 46 C2' 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 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 ... ..T ..... ......T ......... ..........T ............. 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. ............. 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... 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..... ............. 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....... 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......... ............. 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 ... ... ..... ....... ......... ........... ..TT......... 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 ... ... ..... ....... ......... ..TT....... ............. 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 ... ... ..... ....... ..TT..... ........... ......TT..... 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 ... ... ..... ..TT... ......... ......TT... ............. 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 TT. ... ..TT. ....... ......TT. ........... ..........TT. 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 d+g+i+k+m z², z⁴, z⁶ A2 R R_z B2 p+f+h+j+l z, z³, z⁵ E1 p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2 d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3 f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4 g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5 h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6 i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+l E8 k+m E9 l E10 m E37 m E38 l E39 k+m E40 j+l E41 i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E42 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E43 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E44 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E45 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_46d point group is 184, and the order of the principal axis (S₉₂) is 92. The group has 49 irreducible representations. β The D_46d point group is isomorphic to C_92v and D₉₂. γ The D_46d point group is generated by two symmetry elements, S₉₂ and either a perpendicular C₂^′ or a vertical σ_d. Also, the group may be generated from a C₂^′ plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The group contains one set of twofold symmetry axes (C₂^′) perpendicular to the principal (z) axis. Both x and y axes are members of that set. ε The single σ_d set of symmetry planes contains neither the xz nor the yz planes; but it contains the median plane (x+y)z. ζ The lowest nonvanishing multipole moment in D_46d is 4 (quadrupole moment). η This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. θ 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 much less than half the order of the principal axis. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the D_46d point group was created by Gernot Katzer.

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

	D_44d
	D_45d
C₄₆ C_46v C_46h D₄₆ D_46h	D_46d	S₄₆
	D_47d
	D_48d

Character table for the D46d point group

Character table for the D_46d point group