Character Table for Point Group D106d

Character table for the D_106d point group

D106d E 2 S212 2 C106 2 S212^3 2 C53 2 S212^5 2 C106^3 2 S212^7 2 C53^2 2 S212^9 2 C106^5 2 S212^11 2 C53^3 2 S212^13 2 C106^7 2 S212^15 2 C53^4 2 S212^17 2 C106^9 2 S212^19 2 C53^5 2 S212^21 2 C106^11 2 S212^23 2 C53^6 2 S212^25 2 C106^13 2 S212^27 2 C53^7 2 S212^29 2 C106^15 2 S212^31 2 C53^8 2 S212^33 2 C106^17 2 S212^35 2 C53^9 2 S212^37 2 C106^19 2 S212^39 2 C53^10 2 S212^41 2 C106^21 2 S212^43 2 C53^11 2 S212^45 2 C106^23 2 S212^47 2 C53^12 2 S212^49 2 C106^25 2 S212^51 2 C53^13 2 S4 2 C106^27 2 S212^55 2 C53^14 2 S212^57 2 C106^29 2 S212^59 2 C53^15 2 S212^61 2 C106^31 2 S212^63 2 C53^16 2 S212^65 2 C106^33 2 S212^67 2 C53^17 2 S212^69 2 C106^35 2 S212^71 2 C53^18 2 S212^73 2 C106^37 2 S212^75 2 C53^19 2 S212^77 2 C106^39 2 S212^79 2 C53^20 2 S212^81 2 C106^41 2 S212^83 2 C53^21 2 S212^85 2 C106^43 2 S212^87 2 C53^22 2 S212^89 2 C106^45 2 S212^91 2 C53^23 2 S212^93 2 C106^47 2 S212^95 2 C53^24 2 S212^97 2 C106^49 2 S212^99 2 C53^25 2 S212^101 2 C106^51 2 S212^103 2 C53^26 2 S212^105 C2 106 C2' 106 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 ... ... ....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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99912 1.99649 1.99210 1.98596 1.97808 1.96846 1.95711 1.94405 1.92927 1.91280 1.89465 1.87484 1.85338 1.83029 1.80560 1.77931 1.75147 1.72209 1.69119 1.65881 1.62497 1.58971 1.55305 1.51502 1.47567 1.43501 1.39310 1.34997 1.30564 1.26018 1.21360 1.16596 1.11729 1.06765 1.01706 0.96558 0.91326 0.86013 0.80625 0.75166 0.69640 0.64054 0.58411 0.52717 0.46977 0.41196 0.35378 0.29529 0.23655 0.17759 0.11848 0.05927 0.00000 -0.05927 -0.11848 -0.17759 -0.23655 -0.29529 -0.35378 -0.41196 -0.46977 -0.52717 -0.58411 -0.64054 -0.69640 -0.75166 -0.80625 -0.86013 -0.91326 -0.96558 -1.01706 -1.06765 -1.11729 -1.16596 -1.21360 -1.26018 -1.30564 -1.34997 -1.39310 -1.43501 -1.47567 -1.51502 -1.55305 -1.58971 -1.62497 -1.65881 -1.69119 -1.72209 -1.75147 -1.77931 -1.80560 -1.83029 -1.85338 -1.87484 -1.89465 -1.91280 -1.92927 -1.94405 -1.95711 -1.96846 -1.97808 -1.98596 -1.99210 -1.99649 -1.99912 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 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 -0.05927 -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 -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 0.05927 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 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99210 1.96846 1.92927 1.87484 1.80560 1.72209 1.62497 1.51502 1.39310 1.26018 1.11729 0.96558 0.80625 0.64054 0.46977 0.29529 0.11848 -0.05927 -0.23655 -0.41196 -0.58411 -0.75166 -0.91326 -1.06765 -1.21360 -1.34997 -1.47567 -1.58971 -1.69119 -1.77931 -1.85338 -1.91280 -1.95711 -1.98596 -1.99912 -1.99649 -1.97808 -1.94405 -1.89465 -1.83029 -1.75147 -1.65881 -1.55305 -1.43501 -1.30564 -1.16596 -1.01706 -0.86013 -0.69640 -0.52717 -0.35378 -0.17759 0.00000 0.17759 0.35378 0.52717 0.69640 0.86013 1.01706 1.16596 1.30564 1.43501 1.55305 1.65881 1.75147 1.83029 1.89465 1.94405 1.97808 1.99649 1.99912 1.98596 1.95711 1.91280 1.85338 1.77931 1.69119 1.58971 1.47567 1.34997 1.21360 1.06765 0.91326 0.75166 0.58411 0.41196 0.23655 0.05927 -0.11848 -0.29529 -0.46977 -0.64054 -0.80625 -0.96558 -1.11729 -1.26018 -1.39310 -1.51502 -1.62497 -1.72209 -1.80560 -1.87484 -1.92927 -1.96846 -1.99210 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 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 -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 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.97808 1.91280 1.80560 1.65881 1.47567 1.26018 1.01706 0.75166 0.46977 0.17759 -0.11848 -0.41196 -0.69640 -0.96558 -1.21360 -1.43501 -1.62497 -1.77931 -1.89465 -1.96846 -1.99912 -1.98596 -1.92927 -1.83029 -1.69119 -1.51502 -1.30564 -1.06765 -0.80625 -0.52717 -0.23655 0.05927 0.35378 0.64054 0.91326 1.16596 1.39310 1.58971 1.75147 1.87484 1.95711 1.99649 1.99210 1.94405 1.85338 1.72209 1.55305 1.34997 1.11729 0.86013 0.58411 0.29529 0.00000 -0.29529 -0.58411 -0.86013 -1.11729 -1.34997 -1.55305 -1.72209 -1.85338 -1.94405 -1.99210 -1.99649 -1.95711 -1.87484 -1.75147 -1.58971 -1.39310 -1.16596 -0.91326 -0.64054 -0.35378 -0.05927 0.23655 0.52717 0.80625 1.06765 1.30564 1.51502 1.69119 1.83029 1.92927 1.98596 1.99912 1.96846 1.89465 1.77931 1.62497 1.43501 1.21360 0.96558 0.69640 0.41196 0.11848 -0.17759 -0.46977 -0.75166 -1.01706 -1.26018 -1.47567 -1.65881 -1.80560 -1.91280 -1.97808 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 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 0.17759 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 -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 -0.17759 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.95711 1.83029 1.62497 1.34997 1.01706 0.64054 0.23655 -0.17759 -0.58411 -0.96558 -1.30564 -1.58971 -1.80560 -1.94405 -1.99912 -1.96846 -1.85338 -1.65881 -1.39310 -1.06765 -0.69640 -0.29529 0.11848 0.52717 0.91326 1.26018 1.55305 1.77931 1.92927 1.99649 1.97808 1.87484 1.69119 1.43501 1.11729 0.75166 0.35378 -0.05927 -0.46977 -0.86013 -1.21360 -1.51502 -1.75147 -1.91280 -1.99210 -1.98596 -1.89465 -1.72209 -1.47567 -1.16596 -0.80625 -0.41196 0.00000 0.41196 0.80625 1.16596 1.47567 1.72209 1.89465 1.98596 1.99210 1.91280 1.75147 1.51502 1.21360 0.86013 0.46977 0.05927 -0.35378 -0.75166 -1.11729 -1.43501 -1.69119 -1.87484 -1.97808 -1.99649 -1.92927 -1.77931 -1.55305 -1.26018 -0.91326 -0.52717 -0.11848 0.29529 0.69640 1.06765 1.39310 1.65881 1.85338 1.96846 1.99912 1.94405 1.80560 1.58971 1.30564 0.96558 0.58411 0.17759 -0.23655 -0.64054 -1.01706 -1.34997 -1.62497 -1.83029 -1.95711 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 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 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 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.92927 1.72209 1.39310 0.96558 0.46977 -0.05927 -0.58411 -1.06765 -1.47567 -1.77931 -1.95711 -1.99649 -1.89465 -1.65881 -1.30564 -0.86013 -0.35378 0.17759 0.69640 1.16596 1.55305 1.83029 1.97808 1.98596 1.85338 1.58971 1.21360 0.75166 0.23655 -0.29529 -0.80625 -1.26018 -1.62497 -1.87484 -1.99210 -1.96846 -1.80560 -1.51502 -1.11729 -0.64054 -0.11848 0.41196 0.91326 1.34997 1.69119 1.91280 1.99912 1.94405 1.75147 1.43501 1.01706 0.52717 0.00000 -0.52717 -1.01706 -1.43501 -1.75147 -1.94405 -1.99912 -1.91280 -1.69119 -1.34997 -0.91326 -0.41196 0.11848 0.64054 1.11729 1.51502 1.80560 1.96846 1.99210 1.87484 1.62497 1.26018 0.80625 0.29529 -0.23655 -0.75166 -1.21360 -1.58971 -1.85338 -1.98596 -1.97808 -1.83029 -1.55305 -1.16596 -0.69640 -0.17759 0.35378 0.86013 1.30564 1.65881 1.89465 1.99649 1.95711 1.77931 1.47567 1.06765 0.58411 0.05927 -0.46977 -0.96558 -1.39310 -1.72209 -1.92927 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E102 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 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 -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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E103 2.00000 -1.99210 1.96846 -1.92927 1.87484 -1.80560 1.72209 -1.62497 1.51502 -1.39310 1.26018 -1.11729 0.96558 -0.80625 0.64054 -0.46977 0.29529 -0.11848 -0.05927 0.23655 -0.41196 0.58411 -0.75166 0.91326 -1.06765 1.21360 -1.34997 1.47567 -1.58971 1.69119 -1.77931 1.85338 -1.91280 1.95711 -1.98596 1.99912 -1.99649 1.97808 -1.94405 1.89465 -1.83029 1.75147 -1.65881 1.55305 -1.43501 1.30564 -1.16596 1.01706 -0.86013 0.69640 -0.52717 0.35378 -0.17759 0.00000 0.17759 -0.35378 0.52717 -0.69640 0.86013 -1.01706 1.16596 -1.30564 1.43501 -1.55305 1.65881 -1.75147 1.83029 -1.89465 1.94405 -1.97808 1.99649 -1.99912 1.98596 -1.95711 1.91280 -1.85338 1.77931 -1.69119 1.58971 -1.47567 1.34997 -1.21360 1.06765 -0.91326 0.75166 -0.58411 0.41196 -0.23655 0.05927 0.11848 -0.29529 0.46977 -0.64054 0.80625 -0.96558 1.11729 -1.26018 1.39310 -1.51502 1.62497 -1.72209 1.80560 -1.87484 1.92927 -1.96846 1.99210 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E104 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 0.05927 -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 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 0.05927 -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 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E105 2.00000 -1.99912 1.99649 -1.99210 1.98596 -1.97808 1.96846 -1.95711 1.94405 -1.92927 1.91280 -1.89465 1.87484 -1.85338 1.83029 -1.80560 1.77931 -1.75147 1.72209 -1.69119 1.65881 -1.62497 1.58971 -1.55305 1.51502 -1.47567 1.43501 -1.39310 1.34997 -1.30564 1.26018 -1.21360 1.16596 -1.11729 1.06765 -1.01706 0.96558 -0.91326 0.86013 -0.80625 0.75166 -0.69640 0.64054 -0.58411 0.52717 -0.46977 0.41196 -0.35378 0.29529 -0.23655 0.17759 -0.11848 0.05927 0.00000 -0.05927 0.11848 -0.17759 0.23655 -0.29529 0.35378 -0.41196 0.46977 -0.52717 0.58411 -0.64054 0.69640 -0.75166 0.80625 -0.86013 0.91326 -0.96558 1.01706 -1.06765 1.11729 -1.16596 1.21360 -1.26018 1.30564 -1.34997 1.39310 -1.43501 1.47567 -1.51502 1.55305 -1.58971 1.62497 -1.65881 1.69119 -1.72209 1.75147 -1.77931 1.80560 -1.83029 1.85338 -1.87484 1.89465 -1.91280 1.92927 -1.94405 1.95711 -1.96846 1.97808 -1.98596 1.99210 -1.99649 1.99912 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999121673018 = 2*cos(2*π/212) = 2*cos(π/106) 1.996487463529 = 2*cos(4*π/212) = 2*cos(π/53) 1.992099685230 = 2*cos(6*π/212) = 2*cos(3*π/106) 1.985962192027 = 2*cos(8*π/212) = 2*cos(2*π/53) 1.978080374644 = 2*cos(10*π/212) = 2*cos(5*π/106) 1.968461155895 = 2*cos(12*π/212) = 2*cos(3*π/53) 1.957112984599 = 2*cos(14*π/212) = 2*cos(7*π/106) 1.944045828161 = 2*cos(16*π/212) = 2*cos(4*π/53) 1.929271163817 = 2*cos(18*π/212) = 2*cos(9*π/106) 1.912801968553 = 2*cos(20*π/212) = 2*cos(5*π/53) 1.894652707708 = 2*cos(22*π/212) = 2*cos(11*π/106) 1.874839322268 = 2*cos(24*π/212) = 2*cos(6*π/53) 1.853379214864 = 2*cos(26*π/212) = 2*cos(13*π/106) 1.830291234486 = 2*cos(28*π/212) = 2*cos(7*π/53) 1.805595659931 = 2*cos(30*π/212) = 2*cos(15*π/106) 1.779314181989 = 2*cos(32*π/212) = 2*cos(8*π/53) 1.751469884391 = 2*cos(34*π/212) = 2*cos(17*π/106) 1.722087223535 = 2*cos(36*π/212) = 2*cos(9*π/53) 1.691192007004 = 2*cos(38*π/212) = 2*cos(19*π/106) 1.658811370900 = 2*cos(40*π/212) = 2*cos(10*π/53) 1.624973756011 = 2*cos(42*π/212) = 2*cos(21*π/106) 1.589708882827 = 2*cos(44*π/212) = 2*cos(11*π/53) 1.553047725436 = 2*cos(46*π/212) = 2*cos(23*π/106) 1.515022484323 = 2*cos(48*π/212) = 2*cos(12*π/53) 1.475666558083 = 2*cos(50*π/212) = 2*cos(25*π/106) 1.435014514089 = 2*cos(52*π/212) = 2*cos(13*π/53) 1.393102058126 = 2*cos(54*π/212) = 2*cos(27*π/106) 1.349966003036 = 2*cos(56*π/212) = 2*cos(14*π/53) 1.305644236381 = 2*cos(58*π/212) = 2*cos(29*π/106) 1.260175687163 = 2*cos(60*π/212) = 2*cos(15*π/53) 1.213600291637 = 2*cos(62*π/212) = 2*cos(31*π/106) 1.165958958229 = 2*cos(64*π/212) = 2*cos(16*π/53) 1.117293531607 = 2*cos(66*π/212) = 2*cos(33*π/106) 1.067646755930 = 2*cos(68*π/212) = 2*cos(17*π/53) 1.017062237298 = 2*cos(70*π/212) = 2*cos(35*π/106) 0.965584405461 = 2*cos(72*π/212) = 2*cos(18*π/53) 0.913258474787 = 2*cos(74*π/212) = 2*cos(37*π/106) 0.860130404553 = 2*cos(76*π/212) = 2*cos(19*π/53) 0.806246858576 = 2*cos(78*π/212) = 2*cos(39*π/106) 0.751655164228 = 2*cos(80*π/212) = 2*cos(20*π/53) 0.696403270869 = 2*cos(82*π/212) = 2*cos(41*π/106) 0.640539707726 = 2*cos(84*π/212) = 2*cos(21*π/53) 0.584113541274 = 2*cos(86*π/212) = 2*cos(43*π/106) 0.527174332138 = 2*cos(88*π/212) = 2*cos(22*π/53) 0.469772091562 = 2*cos(90*π/212) = 2*cos(45*π/106) 0.411957237482 = 2*cos(92*π/212) = 2*cos(23*π/53) 0.353780550245 = 2*cos(94*π/212) = 2*cos(47*π/106) 0.295293128005 = 2*cos(96*π/212) = 2*cos(24*π/53) 0.236546341843 = 2*cos(98*π/212) = 2*cos(49*π/106) 0.177591790646 = 2*cos(100*π/212) = 2*cos(25*π/53) 0.118481255787 = 2*cos(102*π/212) = 2*cos(51*π/106) 0.059266655645 = 2*cos(104*π/212) = 2*cos(26*π/53) 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 E97 m E98 l E99 k+m E100 j+l E101 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)} E102 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E103 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E104 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E105 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_106d point group is 424, and the order of the principal axis (S₂₁₂) is 212. The group has 109 irreducible representations. β The D_106d point group is isomorphic to C_212v and D₂₁₂. γ The D_106d point group is generated by two symmetry elements, S₂₁₂ 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_106d 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_106d point group was created by Gernot Katzer.

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

	D_104d
	D_105d
C₁₀₆ C_106v C_106h D₁₀₆ D_106h	D_106d	S₁₀₆
	D_107d
	D_108d

Character table for the D106d point group

Character table for the D_106d point group