Character Table for Point Group D100d

Character table for the D_100d point group

D100d E 2 S200 2 C100 2 S200^3 2 C50 2 S40 2 C100^3 2 S200^7 2 C25 2 S200^9 2 C20 2 S200^11 2 C50^3 2 S200^13 2 C100^7 2 S40^3 2 C25^2 2 S200^17 2 C100^9 2 S200^19 2 C10 2 S200^21 2 C100^11 2 S200^23 2 C25^3 2 S8 2 C100^13 2 S200^27 2 C50^7 2 S200^29 2 C20^3 2 S200^31 2 C25^4 2 S200^33 2 C100^17 2 S40^7 2 C50^9 2 S200^37 2 C100^19 2 S200^39 2 C5 2 S200^41 2 C100^21 2 S200^43 2 C50^11 2 S40^9 2 C100^23 2 S200^47 2 C25^6 2 S200^49 2 C4 2 S200^51 2 C50^13 2 S200^53 2 C100^27 2 S40^11 2 C25^7 2 S200^57 2 C100^29 2 S200^59 2 C10^3 2 S200^61 2 C100^31 2 S200^63 2 C25^8 2 S40^13 2 C100^33 2 S200^67 2 C50^17 2 S200^69 2 C20^7 2 S200^71 2 C25^9 2 S200^73 2 C100^37 2 S8^3 2 C50^19 2 S200^77 2 C100^39 2 S200^79 2 C5^2 2 S200^81 2 C100^41 2 S200^83 2 C50^21 2 S40^17 2 C100^43 2 S200^87 2 C25^11 2 S200^89 2 C20^9 2 S200^91 2 C50^23 2 S200^93 2 C100^47 2 S40^19 2 C25^12 2 S200^97 2 C100^49 2 S200^99 C2 100 C2' 100 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 ... ... ....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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99901 1.99605 1.99112 1.98423 1.97538 1.96457 1.95183 1.93717 1.92059 1.90211 1.88176 1.85955 1.83551 1.80965 1.78201 1.75261 1.72148 1.68866 1.65416 1.61803 1.58031 1.54103 1.50022 1.45794 1.41421 1.36909 1.32262 1.27485 1.22581 1.17557 1.12417 1.07165 1.01808 0.96351 0.90798 0.85156 0.79430 0.73625 0.67748 0.61803 0.55798 0.49738 0.43629 0.37476 0.31287 0.25067 0.18822 0.12558 0.06282 0.00000 -0.06282 -0.12558 -0.18822 -0.25067 -0.31287 -0.37476 -0.43629 -0.49738 -0.55798 -0.61803 -0.67748 -0.73625 -0.79430 -0.85156 -0.90798 -0.96351 -1.01808 -1.07165 -1.12417 -1.17557 -1.22581 -1.27485 -1.32262 -1.36909 -1.41421 -1.45794 -1.50022 -1.54103 -1.58031 -1.61803 -1.65416 -1.68866 -1.72148 -1.75261 -1.78201 -1.80965 -1.83551 -1.85955 -1.88176 -1.90211 -1.92059 -1.93717 -1.95183 -1.96457 -1.97538 -1.98423 -1.99112 -1.99605 -1.99901 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99605 1.98423 1.96457 1.93717 1.90211 1.85955 1.80965 1.75261 1.68866 1.61803 1.54103 1.45794 1.36909 1.27485 1.17557 1.07165 0.96351 0.85156 0.73625 0.61803 0.49738 0.37476 0.25067 0.12558 0.00000 -0.12558 -0.25067 -0.37476 -0.49738 -0.61803 -0.73625 -0.85156 -0.96351 -1.07165 -1.17557 -1.27485 -1.36909 -1.45794 -1.54103 -1.61803 -1.68866 -1.75261 -1.80965 -1.85955 -1.90211 -1.93717 -1.96457 -1.98423 -1.99605 -2.00000 -1.99605 -1.98423 -1.96457 -1.93717 -1.90211 -1.85955 -1.80965 -1.75261 -1.68866 -1.61803 -1.54103 -1.45794 -1.36909 -1.27485 -1.17557 -1.07165 -0.96351 -0.85156 -0.73625 -0.61803 -0.49738 -0.37476 -0.25067 -0.12558 0.00000 0.12558 0.25067 0.37476 0.49738 0.61803 0.73625 0.85156 0.96351 1.07165 1.17557 1.27485 1.36909 1.45794 1.54103 1.61803 1.68866 1.75261 1.80965 1.85955 1.90211 1.93717 1.96457 1.98423 1.99605 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99112 1.96457 1.92059 1.85955 1.78201 1.68866 1.58031 1.45794 1.32262 1.17557 1.01808 0.85156 0.67748 0.49738 0.31287 0.12558 -0.06282 -0.25067 -0.43629 -0.61803 -0.79430 -0.96351 -1.12417 -1.27485 -1.41421 -1.54103 -1.65416 -1.75261 -1.83551 -1.90211 -1.95183 -1.98423 -1.99901 -1.99605 -1.97538 -1.93717 -1.88176 -1.80965 -1.72148 -1.61803 -1.50022 -1.36909 -1.22581 -1.07165 -0.90798 -0.73625 -0.55798 -0.37476 -0.18822 0.00000 0.18822 0.37476 0.55798 0.73625 0.90798 1.07165 1.22581 1.36909 1.50022 1.61803 1.72148 1.80965 1.88176 1.93717 1.97538 1.99605 1.99901 1.98423 1.95183 1.90211 1.83551 1.75261 1.65416 1.54103 1.41421 1.27485 1.12417 0.96351 0.79430 0.61803 0.43629 0.25067 0.06282 -0.12558 -0.31287 -0.49738 -0.67748 -0.85156 -1.01808 -1.17557 -1.32262 -1.45794 -1.58031 -1.68866 -1.78201 -1.85955 -1.92059 -1.96457 -1.99112 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 2.00000 1.98423 1.93717 1.85955 1.75261 1.61803 1.45794 1.27485 1.07165 0.85156 0.61803 0.37476 0.12558 -0.12558 -0.37476 -0.61803 -0.85156 -1.07165 -1.27485 -1.45794 -1.61803 -1.75261 -1.85955 -1.93717 -1.98423 -2.00000 -1.98423 -1.93717 -1.85955 -1.75261 -1.61803 -1.45794 -1.27485 -1.07165 -0.85156 -0.61803 -0.37476 -0.12558 0.12558 0.37476 0.61803 0.85156 1.07165 1.27485 1.45794 1.61803 1.75261 1.85955 1.93717 1.98423 2.00000 1.98423 1.93717 1.85955 1.75261 1.61803 1.45794 1.27485 1.07165 0.85156 0.61803 0.37476 0.12558 -0.12558 -0.37476 -0.61803 -0.85156 -1.07165 -1.27485 -1.45794 -1.61803 -1.75261 -1.85955 -1.93717 -1.98423 -2.00000 -1.98423 -1.93717 -1.85955 -1.75261 -1.61803 -1.45794 -1.27485 -1.07165 -0.85156 -0.61803 -0.37476 -0.12558 0.12558 0.37476 0.61803 0.85156 1.07165 1.27485 1.45794 1.61803 1.75261 1.85955 1.93717 1.98423 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 -1.97538 -1.90211 -1.78201 -1.61803 -1.41421 -1.17557 -0.90798 -0.61803 -0.31287 0.00000 0.31287 0.61803 0.90798 1.17557 1.41421 1.61803 1.78201 1.90211 1.97538 2.00000 1.97538 1.90211 1.78201 1.61803 1.41421 1.17557 0.90798 0.61803 0.31287 0.00000 -0.31287 -0.61803 -0.90798 -1.17557 -1.41421 -1.61803 -1.78201 -1.90211 -1.97538 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.96457 1.85955 1.68866 1.45794 1.17557 0.85156 0.49738 0.12558 -0.25067 -0.61803 -0.96351 -1.27485 -1.54103 -1.75261 -1.90211 -1.98423 -1.99605 -1.93717 -1.80965 -1.61803 -1.36909 -1.07165 -0.73625 -0.37476 0.00000 0.37476 0.73625 1.07165 1.36909 1.61803 1.80965 1.93717 1.99605 1.98423 1.90211 1.75261 1.54103 1.27485 0.96351 0.61803 0.25067 -0.12558 -0.49738 -0.85156 -1.17557 -1.45794 -1.68866 -1.85955 -1.96457 -2.00000 -1.96457 -1.85955 -1.68866 -1.45794 -1.17557 -0.85156 -0.49738 -0.12558 0.25067 0.61803 0.96351 1.27485 1.54103 1.75261 1.90211 1.98423 1.99605 1.93717 1.80965 1.61803 1.36909 1.07165 0.73625 0.37476 0.00000 -0.37476 -0.73625 -1.07165 -1.36909 -1.61803 -1.80965 -1.93717 -1.99605 -1.98423 -1.90211 -1.75261 -1.54103 -1.27485 -0.96351 -0.61803 -0.25067 0.12558 0.49738 0.85156 1.17557 1.45794 1.68866 1.85955 1.96457 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.95183 1.80965 1.58031 1.27485 0.90798 0.49738 0.06282 -0.37476 -0.79430 -1.17557 -1.50022 -1.75261 -1.92059 -1.99605 -1.97538 -1.85955 -1.65416 -1.36909 -1.01808 -0.61803 -0.18822 0.25067 0.67748 1.07165 1.41421 1.68866 1.88176 1.98423 1.99112 1.90211 1.72148 1.45794 1.12417 0.73625 0.31287 -0.12558 -0.55798 -0.96351 -1.32262 -1.61803 -1.83551 -1.96457 -1.99901 -1.93717 -1.78201 -1.54103 -1.22581 -0.85156 -0.43629 0.00000 0.43629 0.85156 1.22581 1.54103 1.78201 1.93717 1.99901 1.96457 1.83551 1.61803 1.32262 0.96351 0.55798 0.12558 -0.31287 -0.73625 -1.12417 -1.45794 -1.72148 -1.90211 -1.99112 -1.98423 -1.88176 -1.68866 -1.41421 -1.07165 -0.67748 -0.25067 0.18822 0.61803 1.01808 1.36909 1.65416 1.85955 1.97538 1.99605 1.92059 1.75261 1.50022 1.17557 0.79430 0.37476 -0.06282 -0.49738 -0.90798 -1.27485 -1.58031 -1.80965 -1.95183 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 1.93717 1.75261 1.45794 1.07165 0.61803 0.12558 -0.37476 -0.85156 -1.27485 -1.61803 -1.85955 -1.98423 -1.98423 -1.85955 -1.61803 -1.27485 -0.85156 -0.37476 0.12558 0.61803 1.07165 1.45794 1.75261 1.93717 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.92059 1.68866 1.32262 0.85156 0.31287 -0.25067 -0.79430 -1.27485 -1.65416 -1.90211 -1.99901 -1.93717 -1.72148 -1.36909 -0.90798 -0.37476 0.18822 0.73625 1.22581 1.61803 1.88176 1.99605 1.95183 1.75261 1.41421 0.96351 0.43629 -0.12558 -0.67748 -1.17557 -1.58031 -1.85955 -1.99112 -1.96457 -1.78201 -1.45794 -1.01808 -0.49738 0.06282 0.61803 1.12417 1.54103 1.83551 1.98423 1.97538 1.80965 1.50022 1.07165 0.55798 0.00000 -0.55798 -1.07165 -1.50022 -1.80965 -1.97538 -1.98423 -1.83551 -1.54103 -1.12417 -0.61803 -0.06282 0.49738 1.01808 1.45794 1.78201 1.96457 1.99112 1.85955 1.58031 1.17557 0.67748 0.12558 -0.43629 -0.96351 -1.41421 -1.75261 -1.95183 -1.99605 -1.88176 -1.61803 -1.22581 -0.73625 -0.18822 0.37476 0.90798 1.36909 1.72148 1.93717 1.99901 1.90211 1.65416 1.27485 0.79430 0.25067 -0.31287 -0.85156 -1.32262 -1.68866 -1.92059 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 1.90211 1.61803 1.17557 0.61803 0.00000 -0.61803 -1.17557 -1.61803 -1.90211 -2.00000 -1.90211 -1.61803 -1.17557 -0.61803 0.00000 0.61803 1.17557 1.61803 1.90211 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E98 2.00000 -1.99605 1.98423 -1.96457 1.93717 -1.90211 1.85955 -1.80965 1.75261 -1.68866 1.61803 -1.54103 1.45794 -1.36909 1.27485 -1.17557 1.07165 -0.96351 0.85156 -0.73625 0.61803 -0.49738 0.37476 -0.25067 0.12558 0.00000 -0.12558 0.25067 -0.37476 0.49738 -0.61803 0.73625 -0.85156 0.96351 -1.07165 1.17557 -1.27485 1.36909 -1.45794 1.54103 -1.61803 1.68866 -1.75261 1.80965 -1.85955 1.90211 -1.93717 1.96457 -1.98423 1.99605 -2.00000 1.99605 -1.98423 1.96457 -1.93717 1.90211 -1.85955 1.80965 -1.75261 1.68866 -1.61803 1.54103 -1.45794 1.36909 -1.27485 1.17557 -1.07165 0.96351 -0.85156 0.73625 -0.61803 0.49738 -0.37476 0.25067 -0.12558 0.00000 0.12558 -0.25067 0.37476 -0.49738 0.61803 -0.73625 0.85156 -0.96351 1.07165 -1.17557 1.27485 -1.36909 1.45794 -1.54103 1.61803 -1.68866 1.75261 -1.80965 1.85955 -1.90211 1.93717 -1.96457 1.98423 -1.99605 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E99 2.00000 -1.99901 1.99605 -1.99112 1.98423 -1.97538 1.96457 -1.95183 1.93717 -1.92059 1.90211 -1.88176 1.85955 -1.83551 1.80965 -1.78201 1.75261 -1.72148 1.68866 -1.65416 1.61803 -1.58031 1.54103 -1.50022 1.45794 -1.41421 1.36909 -1.32262 1.27485 -1.22581 1.17557 -1.12417 1.07165 -1.01808 0.96351 -0.90798 0.85156 -0.79430 0.73625 -0.67748 0.61803 -0.55798 0.49738 -0.43629 0.37476 -0.31287 0.25067 -0.18822 0.12558 -0.06282 0.00000 0.06282 -0.12558 0.18822 -0.25067 0.31287 -0.37476 0.43629 -0.49738 0.55798 -0.61803 0.67748 -0.73625 0.79430 -0.85156 0.90798 -0.96351 1.01808 -1.07165 1.12417 -1.17557 1.22581 -1.27485 1.32262 -1.36909 1.41421 -1.45794 1.50022 -1.54103 1.58031 -1.61803 1.65416 -1.68866 1.72148 -1.75261 1.78201 -1.80965 1.83551 -1.85955 1.88176 -1.90211 1.92059 -1.93717 1.95183 -1.96457 1.97538 -1.98423 1.99112 -1.99605 1.99901 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999013120731 = 2*cos(2*π/200) = 2*cos(π/100) 1.996053456857 = 2*cos(4*π/200) = 2*cos(π/50) 1.991123929206 = 2*cos(6*π/200) = 2*cos(3*π/100) 1.984229402629 = 2*cos(8*π/200) = 2*cos(π/25) 1.975376681190 = 2*cos(10*π/200) = 2*cos(π/20) = (√2+√10+2*(√5−√5))/4 1.964574501457 = 2*cos(12*π/200) = 2*cos(3*π/50) 1.951833523877 = 2*cos(14*π/200) = 2*cos(7*π/100) 1.937166322257 = 2*cos(16*π/200) = 2*cos(2*π/25) 1.920587371354 = 2*cos(18*π/200) = 2*cos(9*π/100) 1.902113032590 = 2*cos(20*π/200) = 2*cos(π/10) = (√10+2*√5)/2 1.881761537908 = 2*cos(22*π/200) = 2*cos(11*π/100) 1.859552971777 = 2*cos(24*π/200) = 2*cos(3*π/25) 1.835509251368 = 2*cos(26*π/200) = 2*cos(13*π/100) 1.809654104932 = 2*cos(28*π/200) = 2*cos(7*π/50) 1.782013048377 = 2*cos(30*π/200) = 2*cos(3*π/20) = (√10−√2+2*√5+√5)/4 1.752613360088 = 2*cos(32*π/200) = 2*cos(4*π/25) 1.721484054008 = 2*cos(34*π/200) = 2*cos(17*π/100) 1.688655851004 = 2*cos(36*π/200) = 2*cos(9*π/50) 1.654161148549 = 2*cos(38*π/200) = 2*cos(19*π/100) 1.618033988750 = 2*cos(40*π/200) = 2*cos(π/5) = (√5+1)/2 1.580310024751 = 2*cos(42*π/200) = 2*cos(21*π/100) 1.541026485552 = 2*cos(44*π/200) = 2*cos(11*π/50) 1.500222139261 = 2*cos(46*π/200) = 2*cos(23*π/100) 1.457937254843 = 2*cos(48*π/200) = 2*cos(6*π/25) 1.414213562373 = 2*cos(50*π/200) = 2*cos(π/4) = √2 1.369094211857 = 2*cos(52*π/200) = 2*cos(13*π/50) 1.322623730647 = 2*cos(54*π/200) = 2*cos(27*π/100) 1.274847979497 = 2*cos(56*π/200) = 2*cos(7*π/25) 1.225814107306 = 2*cos(58*π/200) = 2*cos(29*π/100) 1.175570504585 = 2*cos(60*π/200) = 2*cos(3*π/10) = (√10−2*√5)/2 1.124166755704 = 2*cos(62*π/200) = 2*cos(31*π/100) 1.071653589958 = 2*cos(64*π/200) = 2*cos(8*π/25) 1.018082831501 = 2*cos(66*π/200) = 2*cos(33*π/100) 0.963507348203 = 2*cos(68*π/200) = 2*cos(17*π/50) 0.907980999479 = 2*cos(70*π/200) = 2*cos(7*π/20) = (√2−√10+2*√5+√5)/4 0.851558583130 = 2*cos(72*π/200) = 2*cos(9*π/25) 0.794295781270 = 2*cos(74*π/200) = 2*cos(37*π/100) 0.736249105369 = 2*cos(76*π/200) = 2*cos(19*π/50) 0.677475840491 = 2*cos(78*π/200) = 2*cos(39*π/100) 0.618033988750 = 2*cos(80*π/200) = 2*cos(2*π/5) = (√5−1)/2 0.557982212078 = 2*cos(82*π/200) = 2*cos(41*π/100) 0.497379774330 = 2*cos(84*π/200) = 2*cos(21*π/50) 0.436286482793 = 2*cos(86*π/200) = 2*cos(43*π/100) 0.374762629171 = 2*cos(88*π/200) = 2*cos(11*π/25) 0.312868930080 = 2*cos(90*π/200) = 2*cos(9*π/20) = (√2+√10−2*(√5−√5))/4 0.250666467129 = 2*cos(92*π/200) = 2*cos(23*π/50) 0.188216626637 = 2*cos(94*π/200) = 2*cos(47*π/100) 0.125581039059 = 2*cos(96*π/200) = 2*cos(12*π/25) 0.062821518156 = 2*cos(98*π/200) = 2*cos(49*π/100) 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 E91 m E92 l E93 k+m E94 j+l E95 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)} E96 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E97 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E98 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E99 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_100d point group is 400, and the order of the principal axis (S₂₀₀) is 200. The group has 103 irreducible representations. β The D_100d point group is isomorphic to C_200v and D₂₀₀. γ The D_100d point group is generated by two symmetry elements, S₂₀₀ 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_100d 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_100d point group was created by Gernot Katzer.

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

	D_98d
	D_99d
C₁₀₀ C_100v C_100h D₁₀₀ D_100h	D_100d	S₁₀₀
	D_101d
	D_102d

Character table for the D100d point group

Character table for the D_100d point group