Character Table for Point Group C46h

Character table for the C_46h point group

C46h E 2 C46 2 C23 2 C46^3 2 C23^2 2 C46^5 2 C23^3 2 C46^7 2 C23^4 2 C46^9 2 C23^5 2 C46^11 2 C23^6 2 C46^13 2 C23^7 2 C46^15 2 C23^8 2 C46^17 2 C23^9 2 C46^19 2 C23^10 2 C46^21 2 C23^11 C2 i 2 S46 2 S23 2 S46^3 2 S23^2 2 S46^5 2 S23^3 2 S46^7 2 S23^4 2 S46^9 2 S23^5 2 S46^11 2 S23^6 2 S46^13 2 S23^7 2 S46^15 2 S23^8 2 S46^17 2 S23^9 2 S46^19 2 S23^10 2 S46^21 2 S23^11 sh <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> Ag 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 Bg 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. E1g * 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 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 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2g * 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 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 ... ... TT... ....... ....TT... ........... ........TT... E3g * 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 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 ... ... ..... ....... ..TT..... ........... ......TT..... E4g * 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 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 ... ... ..... ....... TT....... ........... ....TT....... E5g * 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 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 ... ... ..... ....... ......... ........... ..TT......... E6g * 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 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 ... ... ..... ....... ......... ........... TT........... E7g * 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 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 ... ... ..... ....... ......... ........... ............. E8g * 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 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 ... ... ..... ....... ......... ........... ............. E9g * 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 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 ... ... ..... ....... ......... ........... ............. E10g * 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 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 ... ... ..... ....... ......... ........... ............. E11g * 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 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 ... ... ..... ....... ......... ........... ............. E12g * 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 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 ... ... ..... ....... ......... ........... ............. E13g * 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 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 ... ... ..... ....... ......... ........... ............. E14g * 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 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 ... ... ..... ....... ......... ........... ............. E15g * 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 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 ... ... ..... ....... ......... ........... ............. E16g * 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 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 ... ... ..... ....... ......... ........... ............. E17g * 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 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 ... ... ..... ....... ......... ........... ............. E18g * 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 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 ... ... ..... ....... ......... ........... ............. E19g * 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 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 ... ... ..... ....... ......... ........... ............. E20g * 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 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 ... ... ..... ....... ......... ........... ............. E21g * 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 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 ... ... ..... ....... ......... ........... ............. E22g * 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 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 ... ... ..... ....... ......... ........... ............. Au 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 ............. Bu 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 -1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 ... ... ..... ....... ......... ........... ............. E1u * 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 -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 ... TT. ..... ....TT. ......... ........TT. ............. E2u * 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 -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 ... ... ..... ..TT... ......... ......TT... ............. E3u * 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 -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 ... ... ..... TT..... ......... ....TT..... ............. E4u * 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 -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 ... ... ..... ....... ......... ..TT....... ............. E5u * 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 -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 ... ... ..... ....... ......... TT......... ............. E6u * 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 -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 ... ... ..... ....... ......... ........... ............. E7u * 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 -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 ... ... ..... ....... ......... ........... ............. E8u * 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 -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 ... ... ..... ....... ......... ........... ............. E9u * 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 -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 ... ... ..... ....... ......... ........... ............. E10u * 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 -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 ... ... ..... ....... ......... ........... ............. E11u * 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 -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 ... ... ..... ....... ......... ........... ............. E12u * 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 -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 ... ... ..... ....... ......... ........... ............. E13u * 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 -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 ... ... ..... ....... ......... ........... ............. E14u * 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 -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 ... ... ..... ....... ......... ........... ............. E15u * 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 -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 ... ... ..... ....... ......... ........... ............. E16u * 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 -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 ... ... ..... ....... ......... ........... ............. E17u * 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 -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 ... ... ..... ....... ......... ........... ............. E18u * 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 -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 ... ... ..... ....... ......... ........... ............. E19u * 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 -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 ... ... ..... ....... ......... ........... ............. E20u * 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 -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 ... ... ..... ....... ......... ........... ............. E21u * 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 -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 ... ... ..... ....... ......... ........... ............. E22u * 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 -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 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.981371892073 = 2*cos(2*π/46) = 2*cos(π/23) 1.925834574696 = 2*cos(4*π/46) = 2*cos(2*π/23) 1.834422603011 = 2*cos(6*π/46) = 2*cos(3*π/23) 1.708838809093 = 2*cos(8*π/46) = 2*cos(4*π/23) 1.551422581409 = 2*cos(10*π/46) = 2*cos(5*π/23) 1.365106286437 = 2*cos(12*π/46) = 2*cos(6*π/23) 1.153360644230 = 2*cos(14*π/46) = 2*cos(7*π/23) 0.920130075462 = 2*cos(16*π/46) = 2*cos(8*π/23) 0.669759224342 = 2*cos(18*π/46) = 2*cos(9*π/23) 0.406912026105 = 2*cos(20*π/46) = 2*cos(10*π/23) 0.136484826729 = 2*cos(22*π/46) = 2*cos(11*π/23) Symmetry of Rotations and Cartesian products Ag R+d+g+i+k+m R_z, z², z⁴, z⁶ E1g R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2g d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3g g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4g g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5g 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)} E6g i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7g k+m E8g k+m E9g m E10g m Au p+f+h+j+l z, z³, z⁵ E1u p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2u f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3u f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4u h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5u 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)} E6u j+l E7u j+l E8u l E9u l Notes: α The order of the C_46h point group is 92, and the order of the principal axis (C₄₆) is 46. The group has 48 irreducible representations. β The C_46h point group is generated by two symmetry elements, which are canonically chosen as C₄₆ and i. Other possible choices are C₄₆ and σ_h, or less commonly S₄₆ with either C₂ or σ_h. γ The lowest nonvanishing multipole moment in C_46h is 4 (quadrupole moment). δ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_46h group is Abelian because all its symmetry operations are coaxial. This is a sufficient condition. In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. ε Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 88 cases have been combined into 44 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 44 pairs of left and right rotations have been combined into one two-membered pseudo-class each. ζ The 44 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. η 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 C_46h point group was created by Gernot Katzer.

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

	C_44h
	C_45h
C₄₆ C_46v	C_46h	D₄₆ D_46h D_46d S₄₆
	C_47h
	C_48h

Character table for the C46h point group

Character table for the C_46h point group