Character Table for Point Group D98d

Character table for the D_98d point group

D98d E 2 S196 2 C98 2 S196^3 2 C49 2 S196^5 2 C98^3 2 S28 2 C49^2 2 S196^9 2 C98^5 2 S196^11 2 C49^3 2 S196^13 2 C14 2 S196^15 2 C49^4 2 S196^17 2 C98^9 2 S196^19 2 C49^5 2 S28^3 2 C98^11 2 S196^23 2 C49^6 2 S196^25 2 C98^13 2 S196^27 2 C7 2 S196^29 2 C98^15 2 S196^31 2 C49^8 2 S196^33 2 C98^17 2 S28^5 2 C49^9 2 S196^37 2 C98^19 2 S196^39 2 C49^10 2 S196^41 2 C14^3 2 S196^43 2 C49^11 2 S196^45 2 C98^23 2 S196^47 2 C49^12 2 S4 2 C98^25 2 S196^51 2 C49^13 2 S196^53 2 C98^27 2 S196^55 2 C7^2 2 S196^57 2 C98^29 2 S196^59 2 C49^15 2 S196^61 2 C98^31 2 S28^9 2 C49^16 2 S196^65 2 C98^33 2 S196^67 2 C49^17 2 S196^69 2 C14^5 2 S196^71 2 C49^18 2 S196^73 2 C98^37 2 S196^75 2 C49^19 2 S28^11 2 C98^39 2 S196^79 2 C49^20 2 S196^81 2 C98^41 2 S196^83 2 C7^3 2 S196^85 2 C98^43 2 S196^87 2 C49^22 2 S196^89 2 C98^45 2 S28^13 2 C49^23 2 S196^93 2 C98^47 2 S196^95 2 C49^24 2 S196^97 C2 98 C2' 98 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ... ....T ....... ........T ........... ............T A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. B1 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99897 1.99589 1.99076 1.98358 1.97436 1.96312 1.94986 1.93459 1.91734 1.89811 1.87694 1.85383 1.82883 1.80194 1.77320 1.74264 1.71029 1.67618 1.64034 1.60283 1.56366 1.52289 1.48056 1.43670 1.39137 1.34460 1.29646 1.24698 1.19622 1.14423 1.09107 1.03679 0.98144 0.92508 0.86777 0.80957 0.75053 0.69073 0.63022 0.56906 0.50731 0.44504 0.38232 0.31920 0.25575 0.19205 0.12814 0.06410 0.00000 -0.06410 -0.12814 -0.19205 -0.25575 -0.31920 -0.38232 -0.44504 -0.50731 -0.56906 -0.63022 -0.69073 -0.75053 -0.80957 -0.86777 -0.92508 -0.98144 -1.03679 -1.09107 -1.14423 -1.19622 -1.24698 -1.29646 -1.34460 -1.39137 -1.43670 -1.48056 -1.52289 -1.56366 -1.60283 -1.64034 -1.67618 -1.71029 -1.74264 -1.77320 -1.80194 -1.82883 -1.85383 -1.87694 -1.89811 -1.91734 -1.93459 -1.94986 -1.96312 -1.97436 -1.98358 -1.99076 -1.99589 -1.99897 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 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 -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... E3 2.00000 1.99076 1.96312 1.91734 1.85383 1.77320 1.67618 1.56366 1.43670 1.29646 1.14423 0.98144 0.80957 0.63022 0.44504 0.25575 0.06410 -0.12814 -0.31920 -0.50731 -0.69073 -0.86777 -1.03679 -1.19622 -1.34460 -1.48056 -1.60283 -1.71029 -1.80194 -1.87694 -1.93459 -1.97436 -1.99589 -1.99897 -1.98358 -1.94986 -1.89811 -1.82883 -1.74264 -1.64034 -1.52289 -1.39137 -1.24698 -1.09107 -0.92508 -0.75053 -0.56906 -0.38232 -0.19205 0.00000 0.19205 0.38232 0.56906 0.75053 0.92508 1.09107 1.24698 1.39137 1.52289 1.64034 1.74264 1.82883 1.89811 1.94986 1.98358 1.99897 1.99589 1.97436 1.93459 1.87694 1.80194 1.71029 1.60283 1.48056 1.34460 1.19622 1.03679 0.86777 0.69073 0.50731 0.31920 0.12814 -0.06410 -0.25575 -0.44504 -0.63022 -0.80957 -0.98144 -1.14423 -1.29646 -1.43670 -1.56366 -1.67618 -1.77320 -1.85383 -1.91734 -1.96312 -1.99076 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 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 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....... E5 2.00000 1.97436 1.89811 1.77320 1.60283 1.39137 1.14423 0.86777 0.56906 0.25575 -0.06410 -0.38232 -0.69073 -0.98144 -1.24698 -1.48056 -1.67618 -1.82883 -1.93459 -1.99076 -1.99589 -1.94986 -1.85383 -1.71029 -1.52289 -1.29646 -1.03679 -0.75053 -0.44504 -0.12814 0.19205 0.50731 0.80957 1.09107 1.34460 1.56366 1.74264 1.87694 1.96312 1.99897 1.98358 1.91734 1.80194 1.64034 1.43670 1.19622 0.92508 0.63022 0.31920 0.00000 -0.31920 -0.63022 -0.92508 -1.19622 -1.43670 -1.64034 -1.80194 -1.91734 -1.98358 -1.99897 -1.96312 -1.87694 -1.74264 -1.56366 -1.34460 -1.09107 -0.80957 -0.50731 -0.19205 0.12814 0.44504 0.75053 1.03679 1.29646 1.52289 1.71029 1.85383 1.94986 1.99589 1.99076 1.93459 1.82883 1.67618 1.48056 1.24698 0.98144 0.69073 0.38232 0.06410 -0.25575 -0.56906 -0.86777 -1.14423 -1.39137 -1.60283 -1.77320 -1.89811 -1.97436 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 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 -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........... E7 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504 0.00000 0.44504 0.86777 1.24698 1.56366 1.80194 1.94986 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504 0.00000 0.44504 0.86777 1.24698 1.56366 1.80194 1.94986 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 -1.94986 -1.80194 -1.56366 -1.24698 -0.86777 -0.44504 0.00000 0.44504 0.86777 1.24698 1.56366 1.80194 1.94986 2.00000 1.94986 1.80194 1.56366 1.24698 0.86777 0.44504 0.00000 -0.44504 -0.86777 -1.24698 -1.56366 -1.80194 -1.94986 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 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 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 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.91734 1.67618 1.29646 0.80957 0.25575 -0.31920 -0.86777 -1.34460 -1.71029 -1.93459 -1.99897 -1.89811 -1.64034 -1.24698 -0.75053 -0.19205 0.38232 0.92508 1.39137 1.74264 1.94986 1.99589 1.87694 1.60283 1.19622 0.69073 0.12814 -0.44504 -0.98144 -1.43670 -1.77320 -1.96312 -1.99076 -1.85383 -1.56366 -1.14423 -0.63022 -0.06410 0.50731 1.03679 1.48056 1.80194 1.97436 1.98358 1.82883 1.52289 1.09107 0.56906 0.00000 -0.56906 -1.09107 -1.52289 -1.82883 -1.98358 -1.97436 -1.80194 -1.48056 -1.03679 -0.50731 0.06410 0.63022 1.14423 1.56366 1.85383 1.99076 1.96312 1.77320 1.43670 0.98144 0.44504 -0.12814 -0.69073 -1.19622 -1.60283 -1.87694 -1.99589 -1.94986 -1.74264 -1.39137 -0.92508 -0.38232 0.19205 0.75053 1.24698 1.64034 1.89811 1.99897 1.93459 1.71029 1.34460 0.86777 0.31920 -0.25575 -0.80957 -1.29646 -1.67618 -1.91734 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10 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 -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 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.87694 1.52289 0.98144 0.31920 -0.38232 -1.03679 -1.56366 -1.89811 -1.99897 -1.85383 -1.48056 -0.92508 -0.25575 0.44504 1.09107 1.60283 1.91734 1.99589 1.82883 1.43670 0.86777 0.19205 -0.50731 -1.14423 -1.64034 -1.93459 -1.99076 -1.80194 -1.39137 -0.80957 -0.12814 0.56906 1.19622 1.67618 1.94986 1.98358 1.77320 1.34460 0.75053 0.06410 -0.63022 -1.24698 -1.71029 -1.96312 -1.97436 -1.74264 -1.29646 -0.69073 0.00000 0.69073 1.29646 1.74264 1.97436 1.96312 1.71029 1.24698 0.63022 -0.06410 -0.75053 -1.34460 -1.77320 -1.98358 -1.94986 -1.67618 -1.19622 -0.56906 0.12814 0.80957 1.39137 1.80194 1.99076 1.93459 1.64034 1.14423 0.50731 -0.19205 -0.86777 -1.43670 -1.82883 -1.99589 -1.91734 -1.60283 -1.09107 -0.44504 0.25575 0.92508 1.48056 1.85383 1.99897 1.89811 1.56366 1.03679 0.38232 -0.31920 -0.98144 -1.52289 -1.87694 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E89 2.00000 -1.91734 1.67618 -1.29646 0.80957 -0.25575 -0.31920 0.86777 -1.34460 1.71029 -1.93459 1.99897 -1.89811 1.64034 -1.24698 0.75053 -0.19205 -0.38232 0.92508 -1.39137 1.74264 -1.94986 1.99589 -1.87694 1.60283 -1.19622 0.69073 -0.12814 -0.44504 0.98144 -1.43670 1.77320 -1.96312 1.99076 -1.85383 1.56366 -1.14423 0.63022 -0.06410 -0.50731 1.03679 -1.48056 1.80194 -1.97436 1.98358 -1.82883 1.52289 -1.09107 0.56906 0.00000 -0.56906 1.09107 -1.52289 1.82883 -1.98358 1.97436 -1.80194 1.48056 -1.03679 0.50731 0.06410 -0.63022 1.14423 -1.56366 1.85383 -1.99076 1.96312 -1.77320 1.43670 -0.98144 0.44504 0.12814 -0.69073 1.19622 -1.60283 1.87694 -1.99589 1.94986 -1.74264 1.39137 -0.92508 0.38232 0.19205 -0.75053 1.24698 -1.64034 1.89811 -1.99897 1.93459 -1.71029 1.34460 -0.86777 0.31920 0.25575 -0.80957 1.29646 -1.67618 1.91734 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E90 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 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 ... ... ..... ....... ......... ........... ............. E91 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 1.94986 -1.80194 1.56366 -1.24698 0.86777 -0.44504 0.00000 0.44504 -0.86777 1.24698 -1.56366 1.80194 -1.94986 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 1.94986 -1.80194 1.56366 -1.24698 0.86777 -0.44504 0.00000 0.44504 -0.86777 1.24698 -1.56366 1.80194 -1.94986 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 1.94986 -1.80194 1.56366 -1.24698 0.86777 -0.44504 0.00000 0.44504 -0.86777 1.24698 -1.56366 1.80194 -1.94986 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E92 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 -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 ... ... ..... ....... ......... ........... ............. E93 2.00000 -1.97436 1.89811 -1.77320 1.60283 -1.39137 1.14423 -0.86777 0.56906 -0.25575 -0.06410 0.38232 -0.69073 0.98144 -1.24698 1.48056 -1.67618 1.82883 -1.93459 1.99076 -1.99589 1.94986 -1.85383 1.71029 -1.52289 1.29646 -1.03679 0.75053 -0.44504 0.12814 0.19205 -0.50731 0.80957 -1.09107 1.34460 -1.56366 1.74264 -1.87694 1.96312 -1.99897 1.98358 -1.91734 1.80194 -1.64034 1.43670 -1.19622 0.92508 -0.63022 0.31920 0.00000 -0.31920 0.63022 -0.92508 1.19622 -1.43670 1.64034 -1.80194 1.91734 -1.98358 1.99897 -1.96312 1.87694 -1.74264 1.56366 -1.34460 1.09107 -0.80957 0.50731 -0.19205 -0.12814 0.44504 -0.75053 1.03679 -1.29646 1.52289 -1.71029 1.85383 -1.94986 1.99589 -1.99076 1.93459 -1.82883 1.67618 -1.48056 1.24698 -0.98144 0.69073 -0.38232 0.06410 0.25575 -0.56906 0.86777 -1.14423 1.39137 -1.60283 1.77320 -1.89811 1.97436 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ..TT......... E94 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 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....... ............. E95 2.00000 -1.99076 1.96312 -1.91734 1.85383 -1.77320 1.67618 -1.56366 1.43670 -1.29646 1.14423 -0.98144 0.80957 -0.63022 0.44504 -0.25575 0.06410 0.12814 -0.31920 0.50731 -0.69073 0.86777 -1.03679 1.19622 -1.34460 1.48056 -1.60283 1.71029 -1.80194 1.87694 -1.93459 1.97436 -1.99589 1.99897 -1.98358 1.94986 -1.89811 1.82883 -1.74264 1.64034 -1.52289 1.39137 -1.24698 1.09107 -0.92508 0.75053 -0.56906 0.38232 -0.19205 0.00000 0.19205 -0.38232 0.56906 -0.75053 0.92508 -1.09107 1.24698 -1.39137 1.52289 -1.64034 1.74264 -1.82883 1.89811 -1.94986 1.98358 -1.99897 1.99589 -1.97436 1.93459 -1.87694 1.80194 -1.71029 1.60283 -1.48056 1.34460 -1.19622 1.03679 -0.86777 0.69073 -0.50731 0.31920 -0.12814 -0.06410 0.25575 -0.44504 0.63022 -0.80957 0.98144 -1.14423 1.29646 -1.43670 1.56366 -1.67618 1.77320 -1.85383 1.91734 -1.96312 1.99076 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E96 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 -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... ............. E97 2.00000 -1.99897 1.99589 -1.99076 1.98358 -1.97436 1.96312 -1.94986 1.93459 -1.91734 1.89811 -1.87694 1.85383 -1.82883 1.80194 -1.77320 1.74264 -1.71029 1.67618 -1.64034 1.60283 -1.56366 1.52289 -1.48056 1.43670 -1.39137 1.34460 -1.29646 1.24698 -1.19622 1.14423 -1.09107 1.03679 -0.98144 0.92508 -0.86777 0.80957 -0.75053 0.69073 -0.63022 0.56906 -0.50731 0.44504 -0.38232 0.31920 -0.25575 0.19205 -0.12814 0.06410 0.00000 -0.06410 0.12814 -0.19205 0.25575 -0.31920 0.38232 -0.44504 0.50731 -0.56906 0.63022 -0.69073 0.75053 -0.80957 0.86777 -0.92508 0.98144 -1.03679 1.09107 -1.14423 1.19622 -1.24698 1.29646 -1.34460 1.39137 -1.43670 1.48056 -1.52289 1.56366 -1.60283 1.64034 -1.67618 1.71029 -1.74264 1.77320 -1.80194 1.82883 -1.85383 1.87694 -1.89811 1.91734 -1.93459 1.94986 -1.96312 1.97436 -1.98358 1.99076 -1.99589 1.99897 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.998972432401 = 2*cos(2*π/196) = 2*cos(π/98) 1.995890785501 = 2*cos(4*π/196) = 2*cos(π/49) 1.990758225898 = 2*cos(6*π/196) = 2*cos(3*π/98) 1.983580027646 = 2*cos(8*π/196) = 2*cos(2*π/49) 1.974363566829 = 2*cos(10*π/196) = 2*cos(5*π/98) 1.963118313982 = 2*cos(12*π/196) = 2*cos(3*π/49) 1.949855824364 = 2*cos(14*π/196) = 2*cos(π/14) 1.934589726078 = 2*cos(16*π/196) = 2*cos(4*π/49) 1.917335706073 = 2*cos(18*π/196) = 2*cos(9*π/98) 1.898111494021 = 2*cos(20*π/196) = 2*cos(5*π/49) 1.876936844100 = 2*cos(22*π/196) = 2*cos(11*π/98) 1.853833514692 = 2*cos(24*π/196) = 2*cos(6*π/49) 1.828825246032 = 2*cos(26*π/196) = 2*cos(13*π/98) 1.801937735805 = 2*cos(28*π/196) = 2*cos(π/7) 1.773198612746 = 2*cos(30*π/196) = 2*cos(15*π/98) 1.742637408247 = 2*cos(32*π/196) = 2*cos(8*π/49) 1.710285526011 = 2*cos(34*π/196) = 2*cos(17*π/98) 1.676176209784 = 2*cos(36*π/196) = 2*cos(9*π/49) 1.640344509194 = 2*cos(38*π/196) = 2*cos(19*π/98) 1.602827243736 = 2*cos(40*π/196) = 2*cos(10*π/49) 1.563662964936 = 2*cos(42*π/196) = 2*cos(3*π/14) 1.522891916738 = 2*cos(44*π/196) = 2*cos(11*π/49) 1.480555994151 = 2*cos(46*π/196) = 2*cos(23*π/98) 1.436698700195 = 2*cos(48*π/196) = 2*cos(12*π/49) 1.391365101207 = 2*cos(50*π/196) = 2*cos(25*π/98) 1.344601780523 = 2*cos(52*π/196) = 2*cos(13*π/49) 1.296456790616 = 2*cos(54*π/196) = 2*cos(27*π/98) 1.246979603717 = 2*cos(56*π/196) = 2*cos(2*π/7) 1.196221060982 = 2*cos(58*π/196) = 2*cos(29*π/98) 1.144233320244 = 2*cos(60*π/196) = 2*cos(15*π/49) 1.091069802421 = 2*cos(62*π/196) = 2*cos(31*π/98) 1.036785136621 = 2*cos(64*π/196) = 2*cos(16*π/49) 0.981435104008 = 2*cos(66*π/196) = 2*cos(33*π/98) 0.925076580482 = 2*cos(68*π/196) = 2*cos(17*π/49) 0.867767478235 = 2*cos(70*π/196) = 2*cos(5*π/14) 0.809566686245 = 2*cos(72*π/196) = 2*cos(18*π/49) 0.750534009759 = 2*cos(74*π/196) = 2*cos(37*π/98) 0.690730108843 = 2*cos(76*π/196) = 2*cos(19*π/49) 0.630216436047 = 2*cos(78*π/196) = 2*cos(39*π/98) 0.569055173262 = 2*cos(80*π/196) = 2*cos(20*π/49) 0.507309167819 = 2*cos(82*π/196) = 2*cos(41*π/98) 0.445041867913 = 2*cos(84*π/196) = 2*cos(3*π/7) 0.382317257403 = 2*cos(86*π/196) = 2*cos(43*π/98) 0.319199790067 = 2*cos(88*π/196) = 2*cos(22*π/49) 0.255754323369 = 2*cos(90*π/196) = 2*cos(45*π/98) 0.192046051815 = 2*cos(92*π/196) = 2*cos(23*π/49) 0.128140439961 = 2*cos(94*π/196) = 2*cos(47*π/98) 0.064103155143 = 2*cos(96*π/196) = 2*cos(24*π/49) Symmetry of Rotations and Cartesian products A1 d+g+i+k+m z², z⁴, z⁶ A2 R R_z B2 p+f+h+j+l z, z³, z⁵ E1 p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2 d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3 f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4 g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5 h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E6 i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+l E8 k+m E9 l E10 m E89 m E90 l E91 k+m E92 j+l E93 i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E94 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E95 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E96 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E97 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_98d point group is 392, and the order of the principal axis (S₁₉₆) is 196. The group has 101 irreducible representations. β The D_98d point group is isomorphic to C_196v and D₁₉₆. γ The D_98d point group is generated by two symmetry elements, S₁₉₆ and either a perpendicular C₂^′ or a vertical σ_d. Also, the group may be generated from a C₂^′ plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The group contains one set of twofold symmetry axes (C₂^′) perpendicular to the principal (z) axis. Both x and y axes are members of that set. ε The single σ_d set of symmetry planes contains neither the xz nor the yz planes; but it contains the median plane (x+y)z. ζ The lowest nonvanishing multipole moment in D_98d is 4 (quadrupole moment). η This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. θ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. For this group, however, none of the irrational characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the D_98d point group was created by Gernot Katzer.

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

	D_96d
	D_97d
C₉₈ C_98v C_98h D₉₈ D_98h	D_98d	S₉₈
	D_99d
	D_100d

Character table for the D98d point group

Character table for the D_98d point group