Character Table for Point Group D110d

Character table for the D_110d point group

D110d E 2 S220 2 C110 2 S220^3 2 C55 2 S44 2 C110^3 2 S220^7 2 C55^2 2 S220^9 2 C22 2 S20 2 C55^3 2 S220^13 2 C110^7 2 S44^3 2 C55^4 2 S220^17 2 C110^9 2 S220^19 2 C11 2 S220^21 2 C10 2 S220^23 2 C55^6 2 S44^5 2 C110^13 2 S220^27 2 C55^7 2 S220^29 2 C22^3 2 S220^31 2 C55^8 2 S20^3 2 C110^17 2 S44^7 2 C55^9 2 S220^37 2 C110^19 2 S220^39 2 C11^2 2 S220^41 2 C110^21 2 S220^43 2 C5 2 S44^9 2 C110^23 2 S220^47 2 C55^12 2 S220^49 2 C22^5 2 S220^51 2 C55^13 2 S220^53 2 C110^27 2 S4 2 C55^14 2 S220^57 2 C110^29 2 S220^59 2 C11^3 2 S220^61 2 C110^31 2 S220^63 2 C55^16 2 S44^13 2 C10^3 2 S220^67 2 C55^17 2 S220^69 2 C22^7 2 S220^71 2 C55^18 2 S220^73 2 C110^37 2 S44^15 2 C55^19 2 S20^7 2 C110^39 2 S220^79 2 C11^4 2 S220^81 2 C110^41 2 S220^83 2 C55^21 2 S44^17 2 C110^43 2 S220^87 2 C5^2 2 S220^89 2 C22^9 2 S220^91 2 C55^23 2 S220^93 2 C110^47 2 S44^19 2 C55^24 2 S220^97 2 C110^49 2 S20^9 2 C11^5 2 S220^101 2 C110^51 2 S220^103 2 C55^26 2 S44^21 2 C110^53 2 S220^107 2 C55^27 2 S220^109 C2 110 C2' 110 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 1.99918 1.99674 1.99266 1.98696 1.97964 1.97071 1.96017 1.94802 1.93429 1.91899 1.90211 1.88369 1.86373 1.84225 1.81926 1.79480 1.76887 1.74149 1.71270 1.68251 1.65094 1.61803 1.58380 1.54828 1.51150 1.47348 1.43426 1.39388 1.35235 1.30972 1.26602 1.22130 1.17557 1.12889 1.08128 1.03279 0.98347 0.93333 0.88244 0.83083 0.77854 0.72562 0.67210 0.61803 0.56347 0.50844 0.45299 0.39718 0.34104 0.28463 0.22798 0.17115 0.11418 0.05711 0.00000 -0.05711 -0.11418 -0.17115 -0.22798 -0.28463 -0.34104 -0.39718 -0.45299 -0.50844 -0.56347 -0.61803 -0.67210 -0.72562 -0.77854 -0.83083 -0.88244 -0.93333 -0.98347 -1.03279 -1.08128 -1.12889 -1.17557 -1.22130 -1.26602 -1.30972 -1.35235 -1.39388 -1.43426 -1.47348 -1.51150 -1.54828 -1.58380 -1.61803 -1.65094 -1.68251 -1.71270 -1.74149 -1.76887 -1.79480 -1.81926 -1.84225 -1.86373 -1.88369 -1.90211 -1.91899 -1.93429 -1.94802 -1.96017 -1.97071 -1.97964 -1.98696 -1.99266 -1.99674 -1.99918 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99674 1.98696 1.97071 1.94802 1.91899 1.88369 1.84225 1.79480 1.74149 1.68251 1.61803 1.54828 1.47348 1.39388 1.30972 1.22130 1.12889 1.03279 0.93333 0.83083 0.72562 0.61803 0.50844 0.39718 0.28463 0.17115 0.05711 -0.05711 -0.17115 -0.28463 -0.39718 -0.50844 -0.61803 -0.72562 -0.83083 -0.93333 -1.03279 -1.12889 -1.22130 -1.30972 -1.39388 -1.47348 -1.54828 -1.61803 -1.68251 -1.74149 -1.79480 -1.84225 -1.88369 -1.91899 -1.94802 -1.97071 -1.98696 -1.99674 -2.00000 -1.99674 -1.98696 -1.97071 -1.94802 -1.91899 -1.88369 -1.84225 -1.79480 -1.74149 -1.68251 -1.61803 -1.54828 -1.47348 -1.39388 -1.30972 -1.22130 -1.12889 -1.03279 -0.93333 -0.83083 -0.72562 -0.61803 -0.50844 -0.39718 -0.28463 -0.17115 -0.05711 0.05711 0.17115 0.28463 0.39718 0.50844 0.61803 0.72562 0.83083 0.93333 1.03279 1.12889 1.22130 1.30972 1.39388 1.47348 1.54828 1.61803 1.68251 1.74149 1.79480 1.84225 1.88369 1.91899 1.94802 1.97071 1.98696 1.99674 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99266 1.97071 1.93429 1.88369 1.81926 1.74149 1.65094 1.54828 1.43426 1.30972 1.17557 1.03279 0.88244 0.72562 0.56347 0.39718 0.22798 0.05711 -0.11418 -0.28463 -0.45299 -0.61803 -0.77854 -0.93333 -1.08128 -1.22130 -1.35235 -1.47348 -1.58380 -1.68251 -1.76887 -1.84225 -1.90211 -1.94802 -1.97964 -1.99674 -1.99918 -1.98696 -1.96017 -1.91899 -1.86373 -1.79480 -1.71270 -1.61803 -1.51150 -1.39388 -1.26602 -1.12889 -0.98347 -0.83083 -0.67210 -0.50844 -0.34104 -0.17115 0.00000 0.17115 0.34104 0.50844 0.67210 0.83083 0.98347 1.12889 1.26602 1.39388 1.51150 1.61803 1.71270 1.79480 1.86373 1.91899 1.96017 1.98696 1.99918 1.99674 1.97964 1.94802 1.90211 1.84225 1.76887 1.68251 1.58380 1.47348 1.35235 1.22130 1.08128 0.93333 0.77854 0.61803 0.45299 0.28463 0.11418 -0.05711 -0.22798 -0.39718 -0.56347 -0.72562 -0.88244 -1.03279 -1.17557 -1.30972 -1.43426 -1.54828 -1.65094 -1.74149 -1.81926 -1.88369 -1.93429 -1.97071 -1.99266 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 2.00000 1.98696 1.94802 1.88369 1.79480 1.68251 1.54828 1.39388 1.22130 1.03279 0.83083 0.61803 0.39718 0.17115 -0.05711 -0.28463 -0.50844 -0.72562 -0.93333 -1.12889 -1.30972 -1.47348 -1.61803 -1.74149 -1.84225 -1.91899 -1.97071 -1.99674 -1.99674 -1.97071 -1.91899 -1.84225 -1.74149 -1.61803 -1.47348 -1.30972 -1.12889 -0.93333 -0.72562 -0.50844 -0.28463 -0.05711 0.17115 0.39718 0.61803 0.83083 1.03279 1.22130 1.39388 1.54828 1.68251 1.79480 1.88369 1.94802 1.98696 2.00000 1.98696 1.94802 1.88369 1.79480 1.68251 1.54828 1.39388 1.22130 1.03279 0.83083 0.61803 0.39718 0.17115 -0.05711 -0.28463 -0.50844 -0.72562 -0.93333 -1.12889 -1.30972 -1.47348 -1.61803 -1.74149 -1.84225 -1.91899 -1.97071 -1.99674 -1.99674 -1.97071 -1.91899 -1.84225 -1.74149 -1.61803 -1.47348 -1.30972 -1.12889 -0.93333 -0.72562 -0.50844 -0.28463 -0.05711 0.17115 0.39718 0.61803 0.83083 1.03279 1.22130 1.39388 1.54828 1.68251 1.79480 1.88369 1.94802 1.98696 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 -2.00000 -1.97964 -1.91899 -1.81926 -1.68251 -1.51150 -1.30972 -1.08128 -0.83083 -0.56347 -0.28463 0.00000 0.28463 0.56347 0.83083 1.08128 1.30972 1.51150 1.68251 1.81926 1.91899 1.97964 2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 -2.00000 -1.97964 -1.91899 -1.81926 -1.68251 -1.51150 -1.30972 -1.08128 -0.83083 -0.56347 -0.28463 0.00000 0.28463 0.56347 0.83083 1.08128 1.30972 1.51150 1.68251 1.81926 1.91899 1.97964 2.00000 1.97964 1.91899 1.81926 1.68251 1.51150 1.30972 1.08128 0.83083 0.56347 0.28463 0.00000 -0.28463 -0.56347 -0.83083 -1.08128 -1.30972 -1.51150 -1.68251 -1.81926 -1.91899 -1.97964 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.97071 1.88369 1.74149 1.54828 1.30972 1.03279 0.72562 0.39718 0.05711 -0.28463 -0.61803 -0.93333 -1.22130 -1.47348 -1.68251 -1.84225 -1.94802 -1.99674 -1.98696 -1.91899 -1.79480 -1.61803 -1.39388 -1.12889 -0.83083 -0.50844 -0.17115 0.17115 0.50844 0.83083 1.12889 1.39388 1.61803 1.79480 1.91899 1.98696 1.99674 1.94802 1.84225 1.68251 1.47348 1.22130 0.93333 0.61803 0.28463 -0.05711 -0.39718 -0.72562 -1.03279 -1.30972 -1.54828 -1.74149 -1.88369 -1.97071 -2.00000 -1.97071 -1.88369 -1.74149 -1.54828 -1.30972 -1.03279 -0.72562 -0.39718 -0.05711 0.28463 0.61803 0.93333 1.22130 1.47348 1.68251 1.84225 1.94802 1.99674 1.98696 1.91899 1.79480 1.61803 1.39388 1.12889 0.83083 0.50844 0.17115 -0.17115 -0.50844 -0.83083 -1.12889 -1.39388 -1.61803 -1.79480 -1.91899 -1.98696 -1.99674 -1.94802 -1.84225 -1.68251 -1.47348 -1.22130 -0.93333 -0.61803 -0.28463 0.05711 0.39718 0.72562 1.03279 1.30972 1.54828 1.74149 1.88369 1.97071 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.96017 1.84225 1.65094 1.39388 1.08128 0.72562 0.34104 -0.05711 -0.45299 -0.83083 -1.17557 -1.47348 -1.71270 -1.88369 -1.97964 -1.99674 -1.93429 -1.79480 -1.58380 -1.30972 -0.98347 -0.61803 -0.22798 0.17115 0.56347 0.93333 1.26602 1.54828 1.76887 1.91899 1.99266 1.98696 1.90211 1.74149 1.51150 1.22130 0.88244 0.50844 0.11418 -0.28463 -0.67210 -1.03279 -1.35235 -1.61803 -1.81926 -1.94802 -1.99918 -1.97071 -1.86373 -1.68251 -1.43426 -1.12889 -0.77854 -0.39718 0.00000 0.39718 0.77854 1.12889 1.43426 1.68251 1.86373 1.97071 1.99918 1.94802 1.81926 1.61803 1.35235 1.03279 0.67210 0.28463 -0.11418 -0.50844 -0.88244 -1.22130 -1.51150 -1.74149 -1.90211 -1.98696 -1.99266 -1.91899 -1.76887 -1.54828 -1.26602 -0.93333 -0.56347 -0.17115 0.22798 0.61803 0.98347 1.30972 1.58380 1.79480 1.93429 1.99674 1.97964 1.88369 1.71270 1.47348 1.17557 0.83083 0.45299 0.05711 -0.34104 -0.72562 -1.08128 -1.39388 -1.65094 -1.84225 -1.96017 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.94802 1.79480 1.54828 1.22130 0.83083 0.39718 -0.05711 -0.50844 -0.93333 -1.30972 -1.61803 -1.84225 -1.97071 -1.99674 -1.91899 -1.74149 -1.47348 -1.12889 -0.72562 -0.28463 0.17115 0.61803 1.03279 1.39388 1.68251 1.88369 1.98696 1.98696 1.88369 1.68251 1.39388 1.03279 0.61803 0.17115 -0.28463 -0.72562 -1.12889 -1.47348 -1.74149 -1.91899 -1.99674 -1.97071 -1.84225 -1.61803 -1.30972 -0.93333 -0.50844 -0.05711 0.39718 0.83083 1.22130 1.54828 1.79480 1.94802 2.00000 1.94802 1.79480 1.54828 1.22130 0.83083 0.39718 -0.05711 -0.50844 -0.93333 -1.30972 -1.61803 -1.84225 -1.97071 -1.99674 -1.91899 -1.74149 -1.47348 -1.12889 -0.72562 -0.28463 0.17115 0.61803 1.03279 1.39388 1.68251 1.88369 1.98696 1.98696 1.88369 1.68251 1.39388 1.03279 0.61803 0.17115 -0.28463 -0.72562 -1.12889 -1.47348 -1.74149 -1.91899 -1.99674 -1.97071 -1.84225 -1.61803 -1.30972 -0.93333 -0.50844 -0.05711 0.39718 0.83083 1.22130 1.54828 1.79480 1.94802 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.93429 1.74149 1.43426 1.03279 0.56347 0.05711 -0.45299 -0.93333 -1.35235 -1.68251 -1.90211 -1.99674 -1.96017 -1.79480 -1.51150 -1.12889 -0.67210 -0.17115 0.34104 0.83083 1.26602 1.61803 1.86373 1.98696 1.97964 1.84225 1.58380 1.22130 0.77854 0.28463 -0.22798 -0.72562 -1.17557 -1.54828 -1.81926 -1.97071 -1.99266 -1.88369 -1.65094 -1.30972 -0.88244 -0.39718 0.11418 0.61803 1.08128 1.47348 1.76887 1.94802 1.99918 1.91899 1.71270 1.39388 0.98347 0.50844 0.00000 -0.50844 -0.98347 -1.39388 -1.71270 -1.91899 -1.99918 -1.94802 -1.76887 -1.47348 -1.08128 -0.61803 -0.11418 0.39718 0.88244 1.30972 1.65094 1.88369 1.99266 1.97071 1.81926 1.54828 1.17557 0.72562 0.22798 -0.28463 -0.77854 -1.22130 -1.58380 -1.84225 -1.97964 -1.98696 -1.86373 -1.61803 -1.26602 -0.83083 -0.34104 0.17115 0.67210 1.12889 1.51150 1.79480 1.96017 1.99674 1.90211 1.68251 1.35235 0.93333 0.45299 -0.05711 -0.56347 -1.03279 -1.43426 -1.74149 -1.93429 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E103 2.00000 -1.96017 1.84225 -1.65094 1.39388 -1.08128 0.72562 -0.34104 -0.05711 0.45299 -0.83083 1.17557 -1.47348 1.71270 -1.88369 1.97964 -1.99674 1.93429 -1.79480 1.58380 -1.30972 0.98347 -0.61803 0.22798 0.17115 -0.56347 0.93333 -1.26602 1.54828 -1.76887 1.91899 -1.99266 1.98696 -1.90211 1.74149 -1.51150 1.22130 -0.88244 0.50844 -0.11418 -0.28463 0.67210 -1.03279 1.35235 -1.61803 1.81926 -1.94802 1.99918 -1.97071 1.86373 -1.68251 1.43426 -1.12889 0.77854 -0.39718 0.00000 0.39718 -0.77854 1.12889 -1.43426 1.68251 -1.86373 1.97071 -1.99918 1.94802 -1.81926 1.61803 -1.35235 1.03279 -0.67210 0.28463 0.11418 -0.50844 0.88244 -1.22130 1.51150 -1.74149 1.90211 -1.98696 1.99266 -1.91899 1.76887 -1.54828 1.26602 -0.93333 0.56347 -0.17115 -0.22798 0.61803 -0.98347 1.30972 -1.58380 1.79480 -1.93429 1.99674 -1.97964 1.88369 -1.71270 1.47348 -1.17557 0.83083 -0.45299 0.05711 0.34104 -0.72562 1.08128 -1.39388 1.65094 -1.84225 1.96017 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E104 2.00000 -1.97071 1.88369 -1.74149 1.54828 -1.30972 1.03279 -0.72562 0.39718 -0.05711 -0.28463 0.61803 -0.93333 1.22130 -1.47348 1.68251 -1.84225 1.94802 -1.99674 1.98696 -1.91899 1.79480 -1.61803 1.39388 -1.12889 0.83083 -0.50844 0.17115 0.17115 -0.50844 0.83083 -1.12889 1.39388 -1.61803 1.79480 -1.91899 1.98696 -1.99674 1.94802 -1.84225 1.68251 -1.47348 1.22130 -0.93333 0.61803 -0.28463 -0.05711 0.39718 -0.72562 1.03279 -1.30972 1.54828 -1.74149 1.88369 -1.97071 2.00000 -1.97071 1.88369 -1.74149 1.54828 -1.30972 1.03279 -0.72562 0.39718 -0.05711 -0.28463 0.61803 -0.93333 1.22130 -1.47348 1.68251 -1.84225 1.94802 -1.99674 1.98696 -1.91899 1.79480 -1.61803 1.39388 -1.12889 0.83083 -0.50844 0.17115 0.17115 -0.50844 0.83083 -1.12889 1.39388 -1.61803 1.79480 -1.91899 1.98696 -1.99674 1.94802 -1.84225 1.68251 -1.47348 1.22130 -0.93333 0.61803 -0.28463 -0.05711 0.39718 -0.72562 1.03279 -1.30972 1.54828 -1.74149 1.88369 -1.97071 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E105 2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 -2.00000 1.97964 -1.91899 1.81926 -1.68251 1.51150 -1.30972 1.08128 -0.83083 0.56347 -0.28463 0.00000 0.28463 -0.56347 0.83083 -1.08128 1.30972 -1.51150 1.68251 -1.81926 1.91899 -1.97964 2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 -2.00000 1.97964 -1.91899 1.81926 -1.68251 1.51150 -1.30972 1.08128 -0.83083 0.56347 -0.28463 0.00000 0.28463 -0.56347 0.83083 -1.08128 1.30972 -1.51150 1.68251 -1.81926 1.91899 -1.97964 2.00000 -1.97964 1.91899 -1.81926 1.68251 -1.51150 1.30972 -1.08128 0.83083 -0.56347 0.28463 0.00000 -0.28463 0.56347 -0.83083 1.08128 -1.30972 1.51150 -1.68251 1.81926 -1.91899 1.97964 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E106 2.00000 -1.98696 1.94802 -1.88369 1.79480 -1.68251 1.54828 -1.39388 1.22130 -1.03279 0.83083 -0.61803 0.39718 -0.17115 -0.05711 0.28463 -0.50844 0.72562 -0.93333 1.12889 -1.30972 1.47348 -1.61803 1.74149 -1.84225 1.91899 -1.97071 1.99674 -1.99674 1.97071 -1.91899 1.84225 -1.74149 1.61803 -1.47348 1.30972 -1.12889 0.93333 -0.72562 0.50844 -0.28463 0.05711 0.17115 -0.39718 0.61803 -0.83083 1.03279 -1.22130 1.39388 -1.54828 1.68251 -1.79480 1.88369 -1.94802 1.98696 -2.00000 1.98696 -1.94802 1.88369 -1.79480 1.68251 -1.54828 1.39388 -1.22130 1.03279 -0.83083 0.61803 -0.39718 0.17115 0.05711 -0.28463 0.50844 -0.72562 0.93333 -1.12889 1.30972 -1.47348 1.61803 -1.74149 1.84225 -1.91899 1.97071 -1.99674 1.99674 -1.97071 1.91899 -1.84225 1.74149 -1.61803 1.47348 -1.30972 1.12889 -0.93333 0.72562 -0.50844 0.28463 -0.05711 -0.17115 0.39718 -0.61803 0.83083 -1.03279 1.22130 -1.39388 1.54828 -1.68251 1.79480 -1.88369 1.94802 -1.98696 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E107 2.00000 -1.99266 1.97071 -1.93429 1.88369 -1.81926 1.74149 -1.65094 1.54828 -1.43426 1.30972 -1.17557 1.03279 -0.88244 0.72562 -0.56347 0.39718 -0.22798 0.05711 0.11418 -0.28463 0.45299 -0.61803 0.77854 -0.93333 1.08128 -1.22130 1.35235 -1.47348 1.58380 -1.68251 1.76887 -1.84225 1.90211 -1.94802 1.97964 -1.99674 1.99918 -1.98696 1.96017 -1.91899 1.86373 -1.79480 1.71270 -1.61803 1.51150 -1.39388 1.26602 -1.12889 0.98347 -0.83083 0.67210 -0.50844 0.34104 -0.17115 0.00000 0.17115 -0.34104 0.50844 -0.67210 0.83083 -0.98347 1.12889 -1.26602 1.39388 -1.51150 1.61803 -1.71270 1.79480 -1.86373 1.91899 -1.96017 1.98696 -1.99918 1.99674 -1.97964 1.94802 -1.90211 1.84225 -1.76887 1.68251 -1.58380 1.47348 -1.35235 1.22130 -1.08128 0.93333 -0.77854 0.61803 -0.45299 0.28463 -0.11418 -0.05711 0.22798 -0.39718 0.56347 -0.72562 0.88244 -1.03279 1.17557 -1.30972 1.43426 -1.54828 1.65094 -1.74149 1.81926 -1.88369 1.93429 -1.97071 1.99266 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E108 2.00000 -1.99674 1.98696 -1.97071 1.94802 -1.91899 1.88369 -1.84225 1.79480 -1.74149 1.68251 -1.61803 1.54828 -1.47348 1.39388 -1.30972 1.22130 -1.12889 1.03279 -0.93333 0.83083 -0.72562 0.61803 -0.50844 0.39718 -0.28463 0.17115 -0.05711 -0.05711 0.17115 -0.28463 0.39718 -0.50844 0.61803 -0.72562 0.83083 -0.93333 1.03279 -1.12889 1.22130 -1.30972 1.39388 -1.47348 1.54828 -1.61803 1.68251 -1.74149 1.79480 -1.84225 1.88369 -1.91899 1.94802 -1.97071 1.98696 -1.99674 2.00000 -1.99674 1.98696 -1.97071 1.94802 -1.91899 1.88369 -1.84225 1.79480 -1.74149 1.68251 -1.61803 1.54828 -1.47348 1.39388 -1.30972 1.22130 -1.12889 1.03279 -0.93333 0.83083 -0.72562 0.61803 -0.50844 0.39718 -0.28463 0.17115 -0.05711 -0.05711 0.17115 -0.28463 0.39718 -0.50844 0.61803 -0.72562 0.83083 -0.93333 1.03279 -1.12889 1.22130 -1.30972 1.39388 -1.47348 1.54828 -1.61803 1.68251 -1.74149 1.79480 -1.84225 1.88369 -1.91899 1.94802 -1.97071 1.98696 -1.99674 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E109 2.00000 -1.99918 1.99674 -1.99266 1.98696 -1.97964 1.97071 -1.96017 1.94802 -1.93429 1.91899 -1.90211 1.88369 -1.86373 1.84225 -1.81926 1.79480 -1.76887 1.74149 -1.71270 1.68251 -1.65094 1.61803 -1.58380 1.54828 -1.51150 1.47348 -1.43426 1.39388 -1.35235 1.30972 -1.26602 1.22130 -1.17557 1.12889 -1.08128 1.03279 -0.98347 0.93333 -0.88244 0.83083 -0.77854 0.72562 -0.67210 0.61803 -0.56347 0.50844 -0.45299 0.39718 -0.34104 0.28463 -0.22798 0.17115 -0.11418 0.05711 0.00000 -0.05711 0.11418 -0.17115 0.22798 -0.28463 0.34104 -0.39718 0.45299 -0.50844 0.56347 -0.61803 0.67210 -0.72562 0.77854 -0.83083 0.88244 -0.93333 0.98347 -1.03279 1.08128 -1.12889 1.17557 -1.22130 1.26602 -1.30972 1.35235 -1.39388 1.43426 -1.47348 1.51150 -1.54828 1.58380 -1.61803 1.65094 -1.68251 1.71270 -1.74149 1.76887 -1.79480 1.81926 -1.84225 1.86373 -1.88369 1.90211 -1.91899 1.93429 -1.94802 1.96017 -1.97071 1.97964 -1.98696 1.99266 -1.99674 1.99918 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999184385656 = 2*cos(2*π/220) = 2*cos(π/110) 1.996738207852 = 2*cos(4*π/220) = 2*cos(π/55) 1.992663461725 = 2*cos(6*π/220) = 2*cos(3*π/110) 1.986963470697 = 2*cos(8*π/220) = 2*cos(2*π/55) 1.979642883762 = 2*cos(10*π/220) = 2*cos(π/22) 1.970707671695 = 2*cos(12*π/220) = 2*cos(3*π/55) 1.960165122185 = 2*cos(14*π/220) = 2*cos(7*π/110) 1.948023833885 = 2*cos(16*π/220) = 2*cos(4*π/55) 1.934293709404 = 2*cos(18*π/220) = 2*cos(9*π/110) 1.918985947229 = 2*cos(20*π/220) = 2*cos(π/11) 1.902113032590 = 2*cos(22*π/220) = 2*cos(π/10) = (√10+2*√5)/2 1.883688727279 = 2*cos(24*π/220) = 2*cos(6*π/55) 1.863728058423 = 2*cos(26*π/220) = 2*cos(13*π/110) 1.842247306230 = 2*cos(28*π/220) = 2*cos(7*π/55) 1.819263990709 = 2*cos(30*π/220) = 2*cos(3*π/22) 1.794796857383 = 2*cos(32*π/220) = 2*cos(8*π/55) 1.768865861996 = 2*cos(34*π/220) = 2*cos(17*π/110) 1.741492154240 = 2*cos(36*π/220) = 2*cos(9*π/55) 1.712698060503 = 2*cos(38*π/220) = 2*cos(19*π/110) 1.682507065662 = 2*cos(40*π/220) = 2*cos(2*π/11) 1.650943793926 = 2*cos(42*π/220) = 2*cos(21*π/110) 1.618033988750 = 2*cos(44*π/220) = 2*cos(π/5) = (√5+1)/2 1.583804491845 = 2*cos(46*π/220) = 2*cos(23*π/110) 1.548283221278 = 2*cos(48*π/220) = 2*cos(12*π/55) 1.511499148709 = 2*cos(50*π/220) = 2*cos(5*π/22) 1.473482275753 = 2*cos(52*π/220) = 2*cos(13*π/55) 1.434263609518 = 2*cos(54*π/220) = 2*cos(27*π/110) 1.393875137311 = 2*cos(56*π/220) = 2*cos(14*π/55) 1.352349800548 = 2*cos(58*π/220) = 2*cos(29*π/110) 1.309721467891 = 2*cos(60*π/220) = 2*cos(3*π/11) 1.266024907618 = 2*cos(62*π/220) = 2*cos(31*π/110) 1.221295759271 = 2*cos(64*π/220) = 2*cos(16*π/55) 1.175570504585 = 2*cos(66*π/220) = 2*cos(3*π/10) = (√10−2*√5)/2 1.128886437734 = 2*cos(68*π/220) = 2*cos(17*π/55) 1.081281634911 = 2*cos(70*π/220) = 2*cos(7*π/22) 1.032794923278 = 2*cos(72*π/220) = 2*cos(18*π/55) 0.983465849291 = 2*cos(74*π/220) = 2*cos(37*π/110) 0.933334646451 = 2*cos(76*π/220) = 2*cos(19*π/55) 0.882442202486 = 2*cos(78*π/220) = 2*cos(39*π/110) 0.830830026004 = 2*cos(80*π/220) = 2*cos(4*π/11) 0.778540212635 = 2*cos(82*π/220) = 2*cos(41*π/110) 0.725615410701 = 2*cos(84*π/220) = 2*cos(21*π/55) 0.672098786431 = 2*cos(86*π/220) = 2*cos(43*π/110) 0.618033988750 = 2*cos(88*π/220) = 2*cos(2*π/5) = (√5−1)/2 0.563465113683 = 2*cos(90*π/220) = 2*cos(9*π/22) 0.508436668387 = 2*cos(92*π/220) = 2*cos(23*π/55) 0.452993534852 = 2*cos(94*π/220) = 2*cos(47*π/110) 0.397180933291 = 2*cos(96*π/220) = 2*cos(24*π/55) 0.341044385265 = 2*cos(98*π/220) = 2*cos(49*π/110) 0.284629676547 = 2*cos(100*π/220) = 2*cos(5*π/11) 0.227982819781 = 2*cos(102*π/220) = 2*cos(51*π/110) 0.171150016958 = 2*cos(104*π/220) = 2*cos(26*π/55) 0.114177621726 = 2*cos(106*π/220) = 2*cos(53*π/110) 0.057112101587 = 2*cos(108*π/220) = 2*cos(27*π/55) 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 E101 m E102 l E103 k+m E104 j+l E105 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)} E106 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E107 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E108 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E109 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_110d point group is 440, and the order of the principal axis (S₂₂₀) is 220. The group has 113 irreducible representations. β The D_110d point group is isomorphic to C_220v and D₂₂₀. γ The D_110d point group is generated by two symmetry elements, S₂₂₀ 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_110d 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, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.

This Character Table for the D_110d point group was created by Gernot Katzer.

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

	D_108d
	D_109d
C₁₁₀ C_110v C_110h D₁₁₀ D_110h	D_110d	S₁₁₀
	D_111d
	D_112d

Character table for the D110d point group

Character table for the D_110d point group