Character table for the D47h point group

D47h     E        2 C47    2 C47^2  2 C47^3  2 C47^4  2 C47^5  2 C47^6  2 C47^7  2 C47^8  2 C47^9  2 C47^10 2 C47^11 2 C47^12 2 C47^13 2 C47^14 2 C47^15 2 C47^16 2 C47^17 2 C47^18 2 C47^19 2 C47^20 2 C47^21 2 C47^22 2 C47^23 47 C2'   sh       2 S47    2 S47^3  2 S47^5  2 S47^7  2 S47^9  2 S47^11 2 S47^13 2 S47^15 2 S47^17 2 S47^19 2 S47^21 2 S47^23 2 S47^25 2 S47^27 2 S47^29 2 S47^31 2 S47^33 2 S47^35 2 S47^37 2 S47^39 2 S47^41 2 S47^43 2 S47^45 47 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     ... ... ....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     ... ... ..... ....... ......... ........... .............
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     ..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     ... ..T ..... ......T ......... ..........T .............
E1'     2.00000  1.98215  1.92894  1.84130  1.72080  1.56960  1.39038  1.18636  0.96116  0.71882  0.46364  0.20019 -0.06683 -0.33266 -0.59255 -0.84187 -1.07616 -1.29126 -1.48330 -1.64888 -1.78504 -1.88934 -1.95992 -1.99553  0.00000  2.00000  1.98215  1.84130  1.56960  1.18636  0.71882  0.20019 -0.33266 -0.84187 -1.29126 -1.64888 -1.88934 -1.99553 -1.95992 -1.78504 -1.48330 -1.07616 -0.59255 -0.06683  0.46364  0.96116  1.39038  1.72080  1.92894  0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E1"     2.00000  1.98215  1.92894  1.84130  1.72080  1.56960  1.39038  1.18636  0.96116  0.71882  0.46364  0.20019 -0.06683 -0.33266 -0.59255 -0.84187 -1.07616 -1.29126 -1.48330 -1.64888 -1.78504 -1.88934 -1.95992 -1.99553  0.00000 -2.00000 -1.98215 -1.84130 -1.56960 -1.18636 -0.71882 -0.20019  0.33266  0.84187  1.29126  1.64888  1.88934  1.99553  1.95992  1.78504  1.48330  1.07616  0.59255  0.06683 -0.46364 -0.96116 -1.39038 -1.72080 -1.92894  0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2'     2.00000  1.92894  1.72080  1.39038  0.96116  0.46364 -0.06683 -0.59255 -1.07616 -1.48330 -1.78504 -1.95992 -1.99553 -1.88934 -1.64888 -1.29126 -0.84187 -0.33266  0.20019  0.71882  1.18636  1.56960  1.84130  1.98215  0.00000  2.00000  1.92894  1.39038  0.46364 -0.59255 -1.48330 -1.95992 -1.88934 -1.29126 -0.33266  0.71882  1.56960  1.98215  1.84130  1.18636  0.20019 -0.84187 -1.64888 -1.99553 -1.78504 -1.07616 -0.06683  0.96116  1.72080  0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E2"     2.00000  1.92894  1.72080  1.39038  0.96116  0.46364 -0.06683 -0.59255 -1.07616 -1.48330 -1.78504 -1.95992 -1.99553 -1.88934 -1.64888 -1.29126 -0.84187 -0.33266  0.20019  0.71882  1.18636  1.56960  1.84130  1.98215  0.00000 -2.00000 -1.92894 -1.39038 -0.46364  0.59255  1.48330  1.95992  1.88934  1.29126  0.33266 -0.71882 -1.56960 -1.98215 -1.84130 -1.18636 -0.20019  0.84187  1.64888  1.99553  1.78504  1.07616  0.06683 -0.96116 -1.72080  0.00000     ... ... ..... ..TT... ......... ......TT... .............
E3'     2.00000  1.84130  1.39038  0.71882 -0.06683 -0.84187 -1.48330 -1.88934 -1.99553 -1.78504 -1.29126 -0.59255  0.20019  0.96116  1.56960  1.92894  1.98215  1.72080  1.18636  0.46364 -0.33266 -1.07616 -1.64888 -1.95992  0.00000  2.00000  1.84130  0.71882 -0.84187 -1.88934 -1.78504 -0.59255  0.96116  1.92894  1.72080  0.46364 -1.07616 -1.95992 -1.64888 -0.33266  1.18636  1.98215  1.56960  0.20019 -1.29126 -1.99553 -1.48330 -0.06683  1.39038  0.00000     ... ... ..... TT..... ......... ....TT..... .............
E3"     2.00000  1.84130  1.39038  0.71882 -0.06683 -0.84187 -1.48330 -1.88934 -1.99553 -1.78504 -1.29126 -0.59255  0.20019  0.96116  1.56960  1.92894  1.98215  1.72080  1.18636  0.46364 -0.33266 -1.07616 -1.64888 -1.95992  0.00000 -2.00000 -1.84130 -0.71882  0.84187  1.88934  1.78504  0.59255 -0.96116 -1.92894 -1.72080 -0.46364  1.07616  1.95992  1.64888  0.33266 -1.18636 -1.98215 -1.56960 -0.20019  1.29126  1.99553  1.48330  0.06683 -1.39038  0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E4'     2.00000  1.72080  0.96116 -0.06683 -1.07616 -1.78504 -1.99553 -1.64888 -0.84187  0.20019  1.18636  1.84130  1.98215  1.56960  0.71882 -0.33266 -1.29126 -1.88934 -1.95992 -1.48330 -0.59255  0.46364  1.39038  1.92894  0.00000  2.00000  1.72080 -0.06683 -1.78504 -1.64888  0.20019  1.84130  1.56960 -0.33266 -1.88934 -1.48330  0.46364  1.92894  1.39038 -0.59255 -1.95992 -1.29126  0.71882  1.98215  1.18636 -0.84187 -1.99553 -1.07616  0.96116  0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E4"     2.00000  1.72080  0.96116 -0.06683 -1.07616 -1.78504 -1.99553 -1.64888 -0.84187  0.20019  1.18636  1.84130  1.98215  1.56960  0.71882 -0.33266 -1.29126 -1.88934 -1.95992 -1.48330 -0.59255  0.46364  1.39038  1.92894  0.00000 -2.00000 -1.72080  0.06683  1.78504  1.64888 -0.20019 -1.84130 -1.56960  0.33266  1.88934  1.48330 -0.46364 -1.92894 -1.39038  0.59255  1.95992  1.29126 -0.71882 -1.98215 -1.18636  0.84187  1.99553  1.07616 -0.96116  0.00000     ... ... ..... ....... ......... ..TT....... .............
E5'     2.00000  1.56960  0.46364 -0.84187 -1.78504 -1.95992 -1.29126 -0.06683  1.18636  1.92894  1.84130  0.96116 -0.33266 -1.48330 -1.99553 -1.64888 -0.59255  0.71882  1.72080  1.98215  1.39038  0.20019 -1.07616 -1.88934  0.00000  2.00000  1.56960 -0.84187 -1.95992 -0.06683  1.92894  0.96116 -1.48330 -1.64888  0.71882  1.98215  0.20019 -1.88934 -1.07616  1.39038  1.72080 -0.59255 -1.99553 -0.33266  1.84130  1.18636 -1.29126 -1.78504  0.46364  0.00000     ... ... ..... ....... ......... TT......... .............
E5"     2.00000  1.56960  0.46364 -0.84187 -1.78504 -1.95992 -1.29126 -0.06683  1.18636  1.92894  1.84130  0.96116 -0.33266 -1.48330 -1.99553 -1.64888 -0.59255  0.71882  1.72080  1.98215  1.39038  0.20019 -1.07616 -1.88934  0.00000 -2.00000 -1.56960  0.84187  1.95992  0.06683 -1.92894 -0.96116  1.48330  1.64888 -0.71882 -1.98215 -0.20019  1.88934  1.07616 -1.39038 -1.72080  0.59255  1.99553  0.33266 -1.84130 -1.18636  1.29126  1.78504 -0.46364  0.00000     ... ... ..... ....... ......... ........... ..TT.........
E6'     2.00000  1.39038 -0.06683 -1.48330 -1.99553 -1.29126  0.20019  1.56960  1.98215  1.18636 -0.33266 -1.64888 -1.95992 -1.07616  0.46364  1.72080  1.92894  0.96116 -0.59255 -1.78504 -1.88934 -0.84187  0.71882  1.84130  0.00000  2.00000  1.39038 -1.48330 -1.29126  1.56960  1.18636 -1.64888 -1.07616  1.72080  0.96116 -1.78504 -0.84187  1.84130  0.71882 -1.88934 -0.59255  1.92894  0.46364 -1.95992 -0.33266  1.98215  0.20019 -1.99553 -0.06683  0.00000     ... ... ..... ....... ......... ........... TT...........
E6"     2.00000  1.39038 -0.06683 -1.48330 -1.99553 -1.29126  0.20019  1.56960  1.98215  1.18636 -0.33266 -1.64888 -1.95992 -1.07616  0.46364  1.72080  1.92894  0.96116 -0.59255 -1.78504 -1.88934 -0.84187  0.71882  1.84130  0.00000 -2.00000 -1.39038  1.48330  1.29126 -1.56960 -1.18636  1.64888  1.07616 -1.72080 -0.96116  1.78504  0.84187 -1.84130 -0.71882  1.88934  0.59255 -1.92894 -0.46364  1.95992  0.33266 -1.98215 -0.20019  1.99553  0.06683  0.00000     ... ... ..... ....... ......... ........... .............
E7'     2.00000  1.18636 -0.59255 -1.88934 -1.64888 -0.06683  1.56960  1.92894  0.71882 -1.07616 -1.99553 -1.29126  0.46364  1.84130  1.72080  0.20019 -1.48330 -1.95992 -0.84187  0.96116  1.98215  1.39038 -0.33266 -1.78504  0.00000  2.00000  1.18636 -1.88934 -0.06683  1.92894 -1.07616 -1.29126  1.84130  0.20019 -1.95992  0.96116  1.39038 -1.78504 -0.33266  1.98215 -0.84187 -1.48330  1.72080  0.46364 -1.99553  0.71882  1.56960 -1.64888 -0.59255  0.00000     ... ... ..... ....... ......... ........... .............
E7"     2.00000  1.18636 -0.59255 -1.88934 -1.64888 -0.06683  1.56960  1.92894  0.71882 -1.07616 -1.99553 -1.29126  0.46364  1.84130  1.72080  0.20019 -1.48330 -1.95992 -0.84187  0.96116  1.98215  1.39038 -0.33266 -1.78504  0.00000 -2.00000 -1.18636  1.88934  0.06683 -1.92894  1.07616  1.29126 -1.84130 -0.20019  1.95992 -0.96116 -1.39038  1.78504  0.33266 -1.98215  0.84187  1.48330 -1.72080 -0.46364  1.99553 -0.71882 -1.56960  1.64888  0.59255  0.00000     ... ... ..... ....... ......... ........... .............
E8'     2.00000  0.96116 -1.07616 -1.99553 -0.84187  1.18636  1.98215  0.71882 -1.29126 -1.95992 -0.59255  1.39038  1.92894  0.46364 -1.48330 -1.88934 -0.33266  1.56960  1.84130  0.20019 -1.64888 -1.78504 -0.06683  1.72080  0.00000  2.00000  0.96116 -1.99553  1.18636  0.71882 -1.95992  1.39038  0.46364 -1.88934  1.56960  0.20019 -1.78504  1.72080 -0.06683 -1.64888  1.84130 -0.33266 -1.48330  1.92894 -0.59255 -1.29126  1.98215 -0.84187 -1.07616  0.00000     ... ... ..... ....... ......... ........... .............
E8"     2.00000  0.96116 -1.07616 -1.99553 -0.84187  1.18636  1.98215  0.71882 -1.29126 -1.95992 -0.59255  1.39038  1.92894  0.46364 -1.48330 -1.88934 -0.33266  1.56960  1.84130  0.20019 -1.64888 -1.78504 -0.06683  1.72080  0.00000 -2.00000 -0.96116  1.99553 -1.18636 -0.71882  1.95992 -1.39038 -0.46364  1.88934 -1.56960 -0.20019  1.78504 -1.72080  0.06683  1.64888 -1.84130  0.33266  1.48330 -1.92894  0.59255  1.29126 -1.98215  0.84187  1.07616  0.00000     ... ... ..... ....... ......... ........... .............
E9'     2.00000  0.71882 -1.48330 -1.78504  0.20019  1.92894  1.18636 -1.07616 -1.95992 -0.33266  1.72080  1.56960 -0.59255 -1.99553 -0.84187  1.39038  1.84130 -0.06683 -1.88934 -1.29126  0.96116  1.98215  0.46364 -1.64888  0.00000  2.00000  0.71882 -1.78504  1.92894 -1.07616 -0.33266  1.56960 -1.99553  1.39038 -0.06683 -1.29126  1.98215 -1.64888  0.46364  0.96116 -1.88934  1.84130 -0.84187 -0.59255  1.72080 -1.95992  1.18636  0.20019 -1.48330  0.00000     ... ... ..... ....... ......... ........... .............
E9"     2.00000  0.71882 -1.48330 -1.78504  0.20019  1.92894  1.18636 -1.07616 -1.95992 -0.33266  1.72080  1.56960 -0.59255 -1.99553 -0.84187  1.39038  1.84130 -0.06683 -1.88934 -1.29126  0.96116  1.98215  0.46364 -1.64888  0.00000 -2.00000 -0.71882  1.78504 -1.92894  1.07616  0.33266 -1.56960  1.99553 -1.39038  0.06683  1.29126 -1.98215  1.64888 -0.46364 -0.96116  1.88934 -1.84130  0.84187  0.59255 -1.72080  1.95992 -1.18636 -0.20019  1.48330  0.00000     ... ... ..... ....... ......... ........... .............
E10'    2.00000  0.46364 -1.78504 -1.29126  1.18636  1.84130 -0.33266 -1.99553 -0.59255  1.72080  1.39038 -1.07616 -1.88934  0.20019  1.98215  0.71882 -1.64888 -1.48330  0.96116  1.92894 -0.06683 -1.95992 -0.84187  1.56960  0.00000  2.00000  0.46364 -1.29126  1.84130 -1.99553  1.72080 -1.07616  0.20019  0.71882 -1.48330  1.92894 -1.95992  1.56960 -0.84187 -0.06683  0.96116 -1.64888  1.98215 -1.88934  1.39038 -0.59255 -0.33266  1.18636 -1.78504  0.00000     ... ... ..... ....... ......... ........... .............
E10"    2.00000  0.46364 -1.78504 -1.29126  1.18636  1.84130 -0.33266 -1.99553 -0.59255  1.72080  1.39038 -1.07616 -1.88934  0.20019  1.98215  0.71882 -1.64888 -1.48330  0.96116  1.92894 -0.06683 -1.95992 -0.84187  1.56960  0.00000 -2.00000 -0.46364  1.29126 -1.84130  1.99553 -1.72080  1.07616 -0.20019 -0.71882  1.48330 -1.92894  1.95992 -1.56960  0.84187  0.06683 -0.96116  1.64888 -1.98215  1.88934 -1.39038  0.59255  0.33266 -1.18636  1.78504  0.00000     ... ... ..... ....... ......... ........... .............
E11'    2.00000  0.20019 -1.95992 -0.59255  1.84130  0.96116 -1.64888 -1.29126  1.39038  1.56960 -1.07616 -1.78504  0.71882  1.92894 -0.33266 -1.99553 -0.06683  1.98215  0.46364 -1.88934 -0.84187  1.72080  1.18636 -1.48330  0.00000  2.00000  0.20019 -0.59255  0.96116 -1.29126  1.56960 -1.78504  1.92894 -1.99553  1.98215 -1.88934  1.72080 -1.48330  1.18636 -0.84187  0.46364 -0.06683 -0.33266  0.71882 -1.07616  1.39038 -1.64888  1.84130 -1.95992  0.00000     ... ... ..... ....... ......... ........... .............
E11"    2.00000  0.20019 -1.95992 -0.59255  1.84130  0.96116 -1.64888 -1.29126  1.39038  1.56960 -1.07616 -1.78504  0.71882  1.92894 -0.33266 -1.99553 -0.06683  1.98215  0.46364 -1.88934 -0.84187  1.72080  1.18636 -1.48330  0.00000 -2.00000 -0.20019  0.59255 -0.96116  1.29126 -1.56960  1.78504 -1.92894  1.99553 -1.98215  1.88934 -1.72080  1.48330 -1.18636  0.84187 -0.46364  0.06683  0.33266 -0.71882  1.07616 -1.39038  1.64888 -1.84130  1.95992  0.00000     ... ... ..... ....... ......... ........... .............
E12'    2.00000 -0.06683 -1.99553  0.20019  1.98215 -0.33266 -1.95992  0.46364  1.92894 -0.59255 -1.88934  0.71882  1.84130 -0.84187 -1.78504  0.96116  1.72080 -1.07616 -1.64888  1.18636  1.56960 -1.29126 -1.48330  1.39038  0.00000  2.00000 -0.06683  0.20019 -0.33266  0.46364 -0.59255  0.71882 -0.84187  0.96116 -1.07616  1.18636 -1.29126  1.39038 -1.48330  1.56960 -1.64888  1.72080 -1.78504  1.84130 -1.88934  1.92894 -1.95992  1.98215 -1.99553  0.00000     ... ... ..... ....... ......... ........... .............
E12"    2.00000 -0.06683 -1.99553  0.20019  1.98215 -0.33266 -1.95992  0.46364  1.92894 -0.59255 -1.88934  0.71882  1.84130 -0.84187 -1.78504  0.96116  1.72080 -1.07616 -1.64888  1.18636  1.56960 -1.29126 -1.48330  1.39038  0.00000 -2.00000  0.06683 -0.20019  0.33266 -0.46364  0.59255 -0.71882  0.84187 -0.96116  1.07616 -1.18636  1.29126 -1.39038  1.48330 -1.56960  1.64888 -1.72080  1.78504 -1.84130  1.88934 -1.92894  1.95992 -1.98215  1.99553  0.00000     ... ... ..... ....... ......... ........... .............
E13'    2.00000 -0.33266 -1.88934  0.96116  1.56960 -1.48330 -1.07616  1.84130  0.46364 -1.99553  0.20019  1.92894 -0.84187 -1.64888  1.39038  1.18636 -1.78504 -0.59255  1.98215 -0.06683 -1.95992  0.71882  1.72080 -1.29126  0.00000  2.00000 -0.33266  0.96116 -1.48330  1.84130 -1.99553  1.92894 -1.64888  1.18636 -0.59255 -0.06683  0.71882 -1.29126  1.72080 -1.95992  1.98215 -1.78504  1.39038 -0.84187  0.20019  0.46364 -1.07616  1.56960 -1.88934  0.00000     ... ... ..... ....... ......... ........... .............
E13"    2.00000 -0.33266 -1.88934  0.96116  1.56960 -1.48330 -1.07616  1.84130  0.46364 -1.99553  0.20019  1.92894 -0.84187 -1.64888  1.39038  1.18636 -1.78504 -0.59255  1.98215 -0.06683 -1.95992  0.71882  1.72080 -1.29126  0.00000 -2.00000  0.33266 -0.96116  1.48330 -1.84130  1.99553 -1.92894  1.64888 -1.18636  0.59255  0.06683 -0.71882  1.29126 -1.72080  1.95992 -1.98215  1.78504 -1.39038  0.84187 -0.20019 -0.46364  1.07616 -1.56960  1.88934  0.00000     ... ... ..... ....... ......... ........... .............
E14'    2.00000 -0.59255 -1.64888  1.56960  0.71882 -1.99553  0.46364  1.72080 -1.48330 -0.84187  1.98215 -0.33266 -1.78504  1.39038  0.96116 -1.95992  0.20019  1.84130 -1.29126 -1.07616  1.92894 -0.06683 -1.88934  1.18636  0.00000  2.00000 -0.59255  1.56960 -1.99553  1.72080 -0.84187 -0.33266  1.39038 -1.95992  1.84130 -1.07616 -0.06683  1.18636 -1.88934  1.92894 -1.29126  0.20019  0.96116 -1.78504  1.98215 -1.48330  0.46364  0.71882 -1.64888  0.00000     ... ... ..... ....... ......... ........... .............
E14"    2.00000 -0.59255 -1.64888  1.56960  0.71882 -1.99553  0.46364  1.72080 -1.48330 -0.84187  1.98215 -0.33266 -1.78504  1.39038  0.96116 -1.95992  0.20019  1.84130 -1.29126 -1.07616  1.92894 -0.06683 -1.88934  1.18636  0.00000 -2.00000  0.59255 -1.56960  1.99553 -1.72080  0.84187  0.33266 -1.39038  1.95992 -1.84130  1.07616  0.06683 -1.18636  1.88934 -1.92894  1.29126 -0.20019 -0.96116  1.78504 -1.98215  1.48330 -0.46364 -0.71882  1.64888  0.00000     ... ... ..... ....... ......... ........... .............
E15'    2.00000 -0.84187 -1.29126  1.92894 -0.33266 -1.64888  1.72080  0.20019 -1.88934  1.39038  0.71882 -1.99553  0.96116  1.18636 -1.95992  0.46364  1.56960 -1.78504 -0.06683  1.84130 -1.48330 -0.59255  1.98215 -1.07616  0.00000  2.00000 -0.84187  1.92894 -1.64888  0.20019  1.39038 -1.99553  1.18636  0.46364 -1.78504  1.84130 -0.59255 -1.07616  1.98215 -1.48330 -0.06683  1.56960 -1.95992  0.96116  0.71882 -1.88934  1.72080 -0.33266 -1.29126  0.00000     ... ... ..... ....... ......... ........... .............
E15"    2.00000 -0.84187 -1.29126  1.92894 -0.33266 -1.64888  1.72080  0.20019 -1.88934  1.39038  0.71882 -1.99553  0.96116  1.18636 -1.95992  0.46364  1.56960 -1.78504 -0.06683  1.84130 -1.48330 -0.59255  1.98215 -1.07616  0.00000 -2.00000  0.84187 -1.92894  1.64888 -0.20019 -1.39038  1.99553 -1.18636 -0.46364  1.78504 -1.84130  0.59255  1.07616 -1.98215  1.48330  0.06683 -1.56960  1.95992 -0.96116 -0.71882  1.88934 -1.72080  0.33266  1.29126  0.00000     ... ... ..... ....... ......... ........... .............
E16'    2.00000 -1.07616 -0.84187  1.98215 -1.29126 -0.59255  1.92894 -1.48330 -0.33266  1.84130 -1.64888 -0.06683  1.72080 -1.78504  0.20019  1.56960 -1.88934  0.46364  1.39038 -1.95992  0.71882  1.18636 -1.99553  0.96116  0.00000  2.00000 -1.07616  1.98215 -0.59255 -1.48330  1.84130 -0.06683 -1.78504  1.56960  0.46364 -1.95992  1.18636  0.96116 -1.99553  0.71882  1.39038 -1.88934  0.20019  1.72080 -1.64888 -0.33266  1.92894 -1.29126 -0.84187  0.00000     ... ... ..... ....... ......... ........... .............
E16"    2.00000 -1.07616 -0.84187  1.98215 -1.29126 -0.59255  1.92894 -1.48330 -0.33266  1.84130 -1.64888 -0.06683  1.72080 -1.78504  0.20019  1.56960 -1.88934  0.46364  1.39038 -1.95992  0.71882  1.18636 -1.99553  0.96116  0.00000 -2.00000  1.07616 -1.98215  0.59255  1.48330 -1.84130  0.06683  1.78504 -1.56960 -0.46364  1.95992 -1.18636 -0.96116  1.99553 -0.71882 -1.39038  1.88934 -0.20019 -1.72080  1.64888  0.33266 -1.92894  1.29126  0.84187  0.00000     ... ... ..... ....... ......... ........... .............
E17'    2.00000 -1.29126 -0.33266  1.72080 -1.88934  0.71882  0.96116 -1.95992  1.56960 -0.06683 -1.48330  1.98215 -1.07616 -0.59255  1.84130 -1.78504  0.46364  1.18636 -1.99553  1.39038  0.20019 -1.64888  1.92894 -0.84187  0.00000  2.00000 -1.29126  1.72080  0.71882 -1.95992 -0.06683  1.98215 -0.59255 -1.78504  1.18636  1.39038 -1.64888 -0.84187  1.92894  0.20019 -1.99553  0.46364  1.84130 -1.07616 -1.48330  1.56960  0.96116 -1.88934 -0.33266  0.00000     ... ... ..... ....... ......... ........... .............
E17"    2.00000 -1.29126 -0.33266  1.72080 -1.88934  0.71882  0.96116 -1.95992  1.56960 -0.06683 -1.48330  1.98215 -1.07616 -0.59255  1.84130 -1.78504  0.46364  1.18636 -1.99553  1.39038  0.20019 -1.64888  1.92894 -0.84187  0.00000 -2.00000  1.29126 -1.72080 -0.71882  1.95992  0.06683 -1.98215  0.59255  1.78504 -1.18636 -1.39038  1.64888  0.84187 -1.92894 -0.20019  1.99553 -0.46364 -1.84130  1.07616  1.48330 -1.56960 -0.96116  1.88934  0.33266  0.00000     ... ... ..... ....... ......... ........... .............
E18'    2.00000 -1.48330  0.20019  1.18636 -1.95992  1.72080 -0.59255 -0.84187  1.84130 -1.88934  0.96116  0.46364 -1.64888  1.98215 -1.29126 -0.06683  1.39038 -1.99553  1.56960 -0.33266 -1.07616  1.92894 -1.78504  0.71882  0.00000  2.00000 -1.48330  1.18636  1.72080 -0.84187 -1.88934  0.46364  1.98215 -0.06683 -1.99553 -0.33266  1.92894  0.71882 -1.78504 -1.07616  1.56960  1.39038 -1.29126 -1.64888  0.96116  1.84130 -0.59255 -1.95992  0.20019  0.00000     ... ... ..... ....... ......... ........... .............
E18"    2.00000 -1.48330  0.20019  1.18636 -1.95992  1.72080 -0.59255 -0.84187  1.84130 -1.88934  0.96116  0.46364 -1.64888  1.98215 -1.29126 -0.06683  1.39038 -1.99553  1.56960 -0.33266 -1.07616  1.92894 -1.78504  0.71882  0.00000 -2.00000  1.48330 -1.18636 -1.72080  0.84187  1.88934 -0.46364 -1.98215  0.06683  1.99553  0.33266 -1.92894 -0.71882  1.78504  1.07616 -1.56960 -1.39038  1.29126  1.64888 -0.96116 -1.84130  0.59255  1.95992 -0.20019  0.00000     ... ... ..... ....... ......... ........... .............
E19'    2.00000 -1.64888  0.71882  0.46364 -1.48330  1.98215 -1.78504  0.96116  0.20019 -1.29126  1.92894 -1.88934  1.18636 -0.06683 -1.07616  1.84130 -1.95992  1.39038 -0.33266 -0.84187  1.72080 -1.99553  1.56960 -0.59255  0.00000  2.00000 -1.64888  0.46364  1.98215  0.96116 -1.29126 -1.88934 -0.06683  1.84130  1.39038 -0.84187 -1.99553 -0.59255  1.56960  1.72080 -0.33266 -1.95992 -1.07616  1.18636  1.92894  0.20019 -1.78504 -1.48330  0.71882  0.00000     ... ... ..... ....... ......... ........... .............
E19"    2.00000 -1.64888  0.71882  0.46364 -1.48330  1.98215 -1.78504  0.96116  0.20019 -1.29126  1.92894 -1.88934  1.18636 -0.06683 -1.07616  1.84130 -1.95992  1.39038 -0.33266 -0.84187  1.72080 -1.99553  1.56960 -0.59255  0.00000 -2.00000  1.64888 -0.46364 -1.98215 -0.96116  1.29126  1.88934  0.06683 -1.84130 -1.39038  0.84187  1.99553  0.59255 -1.56960 -1.72080  0.33266  1.95992  1.07616 -1.18636 -1.92894 -0.20019  1.78504  1.48330 -0.71882  0.00000     ... ... ..... ....... ......... ........... .............
E20'    2.00000 -1.78504  1.18636 -0.33266 -0.59255  1.39038 -1.88934  1.98215 -1.64888  0.96116 -0.06683 -0.84187  1.56960 -1.95992  1.92894 -1.48330  0.71882  0.20019 -1.07616  1.72080 -1.99553  1.84130 -1.29126  0.46364  0.00000  2.00000 -1.78504 -0.33266  1.39038  1.98215  0.96116 -0.84187 -1.95992 -1.48330  0.20019  1.72080  1.84130  0.46364 -1.29126 -1.99553 -1.07616  0.71882  1.92894  1.56960 -0.06683 -1.64888 -1.88934 -0.59255  1.18636  0.00000     ... ... ..... ....... ......... ........... .............
E20"    2.00000 -1.78504  1.18636 -0.33266 -0.59255  1.39038 -1.88934  1.98215 -1.64888  0.96116 -0.06683 -0.84187  1.56960 -1.95992  1.92894 -1.48330  0.71882  0.20019 -1.07616  1.72080 -1.99553  1.84130 -1.29126  0.46364  0.00000 -2.00000  1.78504  0.33266 -1.39038 -1.98215 -0.96116  0.84187  1.95992  1.48330 -0.20019 -1.72080 -1.84130 -0.46364  1.29126  1.99553  1.07616 -0.71882 -1.92894 -1.56960  0.06683  1.64888  1.88934  0.59255 -1.18636  0.00000     ... ... ..... ....... ......... ........... .............
E21'    2.00000 -1.88934  1.56960 -1.07616  0.46364  0.20019 -0.84187  1.39038 -1.78504  1.98215 -1.95992  1.72080 -1.29126  0.71882 -0.06683 -0.59255  1.18636 -1.64888  1.92894 -1.99553  1.84130 -1.48330  0.96116 -0.33266  0.00000  2.00000 -1.88934 -1.07616  0.20019  1.39038  1.98215  1.72080  0.71882 -0.59255 -1.64888 -1.99553 -1.48330 -0.33266  0.96116  1.84130  1.92894  1.18636 -0.06683 -1.29126 -1.95992 -1.78504 -0.84187  0.46364  1.56960  0.00000     ... ... ..... ....... ......... ........... .............
E21"    2.00000 -1.88934  1.56960 -1.07616  0.46364  0.20019 -0.84187  1.39038 -1.78504  1.98215 -1.95992  1.72080 -1.29126  0.71882 -0.06683 -0.59255  1.18636 -1.64888  1.92894 -1.99553  1.84130 -1.48330  0.96116 -0.33266  0.00000 -2.00000  1.88934  1.07616 -0.20019 -1.39038 -1.98215 -1.72080 -0.71882  0.59255  1.64888  1.99553  1.48330  0.33266 -0.96116 -1.84130 -1.92894 -1.18636  0.06683  1.29126  1.95992  1.78504  0.84187 -0.46364 -1.56960  0.00000     ... ... ..... ....... ......... ........... .............
E22'    2.00000 -1.95992  1.84130 -1.64888  1.39038 -1.07616  0.71882 -0.33266 -0.06683  0.46364 -0.84187  1.18636 -1.48330  1.72080 -1.88934  1.98215 -1.99553  1.92894 -1.78504  1.56960 -1.29126  0.96116 -0.59255  0.20019  0.00000  2.00000 -1.95992 -1.64888 -1.07616 -0.33266  0.46364  1.18636  1.72080  1.98215  1.92894  1.56960  0.96116  0.20019 -0.59255 -1.29126 -1.78504 -1.99553 -1.88934 -1.48330 -0.84187 -0.06683  0.71882  1.39038  1.84130  0.00000     ... ... ..... ....... ......... ........... .............
E22"    2.00000 -1.95992  1.84130 -1.64888  1.39038 -1.07616  0.71882 -0.33266 -0.06683  0.46364 -0.84187  1.18636 -1.48330  1.72080 -1.88934  1.98215 -1.99553  1.92894 -1.78504  1.56960 -1.29126  0.96116 -0.59255  0.20019  0.00000 -2.00000  1.95992  1.64888  1.07616  0.33266 -0.46364 -1.18636 -1.72080 -1.98215 -1.92894 -1.56960 -0.96116 -0.20019  0.59255  1.29126  1.78504  1.99553  1.88934  1.48330  0.84187  0.06683 -0.71882 -1.39038 -1.84130  0.00000     ... ... ..... ....... ......... ........... .............
E23'    2.00000 -1.99553  1.98215 -1.95992  1.92894 -1.88934  1.84130 -1.78504  1.72080 -1.64888  1.56960 -1.48330  1.39038 -1.29126  1.18636 -1.07616  0.96116 -0.84187  0.71882 -0.59255  0.46364 -0.33266  0.20019 -0.06683  0.00000  2.00000 -1.99553 -1.95992 -1.88934 -1.78504 -1.64888 -1.48330 -1.29126 -1.07616 -0.84187 -0.59255 -0.33266 -0.06683  0.20019  0.46364  0.71882  0.96116  1.18636  1.39038  1.56960  1.72080  1.84130  1.92894  1.98215  0.00000     ... ... ..... ....... ......... ........... .............
E23"    2.00000 -1.99553  1.98215 -1.95992  1.92894 -1.88934  1.84130 -1.78504  1.72080 -1.64888  1.56960 -1.48330  1.39038 -1.29126  1.18636 -1.07616  0.96116 -0.84187  0.71882 -0.59255  0.46364 -0.33266  0.20019 -0.06683  0.00000 -2.00000  1.99553  1.95992  1.88934  1.78504  1.64888  1.48330  1.29126  1.07616  0.84187  0.59255  0.33266  0.06683 -0.20019 -0.46364 -0.71882 -0.96116 -1.18636 -1.39038 -1.56960 -1.72080 -1.84130 -1.92894 -1.98215  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.995533757246 = 2*cos(2*π/94) = 2*cos(π/47)
                               1.982154976310 = 2*cos(4*π/94) = 2*cos(2*π/47)
                               1.959923410073 = 2*cos(6*π/94) = 2*cos(3*π/47)
                               1.928938350109 = 2*cos(8*π/94) = 2*cos(4*π/47)
                               1.889338183216 = 2*cos(10*π/94) = 2*cos(5*π/47)
                               1.841299773353 = 2*cos(12*π/94) = 2*cos(6*π/47)
                               1.785037671720 = 2*cos(14*π/94) = 2*cos(7*π/47)
                               1.720803158520 = 2*cos(16*π/94) = 2*cos(8*π/47)
                               1.648883120684 = 2*cos(18*π/94) = 2*cos(9*π/47)
                               1.569598770557 = 2*cos(20*π/94) = 2*cos(10*π/47)
                               1.483304211296 = 2*cos(22*π/94) = 2*cos(11*π/47)
                               1.390384855349 = 2*cos(24*π/94) = 2*cos(12*π/47)
                               1.291255703118 = 2*cos(26*π/94) = 2*cos(13*π/47)
                               1.186359489459 = 2*cos(28*π/94) = 2*cos(14*π/47)
                               1.076164706327 = 2*cos(30*π/94) = 2*cos(15*π/47)
                               0.961163510373 = 2*cos(32*π/94) = 2*cos(16*π/47)
                               0.841869524857 = 2*cos(34*π/94) = 2*cos(17*π/47)
                               0.718815545675 = 2*cos(36*π/94) = 2*cos(18*π/47)
                               0.592551161771 = 2*cos(38*π/94) = 2*cos(19*π/47)
                               0.463640300535 = 2*cos(40*π/94) = 2*cos(20*π/47)
                               0.332658709166 = 2*cos(42*π/94) = 2*cos(21*π/47)
                               0.200191383248 = 2*cos(44*π/94) = 2*cos(22*π/47)
                               0.066829954015 = 2*cos(46*π/94) = 2*cos(23*π/47)



 Symmetry of Rotations and Cartesian products

A1'  d+g+i+k+m    z2, z4, z6 
A2'  R            Rz 
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  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2'  d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E2"  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3'  f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E3"  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4'  g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E4"  h+j+l        {z((x2y2)2−4x2y2), xyz(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)} 
E5"  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6'  i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
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 D47h point group is 188, and the order of the principal axis (S47) is 94. The group has 50 irreducible representations.

    β  The D47h point group is isomorphic to D47d, C94v and D94.

    γ  The D47h point group is generated by two symmetry elements, S47 and either a perpendicular C2 or a vertical σv.
       Also, the group may be generated from any two σv planes, or any σv and a non-coplanar C2.
       The canonical choice, however, is to use redundant generators: C47, C2 and σh.

    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 σd contains the xz plane but not the yz plane.

    ε  The lowest nonvanishing multipole moment in D47h 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 D47h point group was created by Gernot Katzer.

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