Character Table for Point Group D53h

Character table for the D_53h point group

D53h E 2 C53 2 C53^2 2 C53^3 2 C53^4 2 C53^5 2 C53^6 2 C53^7 2 C53^8 2 C53^9 2 C53^10 2 C53^11 2 C53^12 2 C53^13 2 C53^14 2 C53^15 2 C53^16 2 C53^17 2 C53^18 2 C53^19 2 C53^20 2 C53^21 2 C53^22 2 C53^23 2 C53^24 2 C53^25 2 C53^26 53 C2' sh 2 S53 2 S53^3 2 S53^5 2 S53^7 2 S53^9 2 S53^11 2 S53^13 2 S53^15 2 S53^17 2 S53^19 2 S53^21 2 S53^23 2 S53^25 2 S53^27 2 S53^29 2 S53^31 2 S53^33 2 S53^35 2 S53^37 2 S53^39 2 S53^41 2 S53^43 2 S53^45 2 S53^47 2 S53^49 2 S53^51 53 sv <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 ... ... ....T ....... ........T ........... ............T 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 ... ... ..... ....... ......... ........... ............. 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 ..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 ... ..T ..... ......T ......... ..........T ............. E1' 2.00000 1.98596 1.94405 1.87484 1.77931 1.65881 1.51502 1.34997 1.16596 0.96558 0.75166 0.52717 0.29529 0.05927 -0.17759 -0.41196 -0.64054 -0.86013 -1.06765 -1.26018 -1.43501 -1.58971 -1.72209 -1.83029 -1.91280 -1.96846 -1.99649 0.00000 2.00000 1.98596 1.87484 1.65881 1.34997 0.96558 0.52717 0.05927 -0.41196 -0.86013 -1.26018 -1.58971 -1.83029 -1.96846 -1.99649 -1.91280 -1.72209 -1.43501 -1.06765 -0.64054 -0.17759 0.29529 0.75166 1.16596 1.51502 1.77931 1.94405 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E1" 2.00000 1.98596 1.94405 1.87484 1.77931 1.65881 1.51502 1.34997 1.16596 0.96558 0.75166 0.52717 0.29529 0.05927 -0.17759 -0.41196 -0.64054 -0.86013 -1.06765 -1.26018 -1.43501 -1.58971 -1.72209 -1.83029 -1.91280 -1.96846 -1.99649 0.00000 -2.00000 -1.98596 -1.87484 -1.65881 -1.34997 -0.96558 -0.52717 -0.05927 0.41196 0.86013 1.26018 1.58971 1.83029 1.96846 1.99649 1.91280 1.72209 1.43501 1.06765 0.64054 0.17759 -0.29529 -0.75166 -1.16596 -1.51502 -1.77931 -1.94405 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2' 2.00000 1.94405 1.77931 1.51502 1.16596 0.75166 0.29529 -0.17759 -0.64054 -1.06765 -1.43501 -1.72209 -1.91280 -1.99649 -1.96846 -1.83029 -1.58971 -1.26018 -0.86013 -0.41196 0.05927 0.52717 0.96558 1.34997 1.65881 1.87484 1.98596 0.00000 2.00000 1.94405 1.51502 0.75166 -0.17759 -1.06765 -1.72209 -1.99649 -1.83029 -1.26018 -0.41196 0.52717 1.34997 1.87484 1.98596 1.65881 0.96558 0.05927 -0.86013 -1.58971 -1.96846 -1.91280 -1.43501 -0.64054 0.29529 1.16596 1.77931 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E2" 2.00000 1.94405 1.77931 1.51502 1.16596 0.75166 0.29529 -0.17759 -0.64054 -1.06765 -1.43501 -1.72209 -1.91280 -1.99649 -1.96846 -1.83029 -1.58971 -1.26018 -0.86013 -0.41196 0.05927 0.52717 0.96558 1.34997 1.65881 1.87484 1.98596 0.00000 -2.00000 -1.94405 -1.51502 -0.75166 0.17759 1.06765 1.72209 1.99649 1.83029 1.26018 0.41196 -0.52717 -1.34997 -1.87484 -1.98596 -1.65881 -0.96558 -0.05927 0.86013 1.58971 1.96846 1.91280 1.43501 0.64054 -0.29529 -1.16596 -1.77931 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3' 2.00000 1.87484 1.51502 0.96558 0.29529 -0.41196 -1.06765 -1.58971 -1.91280 -1.99649 -1.83029 -1.43501 -0.86013 -0.17759 0.52717 1.16596 1.65881 1.94405 1.98596 1.77931 1.34997 0.75166 0.05927 -0.64054 -1.26018 -1.72209 -1.96846 0.00000 2.00000 1.87484 0.96558 -0.41196 -1.58971 -1.99649 -1.43501 -0.17759 1.16596 1.94405 1.77931 0.75166 -0.64054 -1.72209 -1.96846 -1.26018 0.05927 1.34997 1.98596 1.65881 0.52717 -0.86013 -1.83029 -1.91280 -1.06765 0.29529 1.51502 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E3" 2.00000 1.87484 1.51502 0.96558 0.29529 -0.41196 -1.06765 -1.58971 -1.91280 -1.99649 -1.83029 -1.43501 -0.86013 -0.17759 0.52717 1.16596 1.65881 1.94405 1.98596 1.77931 1.34997 0.75166 0.05927 -0.64054 -1.26018 -1.72209 -1.96846 0.00000 -2.00000 -1.87484 -0.96558 0.41196 1.58971 1.99649 1.43501 0.17759 -1.16596 -1.94405 -1.77931 -0.75166 0.64054 1.72209 1.96846 1.26018 -0.05927 -1.34997 -1.98596 -1.65881 -0.52717 0.86013 1.83029 1.91280 1.06765 -0.29529 -1.51502 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4' 2.00000 1.77931 1.16596 0.29529 -0.64054 -1.43501 -1.91280 -1.96846 -1.58971 -0.86013 0.05927 0.96558 1.65881 1.98596 1.87484 1.34997 0.52717 -0.41196 -1.26018 -1.83029 -1.99649 -1.72209 -1.06765 -0.17759 0.75166 1.51502 1.94405 0.00000 2.00000 1.77931 0.29529 -1.43501 -1.96846 -0.86013 0.96558 1.98596 1.34997 -0.41196 -1.83029 -1.72209 -0.17759 1.51502 1.94405 0.75166 -1.06765 -1.99649 -1.26018 0.52717 1.87484 1.65881 0.05927 -1.58971 -1.91280 -0.64054 1.16596 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E4" 2.00000 1.77931 1.16596 0.29529 -0.64054 -1.43501 -1.91280 -1.96846 -1.58971 -0.86013 0.05927 0.96558 1.65881 1.98596 1.87484 1.34997 0.52717 -0.41196 -1.26018 -1.83029 -1.99649 -1.72209 -1.06765 -0.17759 0.75166 1.51502 1.94405 0.00000 -2.00000 -1.77931 -0.29529 1.43501 1.96846 0.86013 -0.96558 -1.98596 -1.34997 0.41196 1.83029 1.72209 0.17759 -1.51502 -1.94405 -0.75166 1.06765 1.99649 1.26018 -0.52717 -1.87484 -1.65881 -0.05927 1.58971 1.91280 0.64054 -1.16596 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5' 2.00000 1.65881 0.75166 -0.41196 -1.43501 -1.96846 -1.83029 -1.06765 0.05927 1.16596 1.87484 1.94405 1.34997 0.29529 -0.86013 -1.72209 -1.99649 -1.58971 -0.64054 0.52717 1.51502 1.98596 1.77931 0.96558 -0.17759 -1.26018 -1.91280 0.00000 2.00000 1.65881 -0.41196 -1.96846 -1.06765 1.16596 1.94405 0.29529 -1.72209 -1.58971 0.52717 1.98596 0.96558 -1.26018 -1.91280 -0.17759 1.77931 1.51502 -0.64054 -1.99649 -0.86013 1.34997 1.87484 0.05927 -1.83029 -1.43501 0.75166 0.00000 ... ... ..... ....... ......... TT......... ............. E5" 2.00000 1.65881 0.75166 -0.41196 -1.43501 -1.96846 -1.83029 -1.06765 0.05927 1.16596 1.87484 1.94405 1.34997 0.29529 -0.86013 -1.72209 -1.99649 -1.58971 -0.64054 0.52717 1.51502 1.98596 1.77931 0.96558 -0.17759 -1.26018 -1.91280 0.00000 -2.00000 -1.65881 0.41196 1.96846 1.06765 -1.16596 -1.94405 -0.29529 1.72209 1.58971 -0.52717 -1.98596 -0.96558 1.26018 1.91280 0.17759 -1.77931 -1.51502 0.64054 1.99649 0.86013 -1.34997 -1.87484 -0.05927 1.83029 1.43501 -0.75166 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6' 2.00000 1.51502 0.29529 -1.06765 -1.91280 -1.83029 -0.86013 0.52717 1.65881 1.98596 1.34997 0.05927 -1.26018 -1.96846 -1.72209 -0.64054 0.75166 1.77931 1.94405 1.16596 -0.17759 -1.43501 -1.99649 -1.58971 -0.41196 0.96558 1.87484 0.00000 2.00000 1.51502 -1.06765 -1.83029 0.52717 1.98596 0.05927 -1.96846 -0.64054 1.77931 1.16596 -1.43501 -1.58971 0.96558 1.87484 -0.41196 -1.99649 -0.17759 1.94405 0.75166 -1.72209 -1.26018 1.34997 1.65881 -0.86013 -1.91280 0.29529 0.00000 ... ... ..... ....... ......... ........... TT........... E6" 2.00000 1.51502 0.29529 -1.06765 -1.91280 -1.83029 -0.86013 0.52717 1.65881 1.98596 1.34997 0.05927 -1.26018 -1.96846 -1.72209 -0.64054 0.75166 1.77931 1.94405 1.16596 -0.17759 -1.43501 -1.99649 -1.58971 -0.41196 0.96558 1.87484 0.00000 -2.00000 -1.51502 1.06765 1.83029 -0.52717 -1.98596 -0.05927 1.96846 0.64054 -1.77931 -1.16596 1.43501 1.58971 -0.96558 -1.87484 0.41196 1.99649 0.17759 -1.94405 -0.75166 1.72209 1.26018 -1.34997 -1.65881 0.86013 1.91280 -0.29529 0.00000 ... ... ..... ....... ......... ........... ............. E7' 2.00000 1.34997 -0.17759 -1.58971 -1.96846 -1.06765 0.52717 1.77931 1.87484 0.75166 -0.86013 -1.91280 -1.72209 -0.41196 1.16596 1.98596 1.51502 0.05927 -1.43501 -1.99649 -1.26018 0.29529 1.65881 1.94405 0.96558 -0.64054 -1.83029 0.00000 2.00000 1.34997 -1.58971 -1.06765 1.77931 0.75166 -1.91280 -0.41196 1.98596 0.05927 -1.99649 0.29529 1.94405 -0.64054 -1.83029 0.96558 1.65881 -1.26018 -1.43501 1.51502 1.16596 -1.72209 -0.86013 1.87484 0.52717 -1.96846 -0.17759 0.00000 ... ... ..... ....... ......... ........... ............. E7" 2.00000 1.34997 -0.17759 -1.58971 -1.96846 -1.06765 0.52717 1.77931 1.87484 0.75166 -0.86013 -1.91280 -1.72209 -0.41196 1.16596 1.98596 1.51502 0.05927 -1.43501 -1.99649 -1.26018 0.29529 1.65881 1.94405 0.96558 -0.64054 -1.83029 0.00000 -2.00000 -1.34997 1.58971 1.06765 -1.77931 -0.75166 1.91280 0.41196 -1.98596 -0.05927 1.99649 -0.29529 -1.94405 0.64054 1.83029 -0.96558 -1.65881 1.26018 1.43501 -1.51502 -1.16596 1.72209 0.86013 -1.87484 -0.52717 1.96846 0.17759 0.00000 ... ... ..... ....... ......... ........... ............. E8' 2.00000 1.16596 -0.64054 -1.91280 -1.58971 0.05927 1.65881 1.87484 0.52717 -1.26018 -1.99649 -1.06765 0.75166 1.94405 1.51502 -0.17759 -1.72209 -1.83029 -0.41196 1.34997 1.98596 0.96558 -0.86013 -1.96846 -1.43501 0.29529 1.77931 0.00000 2.00000 1.16596 -1.91280 0.05927 1.87484 -1.26018 -1.06765 1.94405 -0.17759 -1.83029 1.34997 0.96558 -1.96846 0.29529 1.77931 -1.43501 -0.86013 1.98596 -0.41196 -1.72209 1.51502 0.75166 -1.99649 0.52717 1.65881 -1.58971 -0.64054 0.00000 ... ... ..... ....... ......... ........... ............. E8" 2.00000 1.16596 -0.64054 -1.91280 -1.58971 0.05927 1.65881 1.87484 0.52717 -1.26018 -1.99649 -1.06765 0.75166 1.94405 1.51502 -0.17759 -1.72209 -1.83029 -0.41196 1.34997 1.98596 0.96558 -0.86013 -1.96846 -1.43501 0.29529 1.77931 0.00000 -2.00000 -1.16596 1.91280 -0.05927 -1.87484 1.26018 1.06765 -1.94405 0.17759 1.83029 -1.34997 -0.96558 1.96846 -0.29529 -1.77931 1.43501 0.86013 -1.98596 0.41196 1.72209 -1.51502 -0.75166 1.99649 -0.52717 -1.65881 1.58971 0.64054 0.00000 ... ... ..... ....... ......... ........... ............. E9' 2.00000 0.96558 -1.06765 -1.99649 -0.86013 1.16596 1.98596 0.75166 -1.26018 -1.96846 -0.64054 1.34997 1.94405 0.52717 -1.43501 -1.91280 -0.41196 1.51502 1.87484 0.29529 -1.58971 -1.83029 -0.17759 1.65881 1.77931 0.05927 -1.72209 0.00000 2.00000 0.96558 -1.99649 1.16596 0.75166 -1.96846 1.34997 0.52717 -1.91280 1.51502 0.29529 -1.83029 1.65881 0.05927 -1.72209 1.77931 -0.17759 -1.58971 1.87484 -0.41196 -1.43501 1.94405 -0.64054 -1.26018 1.98596 -0.86013 -1.06765 0.00000 ... ... ..... ....... ......... ........... ............. E9" 2.00000 0.96558 -1.06765 -1.99649 -0.86013 1.16596 1.98596 0.75166 -1.26018 -1.96846 -0.64054 1.34997 1.94405 0.52717 -1.43501 -1.91280 -0.41196 1.51502 1.87484 0.29529 -1.58971 -1.83029 -0.17759 1.65881 1.77931 0.05927 -1.72209 0.00000 -2.00000 -0.96558 1.99649 -1.16596 -0.75166 1.96846 -1.34997 -0.52717 1.91280 -1.51502 -0.29529 1.83029 -1.65881 -0.05927 1.72209 -1.77931 0.17759 1.58971 -1.87484 0.41196 1.43501 -1.94405 0.64054 1.26018 -1.98596 0.86013 1.06765 0.00000 ... ... ..... ....... ......... ........... ............. E10' 2.00000 0.75166 -1.43501 -1.83029 0.05927 1.87484 1.34997 -0.86013 -1.99649 -0.64054 1.51502 1.77931 -0.17759 -1.91280 -1.26018 0.96558 1.98596 0.52717 -1.58971 -1.72209 0.29529 1.94405 1.16596 -1.06765 -1.96846 -0.41196 1.65881 0.00000 2.00000 0.75166 -1.83029 1.87484 -0.86013 -0.64054 1.77931 -1.91280 0.96558 0.52717 -1.72209 1.94405 -1.06765 -0.41196 1.65881 -1.96846 1.16596 0.29529 -1.58971 1.98596 -1.26018 -0.17759 1.51502 -1.99649 1.34997 0.05927 -1.43501 0.00000 ... ... ..... ....... ......... ........... ............. E10" 2.00000 0.75166 -1.43501 -1.83029 0.05927 1.87484 1.34997 -0.86013 -1.99649 -0.64054 1.51502 1.77931 -0.17759 -1.91280 -1.26018 0.96558 1.98596 0.52717 -1.58971 -1.72209 0.29529 1.94405 1.16596 -1.06765 -1.96846 -0.41196 1.65881 0.00000 -2.00000 -0.75166 1.83029 -1.87484 0.86013 0.64054 -1.77931 1.91280 -0.96558 -0.52717 1.72209 -1.94405 1.06765 0.41196 -1.65881 1.96846 -1.16596 -0.29529 1.58971 -1.98596 1.26018 0.17759 -1.51502 1.99649 -1.34997 -0.05927 1.43501 0.00000 ... ... ..... ....... ......... ........... ............. E11' 2.00000 0.52717 -1.72209 -1.43501 0.96558 1.94405 0.05927 -1.91280 -1.06765 1.34997 1.77931 -0.41196 -1.99649 -0.64054 1.65881 1.51502 -0.86013 -1.96846 -0.17759 1.87484 1.16596 -1.26018 -1.83029 0.29529 1.98596 0.75166 -1.58971 0.00000 2.00000 0.52717 -1.43501 1.94405 -1.91280 1.34997 -0.41196 -0.64054 1.51502 -1.96846 1.87484 -1.26018 0.29529 0.75166 -1.58971 1.98596 -1.83029 1.16596 -0.17759 -0.86013 1.65881 -1.99649 1.77931 -1.06765 0.05927 0.96558 -1.72209 0.00000 ... ... ..... ....... ......... ........... ............. E11" 2.00000 0.52717 -1.72209 -1.43501 0.96558 1.94405 0.05927 -1.91280 -1.06765 1.34997 1.77931 -0.41196 -1.99649 -0.64054 1.65881 1.51502 -0.86013 -1.96846 -0.17759 1.87484 1.16596 -1.26018 -1.83029 0.29529 1.98596 0.75166 -1.58971 0.00000 -2.00000 -0.52717 1.43501 -1.94405 1.91280 -1.34997 0.41196 0.64054 -1.51502 1.96846 -1.87484 1.26018 -0.29529 -0.75166 1.58971 -1.98596 1.83029 -1.16596 0.17759 0.86013 -1.65881 1.99649 -1.77931 1.06765 -0.05927 -0.96558 1.72209 0.00000 ... ... ..... ....... ......... ........... ............. E12' 2.00000 0.29529 -1.91280 -0.86013 1.65881 1.34997 -1.26018 -1.72209 0.75166 1.94405 -0.17759 -1.99649 -0.41196 1.87484 0.96558 -1.58971 -1.43501 1.16596 1.77931 -0.64054 -1.96846 0.05927 1.98596 0.52717 -1.83029 -1.06765 1.51502 0.00000 2.00000 0.29529 -0.86013 1.34997 -1.72209 1.94405 -1.99649 1.87484 -1.58971 1.16596 -0.64054 0.05927 0.52717 -1.06765 1.51502 -1.83029 1.98596 -1.96846 1.77931 -1.43501 0.96558 -0.41196 -0.17759 0.75166 -1.26018 1.65881 -1.91280 0.00000 ... ... ..... ....... ......... ........... ............. E12" 2.00000 0.29529 -1.91280 -0.86013 1.65881 1.34997 -1.26018 -1.72209 0.75166 1.94405 -0.17759 -1.99649 -0.41196 1.87484 0.96558 -1.58971 -1.43501 1.16596 1.77931 -0.64054 -1.96846 0.05927 1.98596 0.52717 -1.83029 -1.06765 1.51502 0.00000 -2.00000 -0.29529 0.86013 -1.34997 1.72209 -1.94405 1.99649 -1.87484 1.58971 -1.16596 0.64054 -0.05927 -0.52717 1.06765 -1.51502 1.83029 -1.98596 1.96846 -1.77931 1.43501 -0.96558 0.41196 0.17759 -0.75166 1.26018 -1.65881 1.91280 0.00000 ... ... ..... ....... ......... ........... ............. E13' 2.00000 0.05927 -1.99649 -0.17759 1.98596 0.29529 -1.96846 -0.41196 1.94405 0.52717 -1.91280 -0.64054 1.87484 0.75166 -1.83029 -0.86013 1.77931 0.96558 -1.72209 -1.06765 1.65881 1.16596 -1.58971 -1.26018 1.51502 1.34997 -1.43501 0.00000 2.00000 0.05927 -0.17759 0.29529 -0.41196 0.52717 -0.64054 0.75166 -0.86013 0.96558 -1.06765 1.16596 -1.26018 1.34997 -1.43501 1.51502 -1.58971 1.65881 -1.72209 1.77931 -1.83029 1.87484 -1.91280 1.94405 -1.96846 1.98596 -1.99649 0.00000 ... ... ..... ....... ......... ........... ............. E13" 2.00000 0.05927 -1.99649 -0.17759 1.98596 0.29529 -1.96846 -0.41196 1.94405 0.52717 -1.91280 -0.64054 1.87484 0.75166 -1.83029 -0.86013 1.77931 0.96558 -1.72209 -1.06765 1.65881 1.16596 -1.58971 -1.26018 1.51502 1.34997 -1.43501 0.00000 -2.00000 -0.05927 0.17759 -0.29529 0.41196 -0.52717 0.64054 -0.75166 0.86013 -0.96558 1.06765 -1.16596 1.26018 -1.34997 1.43501 -1.51502 1.58971 -1.65881 1.72209 -1.77931 1.83029 -1.87484 1.91280 -1.94405 1.96846 -1.98596 1.99649 0.00000 ... ... ..... ....... ......... ........... ............. E14' 2.00000 -0.17759 -1.96846 0.52717 1.87484 -0.86013 -1.72209 1.16596 1.51502 -1.43501 -1.26018 1.65881 0.96558 -1.83029 -0.64054 1.94405 0.29529 -1.99649 0.05927 1.98596 -0.41196 -1.91280 0.75166 1.77931 -1.06765 -1.58971 1.34997 0.00000 2.00000 -0.17759 0.52717 -0.86013 1.16596 -1.43501 1.65881 -1.83029 1.94405 -1.99649 1.98596 -1.91280 1.77931 -1.58971 1.34997 -1.06765 0.75166 -0.41196 0.05927 0.29529 -0.64054 0.96558 -1.26018 1.51502 -1.72209 1.87484 -1.96846 0.00000 ... ... ..... ....... ......... ........... ............. E14" 2.00000 -0.17759 -1.96846 0.52717 1.87484 -0.86013 -1.72209 1.16596 1.51502 -1.43501 -1.26018 1.65881 0.96558 -1.83029 -0.64054 1.94405 0.29529 -1.99649 0.05927 1.98596 -0.41196 -1.91280 0.75166 1.77931 -1.06765 -1.58971 1.34997 0.00000 -2.00000 0.17759 -0.52717 0.86013 -1.16596 1.43501 -1.65881 1.83029 -1.94405 1.99649 -1.98596 1.91280 -1.77931 1.58971 -1.34997 1.06765 -0.75166 0.41196 -0.05927 -0.29529 0.64054 -0.96558 1.26018 -1.51502 1.72209 -1.87484 1.96846 0.00000 ... ... ..... ....... ......... ........... ............. E15' 2.00000 -0.41196 -1.83029 1.16596 1.34997 -1.72209 -0.64054 1.98596 -0.17759 -1.91280 0.96558 1.51502 -1.58971 -0.86013 1.94405 0.05927 -1.96846 0.75166 1.65881 -1.43501 -1.06765 1.87484 0.29529 -1.99649 0.52717 1.77931 -1.26018 0.00000 2.00000 -0.41196 1.16596 -1.72209 1.98596 -1.91280 1.51502 -0.86013 0.05927 0.75166 -1.43501 1.87484 -1.99649 1.77931 -1.26018 0.52717 0.29529 -1.06765 1.65881 -1.96846 1.94405 -1.58971 0.96558 -0.17759 -0.64054 1.34997 -1.83029 0.00000 ... ... ..... ....... ......... ........... ............. E15" 2.00000 -0.41196 -1.83029 1.16596 1.34997 -1.72209 -0.64054 1.98596 -0.17759 -1.91280 0.96558 1.51502 -1.58971 -0.86013 1.94405 0.05927 -1.96846 0.75166 1.65881 -1.43501 -1.06765 1.87484 0.29529 -1.99649 0.52717 1.77931 -1.26018 0.00000 -2.00000 0.41196 -1.16596 1.72209 -1.98596 1.91280 -1.51502 0.86013 -0.05927 -0.75166 1.43501 -1.87484 1.99649 -1.77931 1.26018 -0.52717 -0.29529 1.06765 -1.65881 1.96846 -1.94405 1.58971 -0.96558 0.17759 0.64054 -1.34997 1.83029 0.00000 ... ... ..... ....... ......... ........... ............. E16' 2.00000 -0.64054 -1.58971 1.65881 0.52717 -1.99649 0.75166 1.51502 -1.72209 -0.41196 1.98596 -0.86013 -1.43501 1.77931 0.29529 -1.96846 0.96558 1.34997 -1.83029 -0.17759 1.94405 -1.06765 -1.26018 1.87484 0.05927 -1.91280 1.16596 0.00000 2.00000 -0.64054 1.65881 -1.99649 1.51502 -0.41196 -0.86013 1.77931 -1.96846 1.34997 -0.17759 -1.06765 1.87484 -1.91280 1.16596 0.05927 -1.26018 1.94405 -1.83029 0.96558 0.29529 -1.43501 1.98596 -1.72209 0.75166 0.52717 -1.58971 0.00000 ... ... ..... ....... ......... ........... ............. E16" 2.00000 -0.64054 -1.58971 1.65881 0.52717 -1.99649 0.75166 1.51502 -1.72209 -0.41196 1.98596 -0.86013 -1.43501 1.77931 0.29529 -1.96846 0.96558 1.34997 -1.83029 -0.17759 1.94405 -1.06765 -1.26018 1.87484 0.05927 -1.91280 1.16596 0.00000 -2.00000 0.64054 -1.65881 1.99649 -1.51502 0.41196 0.86013 -1.77931 1.96846 -1.34997 0.17759 1.06765 -1.87484 1.91280 -1.16596 -0.05927 1.26018 -1.94405 1.83029 -0.96558 -0.29529 1.43501 -1.98596 1.72209 -0.75166 -0.52717 1.58971 0.00000 ... ... ..... ....... ......... ........... ............. E17' 2.00000 -0.86013 -1.26018 1.94405 -0.41196 -1.58971 1.77931 0.05927 -1.83029 1.51502 0.52717 -1.96846 1.16596 0.96558 -1.99649 0.75166 1.34997 -1.91280 0.29529 1.65881 -1.72209 -0.17759 1.87484 -1.43501 -0.64054 1.98596 -1.06765 0.00000 2.00000 -0.86013 1.94405 -1.58971 0.05927 1.51502 -1.96846 0.96558 0.75166 -1.91280 1.65881 -0.17759 -1.43501 1.98596 -1.06765 -0.64054 1.87484 -1.72209 0.29529 1.34997 -1.99649 1.16596 0.52717 -1.83029 1.77931 -0.41196 -1.26018 0.00000 ... ... ..... ....... ......... ........... ............. E17" 2.00000 -0.86013 -1.26018 1.94405 -0.41196 -1.58971 1.77931 0.05927 -1.83029 1.51502 0.52717 -1.96846 1.16596 0.96558 -1.99649 0.75166 1.34997 -1.91280 0.29529 1.65881 -1.72209 -0.17759 1.87484 -1.43501 -0.64054 1.98596 -1.06765 0.00000 -2.00000 0.86013 -1.94405 1.58971 -0.05927 -1.51502 1.96846 -0.96558 -0.75166 1.91280 -1.65881 0.17759 1.43501 -1.98596 1.06765 0.64054 -1.87484 1.72209 -0.29529 -1.34997 1.99649 -1.16596 -0.52717 1.83029 -1.77931 0.41196 1.26018 0.00000 ... ... ..... ....... ......... ........... ............. E18' 2.00000 -1.06765 -0.86013 1.98596 -1.26018 -0.64054 1.94405 -1.43501 -0.41196 1.87484 -1.58971 -0.17759 1.77931 -1.72209 0.05927 1.65881 -1.83029 0.29529 1.51502 -1.91280 0.52717 1.34997 -1.96846 0.75166 1.16596 -1.99649 0.96558 0.00000 2.00000 -1.06765 1.98596 -0.64054 -1.43501 1.87484 -0.17759 -1.72209 1.65881 0.29529 -1.91280 1.34997 0.75166 -1.99649 0.96558 1.16596 -1.96846 0.52717 1.51502 -1.83029 0.05927 1.77931 -1.58971 -0.41196 1.94405 -1.26018 -0.86013 0.00000 ... ... ..... ....... ......... ........... ............. E18" 2.00000 -1.06765 -0.86013 1.98596 -1.26018 -0.64054 1.94405 -1.43501 -0.41196 1.87484 -1.58971 -0.17759 1.77931 -1.72209 0.05927 1.65881 -1.83029 0.29529 1.51502 -1.91280 0.52717 1.34997 -1.96846 0.75166 1.16596 -1.99649 0.96558 0.00000 -2.00000 1.06765 -1.98596 0.64054 1.43501 -1.87484 0.17759 1.72209 -1.65881 -0.29529 1.91280 -1.34997 -0.75166 1.99649 -0.96558 -1.16596 1.96846 -0.52717 -1.51502 1.83029 -0.05927 -1.77931 1.58971 0.41196 -1.94405 1.26018 0.86013 0.00000 ... ... ..... ....... ......... ........... ............. E19' 2.00000 -1.26018 -0.41196 1.77931 -1.83029 0.52717 1.16596 -1.99649 1.34997 0.29529 -1.72209 1.87484 -0.64054 -1.06765 1.98596 -1.43501 -0.17759 1.65881 -1.91280 0.75166 0.96558 -1.96846 1.51502 0.05927 -1.58971 1.94405 -0.86013 0.00000 2.00000 -1.26018 1.77931 0.52717 -1.99649 0.29529 1.87484 -1.06765 -1.43501 1.65881 0.75166 -1.96846 0.05927 1.94405 -0.86013 -1.58971 1.51502 0.96558 -1.91280 -0.17759 1.98596 -0.64054 -1.72209 1.34997 1.16596 -1.83029 -0.41196 0.00000 ... ... ..... ....... ......... ........... ............. E19" 2.00000 -1.26018 -0.41196 1.77931 -1.83029 0.52717 1.16596 -1.99649 1.34997 0.29529 -1.72209 1.87484 -0.64054 -1.06765 1.98596 -1.43501 -0.17759 1.65881 -1.91280 0.75166 0.96558 -1.96846 1.51502 0.05927 -1.58971 1.94405 -0.86013 0.00000 -2.00000 1.26018 -1.77931 -0.52717 1.99649 -0.29529 -1.87484 1.06765 1.43501 -1.65881 -0.75166 1.96846 -0.05927 -1.94405 0.86013 1.58971 -1.51502 -0.96558 1.91280 0.17759 -1.98596 0.64054 1.72209 -1.34997 -1.16596 1.83029 0.41196 0.00000 ... ... ..... ....... ......... ........... ............. E20' 2.00000 -1.43501 0.05927 1.34997 -1.99649 1.51502 -0.17759 -1.26018 1.98596 -1.58971 0.29529 1.16596 -1.96846 1.65881 -0.41196 -1.06765 1.94405 -1.72209 0.52717 0.96558 -1.91280 1.77931 -0.64054 -0.86013 1.87484 -1.83029 0.75166 0.00000 2.00000 -1.43501 1.34997 1.51502 -1.26018 -1.58971 1.16596 1.65881 -1.06765 -1.72209 0.96558 1.77931 -0.86013 -1.83029 0.75166 1.87484 -0.64054 -1.91280 0.52717 1.94405 -0.41196 -1.96846 0.29529 1.98596 -0.17759 -1.99649 0.05927 0.00000 ... ... ..... ....... ......... ........... ............. E20" 2.00000 -1.43501 0.05927 1.34997 -1.99649 1.51502 -0.17759 -1.26018 1.98596 -1.58971 0.29529 1.16596 -1.96846 1.65881 -0.41196 -1.06765 1.94405 -1.72209 0.52717 0.96558 -1.91280 1.77931 -0.64054 -0.86013 1.87484 -1.83029 0.75166 0.00000 -2.00000 1.43501 -1.34997 -1.51502 1.26018 1.58971 -1.16596 -1.65881 1.06765 1.72209 -0.96558 -1.77931 0.86013 1.83029 -0.75166 -1.87484 0.64054 1.91280 -0.52717 -1.94405 0.41196 1.96846 -0.29529 -1.98596 0.17759 1.99649 -0.05927 0.00000 ... ... ..... ....... ......... ........... ............. E21' 2.00000 -1.58971 0.52717 0.75166 -1.72209 1.98596 -1.43501 0.29529 0.96558 -1.83029 1.94405 -1.26018 0.05927 1.16596 -1.91280 1.87484 -1.06765 -0.17759 1.34997 -1.96846 1.77931 -0.86013 -0.41196 1.51502 -1.99649 1.65881 -0.64054 0.00000 2.00000 -1.58971 0.75166 1.98596 0.29529 -1.83029 -1.26018 1.16596 1.87484 -0.17759 -1.96846 -0.86013 1.51502 1.65881 -0.64054 -1.99649 -0.41196 1.77931 1.34997 -1.06765 -1.91280 0.05927 1.94405 0.96558 -1.43501 -1.72209 0.52717 0.00000 ... ... ..... ....... ......... ........... ............. E21" 2.00000 -1.58971 0.52717 0.75166 -1.72209 1.98596 -1.43501 0.29529 0.96558 -1.83029 1.94405 -1.26018 0.05927 1.16596 -1.91280 1.87484 -1.06765 -0.17759 1.34997 -1.96846 1.77931 -0.86013 -0.41196 1.51502 -1.99649 1.65881 -0.64054 0.00000 -2.00000 1.58971 -0.75166 -1.98596 -0.29529 1.83029 1.26018 -1.16596 -1.87484 0.17759 1.96846 0.86013 -1.51502 -1.65881 0.64054 1.99649 0.41196 -1.77931 -1.34997 1.06765 1.91280 -0.05927 -1.94405 -0.96558 1.43501 1.72209 -0.52717 0.00000 ... ... ..... ....... ......... ........... ............. E22' 2.00000 -1.72209 0.96558 0.05927 -1.06765 1.77931 -1.99649 1.65881 -0.86013 -0.17759 1.16596 -1.83029 1.98596 -1.58971 0.75166 0.29529 -1.26018 1.87484 -1.96846 1.51502 -0.64054 -0.41196 1.34997 -1.91280 1.94405 -1.43501 0.52717 0.00000 2.00000 -1.72209 0.05927 1.77931 1.65881 -0.17759 -1.83029 -1.58971 0.29529 1.87484 1.51502 -0.41196 -1.91280 -1.43501 0.52717 1.94405 1.34997 -0.64054 -1.96846 -1.26018 0.75166 1.98596 1.16596 -0.86013 -1.99649 -1.06765 0.96558 0.00000 ... ... ..... ....... ......... ........... ............. E22" 2.00000 -1.72209 0.96558 0.05927 -1.06765 1.77931 -1.99649 1.65881 -0.86013 -0.17759 1.16596 -1.83029 1.98596 -1.58971 0.75166 0.29529 -1.26018 1.87484 -1.96846 1.51502 -0.64054 -0.41196 1.34997 -1.91280 1.94405 -1.43501 0.52717 0.00000 -2.00000 1.72209 -0.05927 -1.77931 -1.65881 0.17759 1.83029 1.58971 -0.29529 -1.87484 -1.51502 0.41196 1.91280 1.43501 -0.52717 -1.94405 -1.34997 0.64054 1.96846 1.26018 -0.75166 -1.98596 -1.16596 0.86013 1.99649 1.06765 -0.96558 0.00000 ... ... ..... ....... ......... ........... ............. E23' 2.00000 -1.83029 1.34997 -0.64054 -0.17759 0.96558 -1.58971 1.94405 -1.96846 1.65881 -1.06765 0.29529 0.52717 -1.26018 1.77931 -1.99649 1.87484 -1.43501 0.75166 0.05927 -0.86013 1.51502 -1.91280 1.98596 -1.72209 1.16596 -0.41196 0.00000 2.00000 -1.83029 -0.64054 0.96558 1.94405 1.65881 0.29529 -1.26018 -1.99649 -1.43501 0.05927 1.51502 1.98596 1.16596 -0.41196 -1.72209 -1.91280 -0.86013 0.75166 1.87484 1.77931 0.52717 -1.06765 -1.96846 -1.58971 -0.17759 1.34997 0.00000 ... ... ..... ....... ......... ........... ............. E23" 2.00000 -1.83029 1.34997 -0.64054 -0.17759 0.96558 -1.58971 1.94405 -1.96846 1.65881 -1.06765 0.29529 0.52717 -1.26018 1.77931 -1.99649 1.87484 -1.43501 0.75166 0.05927 -0.86013 1.51502 -1.91280 1.98596 -1.72209 1.16596 -0.41196 0.00000 -2.00000 1.83029 0.64054 -0.96558 -1.94405 -1.65881 -0.29529 1.26018 1.99649 1.43501 -0.05927 -1.51502 -1.98596 -1.16596 0.41196 1.72209 1.91280 0.86013 -0.75166 -1.87484 -1.77931 -0.52717 1.06765 1.96846 1.58971 0.17759 -1.34997 0.00000 ... ... ..... ....... ......... ........... ............. E24' 2.00000 -1.91280 1.65881 -1.26018 0.75166 -0.17759 -0.41196 0.96558 -1.43501 1.77931 -1.96846 1.98596 -1.83029 1.51502 -1.06765 0.52717 0.05927 -0.64054 1.16596 -1.58971 1.87484 -1.99649 1.94405 -1.72209 1.34997 -0.86013 0.29529 0.00000 2.00000 -1.91280 -1.26018 -0.17759 0.96558 1.77931 1.98596 1.51502 0.52717 -0.64054 -1.58971 -1.99649 -1.72209 -0.86013 0.29529 1.34997 1.94405 1.87484 1.16596 0.05927 -1.06765 -1.83029 -1.96846 -1.43501 -0.41196 0.75166 1.65881 0.00000 ... ... ..... ....... ......... ........... ............. E24" 2.00000 -1.91280 1.65881 -1.26018 0.75166 -0.17759 -0.41196 0.96558 -1.43501 1.77931 -1.96846 1.98596 -1.83029 1.51502 -1.06765 0.52717 0.05927 -0.64054 1.16596 -1.58971 1.87484 -1.99649 1.94405 -1.72209 1.34997 -0.86013 0.29529 0.00000 -2.00000 1.91280 1.26018 0.17759 -0.96558 -1.77931 -1.98596 -1.51502 -0.52717 0.64054 1.58971 1.99649 1.72209 0.86013 -0.29529 -1.34997 -1.94405 -1.87484 -1.16596 -0.05927 1.06765 1.83029 1.96846 1.43501 0.41196 -0.75166 -1.65881 0.00000 ... ... ..... ....... ......... ........... ............. E25' 2.00000 -1.96846 1.87484 -1.72209 1.51502 -1.26018 0.96558 -0.64054 0.29529 0.05927 -0.41196 0.75166 -1.06765 1.34997 -1.58971 1.77931 -1.91280 1.98596 -1.99649 1.94405 -1.83029 1.65881 -1.43501 1.16596 -0.86013 0.52717 -0.17759 0.00000 2.00000 -1.96846 -1.72209 -1.26018 -0.64054 0.05927 0.75166 1.34997 1.77931 1.98596 1.94405 1.65881 1.16596 0.52717 -0.17759 -0.86013 -1.43501 -1.83029 -1.99649 -1.91280 -1.58971 -1.06765 -0.41196 0.29529 0.96558 1.51502 1.87484 0.00000 ... ... ..... ....... ......... ........... ............. E25" 2.00000 -1.96846 1.87484 -1.72209 1.51502 -1.26018 0.96558 -0.64054 0.29529 0.05927 -0.41196 0.75166 -1.06765 1.34997 -1.58971 1.77931 -1.91280 1.98596 -1.99649 1.94405 -1.83029 1.65881 -1.43501 1.16596 -0.86013 0.52717 -0.17759 0.00000 -2.00000 1.96846 1.72209 1.26018 0.64054 -0.05927 -0.75166 -1.34997 -1.77931 -1.98596 -1.94405 -1.65881 -1.16596 -0.52717 0.17759 0.86013 1.43501 1.83029 1.99649 1.91280 1.58971 1.06765 0.41196 -0.29529 -0.96558 -1.51502 -1.87484 0.00000 ... ... ..... ....... ......... ........... ............. E26' 2.00000 -1.99649 1.98596 -1.96846 1.94405 -1.91280 1.87484 -1.83029 1.77931 -1.72209 1.65881 -1.58971 1.51502 -1.43501 1.34997 -1.26018 1.16596 -1.06765 0.96558 -0.86013 0.75166 -0.64054 0.52717 -0.41196 0.29529 -0.17759 0.05927 0.00000 2.00000 -1.99649 -1.96846 -1.91280 -1.83029 -1.72209 -1.58971 -1.43501 -1.26018 -1.06765 -0.86013 -0.64054 -0.41196 -0.17759 0.05927 0.29529 0.52717 0.75166 0.96558 1.16596 1.34997 1.51502 1.65881 1.77931 1.87484 1.94405 1.98596 0.00000 ... ... ..... ....... ......... ........... ............. E26" 2.00000 -1.99649 1.98596 -1.96846 1.94405 -1.91280 1.87484 -1.83029 1.77931 -1.72209 1.65881 -1.58971 1.51502 -1.43501 1.34997 -1.26018 1.16596 -1.06765 0.96558 -0.86013 0.75166 -0.64054 0.52717 -0.41196 0.29529 -0.17759 0.05927 0.00000 -2.00000 1.99649 1.96846 1.91280 1.83029 1.72209 1.58971 1.43501 1.26018 1.06765 0.86013 0.64054 0.41196 0.17759 -0.05927 -0.29529 -0.52717 -0.75166 -0.96558 -1.16596 -1.34997 -1.51502 -1.65881 -1.77931 -1.87484 -1.94405 -1.98596 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996487463529 = 2*cos(2*π/106) = 2*cos(π/53) 1.985962192027 = 2*cos(4*π/106) = 2*cos(2*π/53) 1.968461155895 = 2*cos(6*π/106) = 2*cos(3*π/53) 1.944045828161 = 2*cos(8*π/106) = 2*cos(4*π/53) 1.912801968553 = 2*cos(10*π/106) = 2*cos(5*π/53) 1.874839322268 = 2*cos(12*π/106) = 2*cos(6*π/53) 1.830291234486 = 2*cos(14*π/106) = 2*cos(7*π/53) 1.779314181989 = 2*cos(16*π/106) = 2*cos(8*π/53) 1.722087223535 = 2*cos(18*π/106) = 2*cos(9*π/53) 1.658811370900 = 2*cos(20*π/106) = 2*cos(10*π/53) 1.589708882827 = 2*cos(22*π/106) = 2*cos(11*π/53) 1.515022484323 = 2*cos(24*π/106) = 2*cos(12*π/53) 1.435014514089 = 2*cos(26*π/106) = 2*cos(13*π/53) 1.349966003036 = 2*cos(28*π/106) = 2*cos(14*π/53) 1.260175687163 = 2*cos(30*π/106) = 2*cos(15*π/53) 1.165958958229 = 2*cos(32*π/106) = 2*cos(16*π/53) 1.067646755930 = 2*cos(34*π/106) = 2*cos(17*π/53) 0.965584405461 = 2*cos(36*π/106) = 2*cos(18*π/53) 0.860130404553 = 2*cos(38*π/106) = 2*cos(19*π/53) 0.751655164228 = 2*cos(40*π/106) = 2*cos(20*π/53) 0.640539707726 = 2*cos(42*π/106) = 2*cos(21*π/53) 0.527174332138 = 2*cos(44*π/106) = 2*cos(22*π/53) 0.411957237482 = 2*cos(46*π/106) = 2*cos(23*π/53) 0.295293128005 = 2*cos(48*π/106) = 2*cos(24*π/53) 0.177591790646 = 2*cos(50*π/106) = 2*cos(25*π/53) 0.059266655645 = 2*cos(52*π/106) = 2*cos(26*π/53) Symmetry of Rotations and Cartesian products A1' d+g+i+k+m z², z⁴, z⁶ A2' R R_z A2" p+f+h+j+l z, z³, z⁵ E1' p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E1" R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2' d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E2" f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3' f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E3" g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4' g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E4" h+j+l {z((x²−y²)²−4x²y²), xyz(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)} E5" 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)} E6' i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the D_53h point group is 212, and the order of the principal axis (S₅₃) is 106. The group has 56 irreducible representations. β The D_53h point group is isomorphic to D_53d, C_106v and D₁₀₆. γ The D_53h point group is generated by two symmetry elements, S₅₃ and either a perpendicular C₂^′ or a vertical σ_v. Also, the group may be generated from any two σ_v planes, or any σ_v and a non-coplanar C₂^′. The canonical choice, however, is to use redundant generators: C₅₃, C₂^′ and σ_h. δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Similarly, the single set of symmetry planes denoted σ_d contains the xz plane but not the yz plane. ε The lowest nonvanishing multipole moment in D_53h is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. 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 just 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_53h point group was created by Gernot Katzer.

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

	D_51h
	D_52h
C₅₃ C_53v C_53h D₅₃	D_53h	D_53d
	D_54h
	D_55h

Character table for the D53h point group

Character table for the D_53h point group