Character table for the D98 point group

D98     E        2 C98    2 C49    2 C98^3  2 C49^2  2 C98^5  2 C49^3  2 C14    2 C49^4  2 C98^9  2 C49^5  2 C98^11 2 C49^6  2 C98^13 2 C7     2 C98^15 2 C49^8  2 C98^17 2 C49^9  2 C98^19 2 C49^10 2 C14^3  2 C49^11 2 C98^23 2 C49^12 2 C98^25 2 C49^13 2 C98^27 2 C7^2   2 C98^29 2 C49^15 2 C98^31 2 C49^16 2 C98^33 2 C49^17 2 C14^5  2 C49^18 2 C98^37 2 C49^19 2 C98^39 2 C49^20 2 C98^41 2 C7^3   2 C98^43 2 C49^22 2 C98^45 2 C49^23 2 C98^47 2 C49^24 C2       49 C2'   49 C2"      <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     ... ... ....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     ..T ..T ..... ......T ......... ..........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     ... ... ..... ....... ......... ........... .............
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     ... ... ..... ....... ......... ........... .............
E1      2.00000  1.99589  1.98358  1.96312  1.93459  1.89811  1.85383  1.80194  1.74264  1.67618  1.60283  1.52289  1.43670  1.34460  1.24698  1.14423  1.03679  0.92508  0.80957  0.69073  0.56906  0.44504  0.31920  0.19205  0.06410 -0.06410 -0.19205 -0.31920 -0.44504 -0.56906 -0.69073 -0.80957 -0.92508 -1.03679 -1.14423 -1.24698 -1.34460 -1.43670 -1.52289 -1.60283 -1.67618 -1.74264 -1.80194 -1.85383 -1.89811 -1.93459 -1.96312 -1.98358 -1.99589 -2.00000  0.00000  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.98358  1.93459  1.85383  1.74264  1.60283  1.43670  1.24698  1.03679  0.80957  0.56906  0.31920  0.06410 -0.19205 -0.44504 -0.69073 -0.92508 -1.14423 -1.34460 -1.52289 -1.67618 -1.80194 -1.89811 -1.96312 -1.99589 -1.99589 -1.96312 -1.89811 -1.80194 -1.67618 -1.52289 -1.34460 -1.14423 -0.92508 -0.69073 -0.44504 -0.19205  0.06410  0.31920  0.56906  0.80957  1.03679  1.24698  1.43670  1.60283  1.74264  1.85383  1.93459  1.98358  2.00000  0.00000  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.96312  1.85383  1.67618  1.43670  1.14423  0.80957  0.44504  0.06410 -0.31920 -0.69073 -1.03679 -1.34460 -1.60283 -1.80194 -1.93459 -1.99589 -1.98358 -1.89811 -1.74264 -1.52289 -1.24698 -0.92508 -0.56906 -0.19205  0.19205  0.56906  0.92508  1.24698  1.52289  1.74264  1.89811  1.98358  1.99589  1.93459  1.80194  1.60283  1.34460  1.03679  0.69073  0.31920 -0.06410 -0.44504 -0.80957 -1.14423 -1.43670 -1.67618 -1.85383 -1.96312 -2.00000  0.00000  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.93459  1.74264  1.43670  1.03679  0.56906  0.06410 -0.44504 -0.92508 -1.34460 -1.67618 -1.89811 -1.99589 -1.96312 -1.80194 -1.52289 -1.14423 -0.69073 -0.19205  0.31920  0.80957  1.24698  1.60283  1.85383  1.98358  1.98358  1.85383  1.60283  1.24698  0.80957  0.31920 -0.19205 -0.69073 -1.14423 -1.52289 -1.80194 -1.96312 -1.99589 -1.89811 -1.67618 -1.34460 -0.92508 -0.44504  0.06410  0.56906  1.03679  1.43670  1.74264  1.93459  2.00000  0.00000  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.89811  1.60283  1.14423  0.56906 -0.06410 -0.69073 -1.24698 -1.67618 -1.93459 -1.99589 -1.85383 -1.52289 -1.03679 -0.44504  0.19205  0.80957  1.34460  1.74264  1.96312  1.98358  1.80194  1.43670  0.92508  0.31920 -0.31920 -0.92508 -1.43670 -1.80194 -1.98358 -1.96312 -1.74264 -1.34460 -0.80957 -0.19205  0.44504  1.03679  1.52289  1.85383  1.99589  1.93459  1.67618  1.24698  0.69073  0.06410 -0.56906 -1.14423 -1.60283 -1.89811 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.85383  1.43670  0.80957  0.06410 -0.69073 -1.34460 -1.80194 -1.99589 -1.89811 -1.52289 -0.92508 -0.19205  0.56906  1.24698  1.74264  1.98358  1.93459  1.60283  1.03679  0.31920 -0.44504 -1.14423 -1.67618 -1.96312 -1.96312 -1.67618 -1.14423 -0.44504  0.31920  1.03679  1.60283  1.93459  1.98358  1.74264  1.24698  0.56906 -0.19205 -0.92508 -1.52289 -1.89811 -1.99589 -1.80194 -1.34460 -0.69073  0.06410  0.80957  1.43670  1.85383  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504  0.44504  1.24698  1.80194  2.00000  1.80194  1.24698  0.44504 -0.44504 -1.24698 -1.80194 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.74264  1.03679  0.06410 -0.92508 -1.67618 -1.99589 -1.80194 -1.14423 -0.19205  0.80957  1.60283  1.98358  1.85383  1.24698  0.31920 -0.69073 -1.52289 -1.96312 -1.89811 -1.34460 -0.44504  0.56906  1.43670  1.93459  1.93459  1.43670  0.56906 -0.44504 -1.34460 -1.89811 -1.96312 -1.52289 -0.69073  0.31920  1.24698  1.85383  1.98358  1.60283  0.80957 -0.19205 -1.14423 -1.80194 -1.99589 -1.67618 -0.92508  0.06410  1.03679  1.74264  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.67618  0.80957 -0.31920 -1.34460 -1.93459 -1.89811 -1.24698 -0.19205  0.92508  1.74264  1.99589  1.60283  0.69073 -0.44504 -1.43670 -1.96312 -1.85383 -1.14423 -0.06410  1.03679  1.80194  1.98358  1.52289  0.56906 -0.56906 -1.52289 -1.98358 -1.80194 -1.03679  0.06410  1.14423  1.85383  1.96312  1.43670  0.44504 -0.69073 -1.60283 -1.99589 -1.74264 -0.92508  0.19205  1.24698  1.89811  1.93459  1.34460  0.31920 -0.80957 -1.67618 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.60283  0.56906 -0.69073 -1.67618 -1.99589 -1.52289 -0.44504  0.80957  1.74264  1.98358  1.43670  0.31920 -0.92508 -1.80194 -1.96312 -1.34460 -0.19205  1.03679  1.85383  1.93459  1.24698  0.06410 -1.14423 -1.89811 -1.89811 -1.14423  0.06410  1.24698  1.93459  1.85383  1.03679 -0.19205 -1.34460 -1.96312 -1.80194 -0.92508  0.31920  1.43670  1.98358  1.74264  0.80957 -0.44504 -1.52289 -1.99589 -1.67618 -0.69073  0.56906  1.60283  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.52289  0.31920 -1.03679 -1.89811 -1.85383 -0.92508  0.44504  1.60283  1.99589  1.43670  0.19205 -1.14423 -1.93459 -1.80194 -0.80957  0.56906  1.67618  1.98358  1.34460  0.06410 -1.24698 -1.96312 -1.74264 -0.69073  0.69073  1.74264  1.96312  1.24698 -0.06410 -1.34460 -1.98358 -1.67618 -0.56906  0.80957  1.80194  1.93459  1.14423 -0.19205 -1.43670 -1.99589 -1.60283 -0.44504  0.92508  1.85383  1.89811  1.03679 -0.31920 -1.52289 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  1.43670  0.06410 -1.34460 -1.99589 -1.52289 -0.19205  1.24698  1.98358  1.60283  0.31920 -1.14423 -1.96312 -1.67618 -0.44504  1.03679  1.93459  1.74264  0.56906 -0.92508 -1.89811 -1.80194 -0.69073  0.80957  1.85383  1.85383  0.80957 -0.69073 -1.80194 -1.89811 -0.92508  0.56906  1.74264  1.93459  1.03679 -0.44504 -1.67618 -1.96312 -1.14423  0.31920  1.60283  1.98358  1.24698 -0.19205 -1.52289 -1.99589 -1.34460  0.06410  1.43670  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  1.34460 -0.19205 -1.60283 -1.96312 -1.03679  0.56906  1.80194  1.85383  0.69073 -0.92508 -1.93459 -1.67618 -0.31920  1.24698  1.99589  1.43670 -0.06410 -1.52289 -1.98358 -1.14423  0.44504  1.74264  1.89811  0.80957 -0.80957 -1.89811 -1.74264 -0.44504  1.14423  1.98358  1.52289  0.06410 -1.43670 -1.99589 -1.24698  0.31920  1.67618  1.93459  0.92508 -0.69073 -1.85383 -1.80194 -0.56906  1.03679  1.96312  1.60283  0.19205 -1.34460 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  1.14423 -0.69073 -1.93459 -1.52289  0.19205  1.74264  1.80194  0.31920 -1.43670 -1.96312 -0.80957  1.03679  1.99589  1.24698 -0.56906 -1.89811 -1.60283  0.06410  1.67618  1.85383  0.44504 -1.34460 -1.98358 -0.92508  0.92508  1.98358  1.34460 -0.44504 -1.85383 -1.67618 -0.06410  1.60283  1.89811  0.56906 -1.24698 -1.99589 -1.03679  0.80957  1.96312  1.43670 -0.31920 -1.80194 -1.74264 -0.19205  1.52289  1.93459  0.69073 -1.14423 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  1.03679 -0.92508 -1.99589 -1.14423  0.80957  1.98358  1.24698 -0.69073 -1.96312 -1.34460  0.56906  1.93459  1.43670 -0.44504 -1.89811 -1.52289  0.31920  1.85383  1.60283 -0.19205 -1.80194 -1.67618  0.06410  1.74264  1.74264  0.06410 -1.67618 -1.80194 -0.19205  1.60283  1.85383  0.31920 -1.52289 -1.89811 -0.44504  1.43670  1.93459  0.56906 -1.34460 -1.96312 -0.69073  1.24698  1.98358  0.80957 -1.14423 -1.99589 -0.92508  1.03679  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.92508 -1.14423 -1.98358 -0.69073  1.34460  1.93459  0.44504 -1.52289 -1.85383 -0.19205  1.67618  1.74264 -0.06410 -1.80194 -1.60283  0.31920  1.89811  1.43670 -0.56906 -1.96312 -1.24698  0.80957  1.99589  1.03679 -1.03679 -1.99589 -0.80957  1.24698  1.96312  0.56906 -1.43670 -1.89811 -0.31920  1.60283  1.80194  0.06410 -1.74264 -1.67618  0.19205  1.85383  1.52289 -0.44504 -1.93459 -1.34460  0.69073  1.98358  1.14423 -0.92508 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000  0.80957 -1.34460 -1.89811 -0.19205  1.74264  1.60283 -0.44504 -1.96312 -1.14423  1.03679  1.98358  0.56906 -1.52289 -1.80194  0.06410  1.85383  1.43670 -0.69073 -1.99589 -0.92508  1.24698  1.93459  0.31920 -1.67618 -1.67618  0.31920  1.93459  1.24698 -0.92508 -1.99589 -0.69073  1.43670  1.85383  0.06410 -1.80194 -1.52289  0.56906  1.98358  1.03679 -1.14423 -1.96312 -0.44504  1.60283  1.74264 -0.19205 -1.89811 -1.34460  0.80957  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000  0.69073 -1.52289 -1.74264  0.31920  1.96312  1.03679 -1.24698 -1.89811 -0.06410  1.85383  1.34460 -0.92508 -1.98358 -0.44504  1.67618  1.60283 -0.56906 -1.99589 -0.80957  1.43670  1.80194 -0.19205 -1.93459 -1.14423  1.14423  1.93459  0.19205 -1.80194 -1.43670  0.80957  1.99589  0.56906 -1.60283 -1.67618  0.44504  1.98358  0.92508 -1.34460 -1.85383  0.06410  1.89811  1.24698 -1.03679 -1.96312 -0.31920  1.74264  1.52289 -0.69073 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000  0.56906 -1.67618 -1.52289  0.80957  1.98358  0.31920 -1.80194 -1.34460  1.03679  1.93459  0.06410 -1.89811 -1.14423  1.24698  1.85383 -0.19205 -1.96312 -0.92508  1.43670  1.74264 -0.44504 -1.99589 -0.69073  1.60283  1.60283 -0.69073 -1.99589 -0.44504  1.74264  1.43670 -0.92508 -1.96312 -0.19205  1.85383  1.24698 -1.14423 -1.89811  0.06410  1.93459  1.03679 -1.34460 -1.80194  0.31920  1.98358  0.80957 -1.52289 -1.67618  0.56906  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000 -0.44504  1.80194  1.24698 -1.24698 -1.80194  0.44504  2.00000  0.44504 -1.80194 -1.24698  1.24698  1.80194 -0.44504 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000  0.31920 -1.89811 -0.92508  1.60283  1.43670 -1.14423 -1.80194  0.56906  1.98358  0.06410 -1.96312 -0.69073  1.74264  1.24698 -1.34460 -1.67618  0.80957  1.93459 -0.19205 -1.99589 -0.44504  1.85383  1.03679 -1.52289 -1.52289  1.03679  1.85383 -0.44504 -1.99589 -0.19205  1.93459  0.80957 -1.67618 -1.34460  1.24698  1.74264 -0.69073 -1.96312  0.06410  1.98358  0.56906 -1.80194 -1.14423  1.43670  1.60283 -0.92508 -1.89811  0.31920  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000  0.19205 -1.96312 -0.56906  1.85383  0.92508 -1.67618 -1.24698  1.43670  1.52289 -1.14423 -1.74264  0.80957  1.89811 -0.44504 -1.98358  0.06410  1.99589  0.31920 -1.93459 -0.69073  1.80194  1.03679 -1.60283 -1.34460  1.34460  1.60283 -1.03679 -1.80194  0.69073  1.93459 -0.31920 -1.99589 -0.06410  1.98358  0.44504 -1.89811 -0.80957  1.74264  1.14423 -1.52289 -1.43670  1.24698  1.67618 -0.92508 -1.85383  0.56906  1.96312 -0.19205 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000  0.06410 -1.99589 -0.19205  1.98358  0.31920 -1.96312 -0.44504  1.93459  0.56906 -1.89811 -0.69073  1.85383  0.80957 -1.80194 -0.92508  1.74264  1.03679 -1.67618 -1.14423  1.60283  1.24698 -1.52289 -1.34460  1.43670  1.43670 -1.34460 -1.52289  1.24698  1.60283 -1.14423 -1.67618  1.03679  1.74264 -0.92508 -1.80194  0.80957  1.85383 -0.69073 -1.89811  0.56906  1.93459 -0.44504 -1.96312  0.31920  1.98358 -0.19205 -1.99589  0.06410  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -0.06410 -1.99589  0.19205  1.98358 -0.31920 -1.96312  0.44504  1.93459 -0.56906 -1.89811  0.69073  1.85383 -0.80957 -1.80194  0.92508  1.74264 -1.03679 -1.67618  1.14423  1.60283 -1.24698 -1.52289  1.34460  1.43670 -1.43670 -1.34460  1.52289  1.24698 -1.60283 -1.14423  1.67618  1.03679 -1.74264 -0.92508  1.80194  0.80957 -1.85383 -0.69073  1.89811  0.56906 -1.93459 -0.44504  1.96312  0.31920 -1.98358 -0.19205  1.99589  0.06410 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -0.19205 -1.96312  0.56906  1.85383 -0.92508 -1.67618  1.24698  1.43670 -1.52289 -1.14423  1.74264  0.80957 -1.89811 -0.44504  1.98358  0.06410 -1.99589  0.31920  1.93459 -0.69073 -1.80194  1.03679  1.60283 -1.34460 -1.34460  1.60283  1.03679 -1.80194 -0.69073  1.93459  0.31920 -1.99589  0.06410  1.98358 -0.44504 -1.89811  0.80957  1.74264 -1.14423 -1.52289  1.43670  1.24698 -1.67618 -0.92508  1.85383  0.56906 -1.96312 -0.19205  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -0.31920 -1.89811  0.92508  1.60283 -1.43670 -1.14423  1.80194  0.56906 -1.98358  0.06410  1.96312 -0.69073 -1.74264  1.24698  1.34460 -1.67618 -0.80957  1.93459  0.19205 -1.99589  0.44504  1.85383 -1.03679 -1.52289  1.52289  1.03679 -1.85383 -0.44504  1.99589 -0.19205 -1.93459  0.80957  1.67618 -1.34460 -1.24698  1.74264  0.69073 -1.96312 -0.06410  1.98358 -0.56906 -1.80194  1.14423  1.43670 -1.60283 -0.92508  1.89811  0.31920 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -0.56906 -1.67618  1.52289  0.80957 -1.98358  0.31920  1.80194 -1.34460 -1.03679  1.93459 -0.06410 -1.89811  1.14423  1.24698 -1.85383 -0.19205  1.96312 -0.92508 -1.43670  1.74264  0.44504 -1.99589  0.69073  1.60283 -1.60283 -0.69073  1.99589 -0.44504 -1.74264  1.43670  0.92508 -1.96312  0.19205  1.85383 -1.24698 -1.14423  1.89811  0.06410 -1.93459  1.03679  1.34460 -1.80194 -0.31920  1.98358 -0.80957 -1.52289  1.67618  0.56906 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -0.69073 -1.52289  1.74264  0.31920 -1.96312  1.03679  1.24698 -1.89811  0.06410  1.85383 -1.34460 -0.92508  1.98358 -0.44504 -1.67618  1.60283  0.56906 -1.99589  0.80957  1.43670 -1.80194 -0.19205  1.93459 -1.14423 -1.14423  1.93459 -0.19205 -1.80194  1.43670  0.80957 -1.99589  0.56906  1.60283 -1.67618 -0.44504  1.98358 -0.92508 -1.34460  1.85383  0.06410 -1.89811  1.24698  1.03679 -1.96312  0.31920  1.74264 -1.52289 -0.69073  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -0.80957 -1.34460  1.89811 -0.19205 -1.74264  1.60283  0.44504 -1.96312  1.14423  1.03679 -1.98358  0.56906  1.52289 -1.80194 -0.06410  1.85383 -1.43670 -0.69073  1.99589 -0.92508 -1.24698  1.93459 -0.31920 -1.67618  1.67618  0.31920 -1.93459  1.24698  0.92508 -1.99589  0.69073  1.43670 -1.85383  0.06410  1.80194 -1.52289 -0.56906  1.98358 -1.03679 -1.14423  1.96312 -0.44504 -1.60283  1.74264  0.19205 -1.89811  1.34460  0.80957 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -0.92508 -1.14423  1.98358 -0.69073 -1.34460  1.93459 -0.44504 -1.52289  1.85383 -0.19205 -1.67618  1.74264  0.06410 -1.80194  1.60283  0.31920 -1.89811  1.43670  0.56906 -1.96312  1.24698  0.80957 -1.99589  1.03679  1.03679 -1.99589  0.80957  1.24698 -1.96312  0.56906  1.43670 -1.89811  0.31920  1.60283 -1.80194  0.06410  1.74264 -1.67618 -0.19205  1.85383 -1.52289 -0.44504  1.93459 -1.34460 -0.69073  1.98358 -1.14423 -0.92508  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.03679 -0.92508  1.99589 -1.14423 -0.80957  1.98358 -1.24698 -0.69073  1.96312 -1.34460 -0.56906  1.93459 -1.43670 -0.44504  1.89811 -1.52289 -0.31920  1.85383 -1.60283 -0.19205  1.80194 -1.67618 -0.06410  1.74264 -1.74264  0.06410  1.67618 -1.80194  0.19205  1.60283 -1.85383  0.31920  1.52289 -1.89811  0.44504  1.43670 -1.93459  0.56906  1.34460 -1.96312  0.69073  1.24698 -1.98358  0.80957  1.14423 -1.99589  0.92508  1.03679 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.14423 -0.69073  1.93459 -1.52289 -0.19205  1.74264 -1.80194  0.31920  1.43670 -1.96312  0.80957  1.03679 -1.99589  1.24698  0.56906 -1.89811  1.60283  0.06410 -1.67618  1.85383 -0.44504 -1.34460  1.98358 -0.92508 -0.92508  1.98358 -1.34460 -0.44504  1.85383 -1.67618  0.06410  1.60283 -1.89811  0.56906  1.24698 -1.99589  1.03679  0.80957 -1.96312  1.43670  0.31920 -1.80194  1.74264 -0.19205 -1.52289  1.93459 -0.69073 -1.14423  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  1.24698  0.44504 -1.80194  1.80194 -0.44504 -1.24698  2.00000 -1.24698 -0.44504  1.80194 -1.80194  0.44504  1.24698 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E36     2.00000 -1.34460 -0.19205  1.60283 -1.96312  1.03679  0.56906 -1.80194  1.85383 -0.69073 -0.92508  1.93459 -1.67618  0.31920  1.24698 -1.99589  1.43670  0.06410 -1.52289  1.98358 -1.14423 -0.44504  1.74264 -1.89811  0.80957  0.80957 -1.89811  1.74264 -0.44504 -1.14423  1.98358 -1.52289  0.06410  1.43670 -1.99589  1.24698  0.31920 -1.67618  1.93459 -0.92508 -0.69073  1.85383 -1.80194  0.56906  1.03679 -1.96312  1.60283 -0.19205 -1.34460  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E37     2.00000 -1.43670  0.06410  1.34460 -1.99589  1.52289 -0.19205 -1.24698  1.98358 -1.60283  0.31920  1.14423 -1.96312  1.67618 -0.44504 -1.03679  1.93459 -1.74264  0.56906  0.92508 -1.89811  1.80194 -0.69073 -0.80957  1.85383 -1.85383  0.80957  0.69073 -1.80194  1.89811 -0.92508 -0.56906  1.74264 -1.93459  1.03679  0.44504 -1.67618  1.96312 -1.14423 -0.31920  1.60283 -1.98358  1.24698  0.19205 -1.52289  1.99589 -1.34460 -0.06410  1.43670 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E38     2.00000 -1.52289  0.31920  1.03679 -1.89811  1.85383 -0.92508 -0.44504  1.60283 -1.99589  1.43670 -0.19205 -1.14423  1.93459 -1.80194  0.80957  0.56906 -1.67618  1.98358 -1.34460  0.06410  1.24698 -1.96312  1.74264 -0.69073 -0.69073  1.74264 -1.96312  1.24698  0.06410 -1.34460  1.98358 -1.67618  0.56906  0.80957 -1.80194  1.93459 -1.14423 -0.19205  1.43670 -1.99589  1.60283 -0.44504 -0.92508  1.85383 -1.89811  1.03679  0.31920 -1.52289  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E39     2.00000 -1.60283  0.56906  0.69073 -1.67618  1.99589 -1.52289  0.44504  0.80957 -1.74264  1.98358 -1.43670  0.31920  0.92508 -1.80194  1.96312 -1.34460  0.19205  1.03679 -1.85383  1.93459 -1.24698  0.06410  1.14423 -1.89811  1.89811 -1.14423 -0.06410  1.24698 -1.93459  1.85383 -1.03679 -0.19205  1.34460 -1.96312  1.80194 -0.92508 -0.31920  1.43670 -1.98358  1.74264 -0.80957 -0.44504  1.52289 -1.99589  1.67618 -0.69073 -0.56906  1.60283 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E40     2.00000 -1.67618  0.80957  0.31920 -1.34460  1.93459 -1.89811  1.24698 -0.19205 -0.92508  1.74264 -1.99589  1.60283 -0.69073 -0.44504  1.43670 -1.96312  1.85383 -1.14423  0.06410  1.03679 -1.80194  1.98358 -1.52289  0.56906  0.56906 -1.52289  1.98358 -1.80194  1.03679  0.06410 -1.14423  1.85383 -1.96312  1.43670 -0.44504 -0.69073  1.60283 -1.99589  1.74264 -0.92508 -0.19205  1.24698 -1.89811  1.93459 -1.34460  0.31920  0.80957 -1.67618  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E41     2.00000 -1.74264  1.03679 -0.06410 -0.92508  1.67618 -1.99589  1.80194 -1.14423  0.19205  0.80957 -1.60283  1.98358 -1.85383  1.24698 -0.31920 -0.69073  1.52289 -1.96312  1.89811 -1.34460  0.44504  0.56906 -1.43670  1.93459 -1.93459  1.43670 -0.56906 -0.44504  1.34460 -1.89811  1.96312 -1.52289  0.69073  0.31920 -1.24698  1.85383 -1.98358  1.60283 -0.80957 -0.19205  1.14423 -1.80194  1.99589 -1.67618  0.92508  0.06410 -1.03679  1.74264 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E42     2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E43     2.00000 -1.85383  1.43670 -0.80957  0.06410  0.69073 -1.34460  1.80194 -1.99589  1.89811 -1.52289  0.92508 -0.19205 -0.56906  1.24698 -1.74264  1.98358 -1.93459  1.60283 -1.03679  0.31920  0.44504 -1.14423  1.67618 -1.96312  1.96312 -1.67618  1.14423 -0.44504 -0.31920  1.03679 -1.60283  1.93459 -1.98358  1.74264 -1.24698  0.56906  0.19205 -0.92508  1.52289 -1.89811  1.99589 -1.80194  1.34460 -0.69073 -0.06410  0.80957 -1.43670  1.85383 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E44     2.00000 -1.89811  1.60283 -1.14423  0.56906  0.06410 -0.69073  1.24698 -1.67618  1.93459 -1.99589  1.85383 -1.52289  1.03679 -0.44504 -0.19205  0.80957 -1.34460  1.74264 -1.96312  1.98358 -1.80194  1.43670 -0.92508  0.31920  0.31920 -0.92508  1.43670 -1.80194  1.98358 -1.96312  1.74264 -1.34460  0.80957 -0.19205 -0.44504  1.03679 -1.52289  1.85383 -1.99589  1.93459 -1.67618  1.24698 -0.69073  0.06410  0.56906 -1.14423  1.60283 -1.89811  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E45     2.00000 -1.93459  1.74264 -1.43670  1.03679 -0.56906  0.06410  0.44504 -0.92508  1.34460 -1.67618  1.89811 -1.99589  1.96312 -1.80194  1.52289 -1.14423  0.69073 -0.19205 -0.31920  0.80957 -1.24698  1.60283 -1.85383  1.98358 -1.98358  1.85383 -1.60283  1.24698 -0.80957  0.31920  0.19205 -0.69073  1.14423 -1.52289  1.80194 -1.96312  1.99589 -1.89811  1.67618 -1.34460  0.92508 -0.44504 -0.06410  0.56906 -1.03679  1.43670 -1.74264  1.93459 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E46     2.00000 -1.96312  1.85383 -1.67618  1.43670 -1.14423  0.80957 -0.44504  0.06410  0.31920 -0.69073  1.03679 -1.34460  1.60283 -1.80194  1.93459 -1.99589  1.98358 -1.89811  1.74264 -1.52289  1.24698 -0.92508  0.56906 -0.19205 -0.19205  0.56906 -0.92508  1.24698 -1.52289  1.74264 -1.89811  1.98358 -1.99589  1.93459 -1.80194  1.60283 -1.34460  1.03679 -0.69073  0.31920  0.06410 -0.44504  0.80957 -1.14423  1.43670 -1.67618  1.85383 -1.96312  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E47     2.00000 -1.98358  1.93459 -1.85383  1.74264 -1.60283  1.43670 -1.24698  1.03679 -0.80957  0.56906 -0.31920  0.06410  0.19205 -0.44504  0.69073 -0.92508  1.14423 -1.34460  1.52289 -1.67618  1.80194 -1.89811  1.96312 -1.99589  1.99589 -1.96312  1.89811 -1.80194  1.67618 -1.52289  1.34460 -1.14423  0.92508 -0.69073  0.44504 -0.19205 -0.06410  0.31920 -0.56906  0.80957 -1.03679  1.24698 -1.43670  1.60283 -1.74264  1.85383 -1.93459  1.98358 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E48     2.00000 -1.99589  1.98358 -1.96312  1.93459 -1.89811  1.85383 -1.80194  1.74264 -1.67618  1.60283 -1.52289  1.43670 -1.34460  1.24698 -1.14423  1.03679 -0.92508  0.80957 -0.69073  0.56906 -0.44504  0.31920 -0.19205  0.06410  0.06410 -0.19205  0.31920 -0.44504  0.56906 -0.69073  0.80957 -0.92508  1.03679 -1.14423  1.24698 -1.34460  1.43670 -1.52289  1.60283 -1.67618  1.74264 -1.80194  1.85383 -1.89811  1.93459 -1.96312  1.98358 -1.99589  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.995890785501 = 2*cos(2*π/98) = 2*cos(π/49)
                               1.983580027646 = 2*cos(4*π/98) = 2*cos(2*π/49)
                               1.963118313982 = 2*cos(6*π/98) = 2*cos(3*π/49)
                               1.934589726078 = 2*cos(8*π/98) = 2*cos(4*π/49)
                               1.898111494021 = 2*cos(10*π/98) = 2*cos(5*π/49)
                               1.853833514692 = 2*cos(12*π/98) = 2*cos(6*π/49)
                               1.801937735805 = 2*cos(14*π/98) = 2*cos(π/7)
                               1.742637408247 = 2*cos(16*π/98) = 2*cos(8*π/49)
                               1.676176209784 = 2*cos(18*π/98) = 2*cos(9*π/49)
                               1.602827243736 = 2*cos(20*π/98) = 2*cos(10*π/49)
                               1.522891916738 = 2*cos(22*π/98) = 2*cos(11*π/49)
                               1.436698700195 = 2*cos(24*π/98) = 2*cos(12*π/49)
                               1.344601780523 = 2*cos(26*π/98) = 2*cos(13*π/49)
                               1.246979603717 = 2*cos(28*π/98) = 2*cos(2*π/7)
                               1.144233320244 = 2*cos(30*π/98) = 2*cos(15*π/49)
                               1.036785136621 = 2*cos(32*π/98) = 2*cos(16*π/49)
                               0.925076580482 = 2*cos(34*π/98) = 2*cos(17*π/49)
                               0.809566686245 = 2*cos(36*π/98) = 2*cos(18*π/49)
                               0.690730108842 = 2*cos(38*π/98) = 2*cos(19*π/49)
                               0.569055173262 = 2*cos(40*π/98) = 2*cos(20*π/49)
                               0.445041867912 = 2*cos(42*π/98) = 2*cos(3*π/7)
                               0.319199790067 = 2*cos(44*π/98) = 2*cos(22*π/49)
                               0.192046051815 = 2*cos(46*π/98) = 2*cos(23*π/49)
                               0.064103155143 = 2*cos(48*π/98) = 2*cos(24*π/49)



 Symmetry of Rotations and Cartesian products

A1   d+g+i          z2, z4, z6 
A2   R+p+f+h        z, Rz, z3, z5 
E1   R+p+d+f+g+h+i  {x, y}, {Rx, Ry}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} 
E2   d+f+g+h+i      {x2y2, xy}, {z(x2y2), xyz}, {z2(x2y2), xyz2}, {z3(x2y2), xyz3}, {z4(x2y2), xyz4} 
E3   f+g+h+i        {x(x2–3y2), y(3x2y2)}, {xz(x2–3y2), yz(3x2y2)}, {xz2(x2–3y2), yz2(3x2y2)}, {xz3(x2–3y2), yz3(3x2y2)} 
E4   g+h+i          {(x2y2)2–2x2y2, xy(x2y2)}, {z((x2y2)2–4x2y2), xyz(x2y2)}, {z2((x2y2)2–4x2y2), xyz2(x2y2)} 
E5   h+i            {x(x2–(5+2√5)y2)(x2–(5–2√5)y2), y(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)}, {xz(x2–(5+2√5)y2)(x2–(5–2√5)y2), yz(y2–(5+2√5)x2)(y2–(5–2√5)x2)(y2–(5–2√5)x2)} 
E6   i              {x2(x2–3y2)2y2(3x2y2)2, xy(x2–3y2)(3x2y2)} 

 Notes:

    1  The order of the D98 point group is 196, and the order of the principal axis is 98.

    2  There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation).
       By convention, the set denoted as C2 has the x axis as a member, while the y axis is a member of the C2 set.

    3  This point group is non-Abelian (some symmetry operations are not commutative).
       Therefore, the character table contains multi-membered classes and degenerate irreducible representations.

    4  The point group is chiral, as it does not contain any mirroring operation.

    5  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 less than half the order of the principal axis (and often much less).
       For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the D98 point group was created by Gernot Katzer.

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