Character table for the S100 point group

S100    E         2 S100    2 C50     2 S100^3  2 C25     2 S20     2 C50^3   2 S100^7  2 C25^2   2 S100^9  2 C10     2 S100^11 2 C25^3   2 S100^13 2 C50^7   2 S20^3   2 C25^4   2 S100^17 2 C50^9   2 S100^19 2 C5      2 S100^21 2 C50^11  2 S100^23 2 C25^6   2 S4      2 C50^13  2 S100^27 2 C25^7   2 S100^29 2 C10^3   2 S100^31 2 C25^8   2 S100^33 2 C50^17  2 S20^7   2 C25^9   2 S100^37 2 C50^19  2 S100^39 2 C5^2    2 S100^41 2 C50^21  2 S100^43 2 C25^11  2 S20^9   2 C50^23  2 S100^47 2 C25^12  2 S100^49 C2           <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A        1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000   1.00000     ..T ... ....T ....... ........T ........... ............T
B        1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -1.00000   1.00000  -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   1.99605   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     ... TT. ..... ....TT. ......... ........TT. .............
E2  *    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     ... ... TT... ....... ....TT... ........... ........TT...
E3  *    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     ... ... ..... TT..... ......... ....TT..... .............
E4  *    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     ... ... ..... ....... TT....... ........... ....TT.......
E5  *    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     ... ... ..... ....... ......... TT......... .............
E6  *    2.00000   1.85955   1.45794   0.85156   0.12558  -0.61803  -1.27485  -1.75261  -1.98423  -1.93717  -1.61803  -1.07165  -0.37476   0.37476   1.07165   1.61803   1.93717   1.98423   1.75261   1.27485   0.61803  -0.12558  -0.85156  -1.45794  -1.85955  -2.00000  -1.85955  -1.45794  -0.85156  -0.12558   0.61803   1.27485   1.75261   1.98423   1.93717   1.61803   1.07165   0.37476  -0.37476  -1.07165  -1.61803  -1.93717  -1.98423  -1.75261  -1.27485  -0.61803   0.12558   0.85156   1.45794   1.85955   2.00000     ... ... ..... ....... ......... ........... TT...........
E7  *    2.00000   1.80965   1.27485   0.49738  -0.37476  -1.17557  -1.75261  -1.99605  -1.85955  -1.36909  -0.61803   0.25067   1.07165   1.68866   1.98423   1.90211   1.45794   0.73625  -0.12558  -0.96351  -1.61803  -1.96457  -1.93717  -1.54103  -0.85156   0.00000   0.85156   1.54103   1.93717   1.96457   1.61803   0.96351   0.12558  -0.73625  -1.45794  -1.90211  -1.98423  -1.68866  -1.07165  -0.25067   0.61803   1.36909   1.85955   1.99605   1.75261   1.17557   0.37476  -0.49738  -1.27485  -1.80965  -2.00000     ... ... ..... ....... ......... ........... .............
E8  *    2.00000   1.75261   1.07165   0.12558  -0.85156  -1.61803  -1.98423  -1.85955  -1.27485  -0.37476   0.61803   1.45794   1.93717   1.93717   1.45794   0.61803  -0.37476  -1.27485  -1.85955  -1.98423  -1.61803  -0.85156   0.12558   1.07165   1.75261   2.00000   1.75261   1.07165   0.12558  -0.85156  -1.61803  -1.98423  -1.85955  -1.27485  -0.37476   0.61803   1.45794   1.93717   1.93717   1.45794   0.61803  -0.37476  -1.27485  -1.85955  -1.98423  -1.61803  -0.85156   0.12558   1.07165   1.75261   2.00000     ... ... ..... ....... ......... ........... .............
E9  *    2.00000   1.68866   0.85156  -0.25067  -1.27485  -1.90211  -1.93717  -1.36909  -0.37476   0.73625   1.61803   1.99605   1.75261   0.96351  -0.12558  -1.17557  -1.85955  -1.96457  -1.45794  -0.49738   0.61803   1.54103   1.98423   1.80965   1.07165   0.00000  -1.07165  -1.80965  -1.98423  -1.54103  -0.61803   0.49738   1.45794   1.96457   1.85955   1.17557   0.12558  -0.96351  -1.75261  -1.99605  -1.61803  -0.73625   0.37476   1.36909   1.93717   1.90211   1.27485   0.25067  -0.85156  -1.68866  -2.00000     ... ... ..... ....... ......... ........... .............
E10 *    2.00000   1.61803   0.61803  -0.61803  -1.61803  -2.00000  -1.61803  -0.61803   0.61803   1.61803   2.00000   1.61803   0.61803  -0.61803  -1.61803  -2.00000  -1.61803  -0.61803   0.61803   1.61803   2.00000   1.61803   0.61803  -0.61803  -1.61803  -2.00000  -1.61803  -0.61803   0.61803   1.61803   2.00000   1.61803   0.61803  -0.61803  -1.61803  -2.00000  -1.61803  -0.61803   0.61803   1.61803   2.00000   1.61803   0.61803  -0.61803  -1.61803  -2.00000  -1.61803  -0.61803   0.61803   1.61803   2.00000     ... ... ..... ....... ......... ........... .............
E11 *    2.00000   1.54103   0.37476  -0.96351  -1.85955  -1.90211  -1.07165   0.25067   1.45794   1.99605   1.61803   0.49738  -0.85156  -1.80965  -1.93717  -1.17557   0.12558   1.36909   1.98423   1.68866   0.61803  -0.73625  -1.75261  -1.96457  -1.27485   0.00000   1.27485   1.96457   1.75261   0.73625  -0.61803  -1.68866  -1.98423  -1.36909  -0.12558   1.17557   1.93717   1.80965   0.85156  -0.49738  -1.61803  -1.99605  -1.45794  -0.25067   1.07165   1.90211   1.85955   0.96351  -0.37476  -1.54103  -2.00000     ... ... ..... ....... ......... ........... .............
E12 *    2.00000   1.45794   0.12558  -1.27485  -1.98423  -1.61803  -0.37476   1.07165   1.93717   1.75261   0.61803  -0.85156  -1.85955  -1.85955  -0.85156   0.61803   1.75261   1.93717   1.07165  -0.37476  -1.61803  -1.98423  -1.27485   0.12558   1.45794   2.00000   1.45794   0.12558  -1.27485  -1.98423  -1.61803  -0.37476   1.07165   1.93717   1.75261   0.61803  -0.85156  -1.85955  -1.85955  -0.85156   0.61803   1.75261   1.93717   1.07165  -0.37476  -1.61803  -1.98423  -1.27485   0.12558   1.45794   2.00000     ... ... ..... ....... ......... ........... .............
E13 *    2.00000   1.36909  -0.12558  -1.54103  -1.98423  -1.17557   0.37476   1.68866   1.93717   0.96351  -0.61803  -1.80965  -1.85955  -0.73625   0.85156   1.90211   1.75261   0.49738  -1.07165  -1.96457  -1.61803  -0.25067   1.27485   1.99605   1.45794   0.00000  -1.45794  -1.99605  -1.27485   0.25067   1.61803   1.96457   1.07165  -0.49738  -1.75261  -1.90211  -0.85156   0.73625   1.85955   1.80965   0.61803  -0.96351  -1.93717  -1.68866  -0.37476   1.17557   1.98423   1.54103   0.12558  -1.36909  -2.00000     ... ... ..... ....... ......... ........... .............
E14 *    2.00000   1.27485  -0.37476  -1.75261  -1.85955  -0.61803   1.07165   1.98423   1.45794  -0.12558  -1.61803  -1.93717  -0.85156   0.85156   1.93717   1.61803   0.12558  -1.45794  -1.98423  -1.07165   0.61803   1.85955   1.75261   0.37476  -1.27485  -2.00000  -1.27485   0.37476   1.75261   1.85955   0.61803  -1.07165  -1.98423  -1.45794   0.12558   1.61803   1.93717   0.85156  -0.85156  -1.93717  -1.61803  -0.12558   1.45794   1.98423   1.07165  -0.61803  -1.85955  -1.75261  -0.37476   1.27485   2.00000     ... ... ..... ....... ......... ........... .............
E15 *    2.00000   1.17557  -0.61803  -1.90211  -1.61803   0.00000   1.61803   1.90211   0.61803  -1.17557  -2.00000  -1.17557   0.61803   1.90211   1.61803   0.00000  -1.61803  -1.90211  -0.61803   1.17557   2.00000   1.17557  -0.61803  -1.90211  -1.61803   0.00000   1.61803   1.90211   0.61803  -1.17557  -2.00000  -1.17557   0.61803   1.90211   1.61803   0.00000  -1.61803  -1.90211  -0.61803   1.17557   2.00000   1.17557  -0.61803  -1.90211  -1.61803   0.00000   1.61803   1.90211   0.61803  -1.17557  -2.00000     ... ... ..... ....... ......... ........... .............
E16 *    2.00000   1.07165  -0.85156  -1.98423  -1.27485   0.61803   1.93717   1.45794  -0.37476  -1.85955  -1.61803   0.12558   1.75261   1.75261   0.12558  -1.61803  -1.85955  -0.37476   1.45794   1.93717   0.61803  -1.27485  -1.98423  -0.85156   1.07165   2.00000   1.07165  -0.85156  -1.98423  -1.27485   0.61803   1.93717   1.45794  -0.37476  -1.85955  -1.61803   0.12558   1.75261   1.75261   0.12558  -1.61803  -1.85955  -0.37476   1.45794   1.93717   0.61803  -1.27485  -1.98423  -0.85156   1.07165   2.00000     ... ... ..... ....... ......... ........... .............
E17 *    2.00000   0.96351  -1.07165  -1.99605  -0.85156   1.17557   1.98423   0.73625  -1.27485  -1.96457  -0.61803   1.36909   1.93717   0.49738  -1.45794  -1.90211  -0.37476   1.54103   1.85955   0.25067  -1.61803  -1.80965  -0.12558   1.68866   1.75261   0.00000  -1.75261  -1.68866   0.12558   1.80965   1.61803  -0.25067  -1.85955  -1.54103   0.37476   1.90211   1.45794  -0.49738  -1.93717  -1.36909   0.61803   1.96457   1.27485  -0.73625  -1.98423  -1.17557   0.85156   1.99605   1.07165  -0.96351  -2.00000     ... ... ..... ....... ......... ........... .............
E18 *    2.00000   0.85156  -1.27485  -1.93717  -0.37476   1.61803   1.75261  -0.12558  -1.85955  -1.45794   0.61803   1.98423   1.07165  -1.07165  -1.98423  -0.61803   1.45794   1.85955   0.12558  -1.75261  -1.61803   0.37476   1.93717   1.27485  -0.85156  -2.00000  -0.85156   1.27485   1.93717   0.37476  -1.61803  -1.75261   0.12558   1.85955   1.45794  -0.61803  -1.98423  -1.07165   1.07165   1.98423   0.61803  -1.45794  -1.85955  -0.12558   1.75261   1.61803  -0.37476  -1.93717  -1.27485   0.85156   2.00000     ... ... ..... ....... ......... ........... .............
E19 *    2.00000   0.73625  -1.45794  -1.80965   0.12558   1.90211   1.27485  -0.96351  -1.98423  -0.49738   1.61803   1.68866  -0.37476  -1.96457  -1.07165   1.17557   1.93717   0.25067  -1.75261  -1.54103   0.61803   1.99605   0.85156  -1.36909  -1.85955   0.00000   1.85955   1.36909  -0.85156  -1.99605  -0.61803   1.54103   1.75261  -0.25067  -1.93717  -1.17557   1.07165   1.96457   0.37476  -1.68866  -1.61803   0.49738   1.98423   0.96351  -1.27485  -1.90211  -0.12558   1.80965   1.45794  -0.73625  -2.00000     ... ... ..... ....... ......... ........... .............
E20 *    2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000   0.61803  -1.61803  -1.61803   0.61803   2.00000     ... ... ..... ....... ......... ........... .............
E21 *    2.00000   0.49738  -1.75261  -1.36909   1.07165   1.90211  -0.12558  -1.96457  -0.85156   1.54103   1.61803  -0.73625  -1.98423  -0.25067   1.85955   1.17557  -1.27485  -1.80965   0.37476   1.99605   0.61803  -1.68866  -1.45794   0.96351   1.93717   0.00000  -1.93717  -0.96351   1.45794   1.68866  -0.61803  -1.99605  -0.37476   1.80965   1.27485  -1.17557  -1.85955   0.25067   1.98423   0.73625  -1.61803  -1.54103   0.85156   1.96457   0.12558  -1.90211  -1.07165   1.36909   1.75261  -0.49738  -2.00000     ... ... ..... ....... ......... ........... .............
E22 *    2.00000   0.37476  -1.85955  -1.07165   1.45794   1.61803  -0.85156  -1.93717   0.12558   1.98423   0.61803  -1.75261  -1.27485   1.27485   1.75261  -0.61803  -1.98423  -0.12558   1.93717   0.85156  -1.61803  -1.45794   1.07165   1.85955  -0.37476  -2.00000  -0.37476   1.85955   1.07165  -1.45794  -1.61803   0.85156   1.93717  -0.12558  -1.98423  -0.61803   1.75261   1.27485  -1.27485  -1.75261   0.61803   1.98423   0.12558  -1.93717  -0.85156   1.61803   1.45794  -1.07165  -1.85955   0.37476   2.00000     ... ... ..... ....... ......... ........... .............
E23 *    2.00000   0.25067  -1.93717  -0.73625   1.75261   1.17557  -1.45794  -1.54103   1.07165   1.80965  -0.61803  -1.96457   0.12558   1.99605   0.37476  -1.90211  -0.85156   1.68866   1.27485  -1.36909  -1.61803   0.96351   1.85955  -0.49738  -1.98423   0.00000   1.98423   0.49738  -1.85955  -0.96351   1.61803   1.36909  -1.27485  -1.68866   0.85156   1.90211  -0.37476  -1.99605  -0.12558   1.96457   0.61803  -1.80965  -1.07165   1.54103   1.45794  -1.17557  -1.75261   0.73625   1.93717  -0.25067  -2.00000     ... ... ..... ....... ......... ........... .............
E24 *    2.00000   0.12558  -1.98423  -0.37476   1.93717   0.61803  -1.85955  -0.85156   1.75261   1.07165  -1.61803  -1.27485   1.45794   1.45794  -1.27485  -1.61803   1.07165   1.75261  -0.85156  -1.85955   0.61803   1.93717  -0.37476  -1.98423   0.12558   2.00000   0.12558  -1.98423  -0.37476   1.93717   0.61803  -1.85955  -0.85156   1.75261   1.07165  -1.61803  -1.27485   1.45794   1.45794  -1.27485  -1.61803   1.07165   1.75261  -0.85156  -1.85955   0.61803   1.93717  -0.37476  -1.98423   0.12558   2.00000     ... ... ..... ....... ......... ........... .............
E25 *    2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000   0.00000   2.00000   0.00000  -2.00000     ... ... ..... ....... ......... ........... .............
E26 *    2.00000  -0.12558  -1.98423   0.37476   1.93717  -0.61803  -1.85955   0.85156   1.75261  -1.07165  -1.61803   1.27485   1.45794  -1.45794  -1.27485   1.61803   1.07165  -1.75261  -0.85156   1.85955   0.61803  -1.93717  -0.37476   1.98423   0.12558  -2.00000   0.12558   1.98423  -0.37476  -1.93717   0.61803   1.85955  -0.85156  -1.75261   1.07165   1.61803  -1.27485  -1.45794   1.45794   1.27485  -1.61803  -1.07165   1.75261   0.85156  -1.85955  -0.61803   1.93717   0.37476  -1.98423  -0.12558   2.00000     ... ... ..... ....... ......... ........... .............
E27 *    2.00000  -0.25067  -1.93717   0.73625   1.75261  -1.17557  -1.45794   1.54103   1.07165  -1.80965  -0.61803   1.96457   0.12558  -1.99605   0.37476   1.90211  -0.85156  -1.68866   1.27485   1.36909  -1.61803  -0.96351   1.85955   0.49738  -1.98423   0.00000   1.98423  -0.49738  -1.85955   0.96351   1.61803  -1.36909  -1.27485   1.68866   0.85156  -1.90211  -0.37476   1.99605  -0.12558  -1.96457   0.61803   1.80965  -1.07165  -1.54103   1.45794   1.17557  -1.75261  -0.73625   1.93717   0.25067  -2.00000     ... ... ..... ....... ......... ........... .............
E28 *    2.00000  -0.37476  -1.85955   1.07165   1.45794  -1.61803  -0.85156   1.93717   0.12558  -1.98423   0.61803   1.75261  -1.27485  -1.27485   1.75261   0.61803  -1.98423   0.12558   1.93717  -0.85156  -1.61803   1.45794   1.07165  -1.85955  -0.37476   2.00000  -0.37476  -1.85955   1.07165   1.45794  -1.61803  -0.85156   1.93717   0.12558  -1.98423   0.61803   1.75261  -1.27485  -1.27485   1.75261   0.61803  -1.98423   0.12558   1.93717  -0.85156  -1.61803   1.45794   1.07165  -1.85955  -0.37476   2.00000     ... ... ..... ....... ......... ........... .............
E29 *    2.00000  -0.49738  -1.75261   1.36909   1.07165  -1.90211  -0.12558   1.96457  -0.85156  -1.54103   1.61803   0.73625  -1.98423   0.25067   1.85955  -1.17557  -1.27485   1.80965   0.37476  -1.99605   0.61803   1.68866  -1.45794  -0.96351   1.93717   0.00000  -1.93717   0.96351   1.45794  -1.68866  -0.61803   1.99605  -0.37476  -1.80965   1.27485   1.17557  -1.85955  -0.25067   1.98423  -0.73625  -1.61803   1.54103   0.85156  -1.96457   0.12558   1.90211  -1.07165  -1.36909   1.75261   0.49738  -2.00000     ... ... ..... ....... ......... ........... .............
E30 *    2.00000  -0.61803  -1.61803   1.61803   0.61803  -2.00000   0.61803   1.61803  -1.61803  -0.61803   2.00000  -0.61803  -1.61803   1.61803   0.61803  -2.00000   0.61803   1.61803  -1.61803  -0.61803   2.00000  -0.61803  -1.61803   1.61803   0.61803  -2.00000   0.61803   1.61803  -1.61803  -0.61803   2.00000  -0.61803  -1.61803   1.61803   0.61803  -2.00000   0.61803   1.61803  -1.61803  -0.61803   2.00000  -0.61803  -1.61803   1.61803   0.61803  -2.00000   0.61803   1.61803  -1.61803  -0.61803   2.00000     ... ... ..... ....... ......... ........... .............
E31 *    2.00000  -0.73625  -1.45794   1.80965   0.12558  -1.90211   1.27485   0.96351  -1.98423   0.49738   1.61803  -1.68866  -0.37476   1.96457  -1.07165  -1.17557   1.93717  -0.25067  -1.75261   1.54103   0.61803  -1.99605   0.85156   1.36909  -1.85955   0.00000   1.85955  -1.36909  -0.85156   1.99605  -0.61803  -1.54103   1.75261   0.25067  -1.93717   1.17557   1.07165  -1.96457   0.37476   1.68866  -1.61803  -0.49738   1.98423  -0.96351  -1.27485   1.90211  -0.12558  -1.80965   1.45794   0.73625  -2.00000     ... ... ..... ....... ......... ........... .............
E32 *    2.00000  -0.85156  -1.27485   1.93717  -0.37476  -1.61803   1.75261   0.12558  -1.85955   1.45794   0.61803  -1.98423   1.07165   1.07165  -1.98423   0.61803   1.45794  -1.85955   0.12558   1.75261  -1.61803  -0.37476   1.93717  -1.27485  -0.85156   2.00000  -0.85156  -1.27485   1.93717  -0.37476  -1.61803   1.75261   0.12558  -1.85955   1.45794   0.61803  -1.98423   1.07165   1.07165  -1.98423   0.61803   1.45794  -1.85955   0.12558   1.75261  -1.61803  -0.37476   1.93717  -1.27485  -0.85156   2.00000     ... ... ..... ....... ......... ........... .............
E33 *    2.00000  -0.96351  -1.07165   1.99605  -0.85156  -1.17557   1.98423  -0.73625  -1.27485   1.96457  -0.61803  -1.36909   1.93717  -0.49738  -1.45794   1.90211  -0.37476  -1.54103   1.85955  -0.25067  -1.61803   1.80965  -0.12558  -1.68866   1.75261   0.00000  -1.75261   1.68866   0.12558  -1.80965   1.61803   0.25067  -1.85955   1.54103   0.37476  -1.90211   1.45794   0.49738  -1.93717   1.36909   0.61803  -1.96457   1.27485   0.73625  -1.98423   1.17557   0.85156  -1.99605   1.07165   0.96351  -2.00000     ... ... ..... ....... ......... ........... .............
E34 *    2.00000  -1.07165  -0.85156   1.98423  -1.27485  -0.61803   1.93717  -1.45794  -0.37476   1.85955  -1.61803  -0.12558   1.75261  -1.75261   0.12558   1.61803  -1.85955   0.37476   1.45794  -1.93717   0.61803   1.27485  -1.98423   0.85156   1.07165  -2.00000   1.07165   0.85156  -1.98423   1.27485   0.61803  -1.93717   1.45794   0.37476  -1.85955   1.61803   0.12558  -1.75261   1.75261  -0.12558  -1.61803   1.85955  -0.37476  -1.45794   1.93717  -0.61803  -1.27485   1.98423  -0.85156  -1.07165   2.00000     ... ... ..... ....... ......... ........... .............
E35 *    2.00000  -1.17557  -0.61803   1.90211  -1.61803   0.00000   1.61803  -1.90211   0.61803   1.17557  -2.00000   1.17557   0.61803  -1.90211   1.61803   0.00000  -1.61803   1.90211  -0.61803  -1.17557   2.00000  -1.17557  -0.61803   1.90211  -1.61803   0.00000   1.61803  -1.90211   0.61803   1.17557  -2.00000   1.17557   0.61803  -1.90211   1.61803   0.00000  -1.61803   1.90211  -0.61803  -1.17557   2.00000  -1.17557  -0.61803   1.90211  -1.61803   0.00000   1.61803  -1.90211   0.61803   1.17557  -2.00000     ... ... ..... ....... ......... ........... .............
E36 *    2.00000  -1.27485  -0.37476   1.75261  -1.85955   0.61803   1.07165  -1.98423   1.45794   0.12558  -1.61803   1.93717  -0.85156  -0.85156   1.93717  -1.61803   0.12558   1.45794  -1.98423   1.07165   0.61803  -1.85955   1.75261  -0.37476  -1.27485   2.00000  -1.27485  -0.37476   1.75261  -1.85955   0.61803   1.07165  -1.98423   1.45794   0.12558  -1.61803   1.93717  -0.85156  -0.85156   1.93717  -1.61803   0.12558   1.45794  -1.98423   1.07165   0.61803  -1.85955   1.75261  -0.37476  -1.27485   2.00000     ... ... ..... ....... ......... ........... .............
E37 *    2.00000  -1.36909  -0.12558   1.54103  -1.98423   1.17557   0.37476  -1.68866   1.93717  -0.96351  -0.61803   1.80965  -1.85955   0.73625   0.85156  -1.90211   1.75261  -0.49738  -1.07165   1.96457  -1.61803   0.25067   1.27485  -1.99605   1.45794   0.00000  -1.45794   1.99605  -1.27485  -0.25067   1.61803  -1.96457   1.07165   0.49738  -1.75261   1.90211  -0.85156  -0.73625   1.85955  -1.80965   0.61803   0.96351  -1.93717   1.68866  -0.37476  -1.17557   1.98423  -1.54103   0.12558   1.36909  -2.00000     ... ... ..... ....... ......... ........... .............
E38 *    2.00000  -1.45794   0.12558   1.27485  -1.98423   1.61803  -0.37476  -1.07165   1.93717  -1.75261   0.61803   0.85156  -1.85955   1.85955  -0.85156  -0.61803   1.75261  -1.93717   1.07165   0.37476  -1.61803   1.98423  -1.27485  -0.12558   1.45794  -2.00000   1.45794  -0.12558  -1.27485   1.98423  -1.61803   0.37476   1.07165  -1.93717   1.75261  -0.61803  -0.85156   1.85955  -1.85955   0.85156   0.61803  -1.75261   1.93717  -1.07165  -0.37476   1.61803  -1.98423   1.27485   0.12558  -1.45794   2.00000     ... ... ..... ....... ......... ........... .............
E39 *    2.00000  -1.54103   0.37476   0.96351  -1.85955   1.90211  -1.07165  -0.25067   1.45794  -1.99605   1.61803  -0.49738  -0.85156   1.80965  -1.93717   1.17557   0.12558  -1.36909   1.98423  -1.68866   0.61803   0.73625  -1.75261   1.96457  -1.27485   0.00000   1.27485  -1.96457   1.75261  -0.73625  -0.61803   1.68866  -1.98423   1.36909  -0.12558  -1.17557   1.93717  -1.80965   0.85156   0.49738  -1.61803   1.99605  -1.45794   0.25067   1.07165  -1.90211   1.85955  -0.96351  -0.37476   1.54103  -2.00000     ... ... ..... ....... ......... ........... .............
E40 *    2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000  -1.61803   0.61803   0.61803  -1.61803   2.00000     ... ... ..... ....... ......... ........... .............
E41 *    2.00000  -1.68866   0.85156   0.25067  -1.27485   1.90211  -1.93717   1.36909  -0.37476  -0.73625   1.61803  -1.99605   1.75261  -0.96351  -0.12558   1.17557  -1.85955   1.96457  -1.45794   0.49738   0.61803  -1.54103   1.98423  -1.80965   1.07165   0.00000  -1.07165   1.80965  -1.98423   1.54103  -0.61803  -0.49738   1.45794  -1.96457   1.85955  -1.17557   0.12558   0.96351  -1.75261   1.99605  -1.61803   0.73625   0.37476  -1.36909   1.93717  -1.90211   1.27485  -0.25067  -0.85156   1.68866  -2.00000     ... ... ..... ....... ......... ........... .............
E42 *    2.00000  -1.75261   1.07165  -0.12558  -0.85156   1.61803  -1.98423   1.85955  -1.27485   0.37476   0.61803  -1.45794   1.93717  -1.93717   1.45794  -0.61803  -0.37476   1.27485  -1.85955   1.98423  -1.61803   0.85156   0.12558  -1.07165   1.75261  -2.00000   1.75261  -1.07165   0.12558   0.85156  -1.61803   1.98423  -1.85955   1.27485  -0.37476  -0.61803   1.45794  -1.93717   1.93717  -1.45794   0.61803   0.37476  -1.27485   1.85955  -1.98423   1.61803  -0.85156  -0.12558   1.07165  -1.75261   2.00000     ... ... ..... ....... ......... ........... .............
E43 *    2.00000  -1.80965   1.27485  -0.49738  -0.37476   1.17557  -1.75261   1.99605  -1.85955   1.36909  -0.61803  -0.25067   1.07165  -1.68866   1.98423  -1.90211   1.45794  -0.73625  -0.12558   0.96351  -1.61803   1.96457  -1.93717   1.54103  -0.85156   0.00000   0.85156  -1.54103   1.93717  -1.96457   1.61803  -0.96351   0.12558   0.73625  -1.45794   1.90211  -1.98423   1.68866  -1.07165   0.25067   0.61803  -1.36909   1.85955  -1.99605   1.75261  -1.17557   0.37476   0.49738  -1.27485   1.80965  -2.00000     ... ... ..... ....... ......... ........... .............
E44 *    2.00000  -1.85955   1.45794  -0.85156   0.12558   0.61803  -1.27485   1.75261  -1.98423   1.93717  -1.61803   1.07165  -0.37476  -0.37476   1.07165  -1.61803   1.93717  -1.98423   1.75261  -1.27485   0.61803   0.12558  -0.85156   1.45794  -1.85955   2.00000  -1.85955   1.45794  -0.85156   0.12558   0.61803  -1.27485   1.75261  -1.98423   1.93717  -1.61803   1.07165  -0.37476  -0.37476   1.07165  -1.61803   1.93717  -1.98423   1.75261  -1.27485   0.61803   0.12558  -0.85156   1.45794  -1.85955   2.00000     ... ... ..... ....... ......... ........... .............
E45 *    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     ... ... ..... ....... ......... ........... ..TT.........
E46 *    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     ... ... ..... ....... ......... ..TT....... .............
E47 *    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     ... ... ..... ....... ..TT..... ........... ......TT.....
E48 *    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     ... ... ..... ..TT... ......... ......TT... .............
E49 *    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     TT. ... ..TT. ....... ......TT. ........... ..........TT.

 Irrational character values:  1.996053456857 = 2*cos(2*π/100) = 2*cos(π/50)
                               1.984229402629 = 2*cos(4*π/100) = 2*cos(π/25)
                               1.964574501457 = 2*cos(6*π/100) = 2*cos(3*π/50)
                               1.937166322257 = 2*cos(8*π/100) = 2*cos(2*π/25)
                               1.902113032590 = 2*cos(10*π/100) = 2*cos(π/10) = (√10+2*√5)/2
                               1.859552971777 = 2*cos(12*π/100) = 2*cos(3*π/25)
                               1.809654104932 = 2*cos(14*π/100) = 2*cos(7*π/50)
                               1.752613360088 = 2*cos(16*π/100) = 2*cos(4*π/25)
                               1.688655851004 = 2*cos(18*π/100) = 2*cos(9*π/50)
                               1.618033988750 = 2*cos(20*π/100) = 2*cos(π/5) = (√5+1)/2
                               1.541026485552 = 2*cos(22*π/100) = 2*cos(11*π/50)
                               1.457937254843 = 2*cos(24*π/100) = 2*cos(6*π/25)
                               1.369094211857 = 2*cos(26*π/100) = 2*cos(13*π/50)
                               1.274847979497 = 2*cos(28*π/100) = 2*cos(7*π/25)
                               1.175570504585 = 2*cos(30*π/100) = 2*cos(3*π/10) = (√10−2*√5)/2
                               1.071653589958 = 2*cos(32*π/100) = 2*cos(8*π/25)
                               0.963507348203 = 2*cos(34*π/100) = 2*cos(17*π/50)
                               0.851558583130 = 2*cos(36*π/100) = 2*cos(9*π/25)
                               0.736249105369 = 2*cos(38*π/100) = 2*cos(19*π/50)
                               0.618033988750 = 2*cos(40*π/100) = 2*cos(2*π/5) = (√5−1)/2
                               0.497379774330 = 2*cos(42*π/100) = 2*cos(21*π/50)
                               0.374762629171 = 2*cos(44*π/100) = 2*cos(11*π/25)
                               0.250666467129 = 2*cos(46*π/100) = 2*cos(23*π/50)
                               0.125581039059 = 2*cos(48*π/100) = 2*cos(12*π/25)



 Symmetry of Rotations and Cartesian products

A    R+d+g+i+k+m  Rz, z2, z4, z6 
B    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    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3   f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4   g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+l 
E8   k+m 
E9   l 
E10  m 
E41  m 
E42  l 
E43  k+m 
E44  j+l 
E45  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E46  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E47  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E48  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E49  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 

 Notes:

    α  The order of the S100 point group is 100, and the order of the principal axis (S100) is 100. The group has 51 irreducible representations.

    β  The S100 point group could also be named C100i, because the S100 axis is identical to a roto-inversion axis of order 100.

    γ  The S100 point group is isomorphic to C100.

    δ  The S100 point group is generated by one single symmetry element, S100. Therefore, it is a cyclic group.

    ε  The lowest nonvanishing multipole moment in S100 is 4 (quadrupole moment).

    ζ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The S100 group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition).
       In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional.

    η  Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters.
       These 98 cases have been combined into 49 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 49 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    θ  The 49 reducible “E” representations almost behave like true irreducible representations.
       Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table.
       This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula.

    ι  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 S100 point group was created by Gernot Katzer.

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