Character Table for Point Group C94v

Character table for the C_94v point group

C94v E 2 C94 2 C47 2 C94^3 2 C47^2 2 C94^5 2 C47^3 2 C94^7 2 C47^4 2 C94^9 2 C47^5 2 C94^11 2 C47^6 2 C94^13 2 C47^7 2 C94^15 2 C47^8 2 C94^17 2 C47^9 2 C94^19 2 C47^10 2 C94^21 2 C47^11 2 C94^23 2 C47^12 2 C94^25 2 C47^13 2 C94^27 2 C47^14 2 C94^29 2 C47^15 2 C94^31 2 C47^16 2 C94^33 2 C47^17 2 C94^35 2 C47^18 2 C94^37 2 C47^19 2 C94^39 2 C47^20 2 C94^41 2 C47^21 2 C94^43 2 C47^22 2 C94^45 2 C47^23 C2 47 sv 47 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 ... ..T ....T ......T ........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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ... ..... ....... ......... ........... ............. E1 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 -0.06683 -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 -2.00000 0.00000 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 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 -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 2.00000 0.00000 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 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 0.20019 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 -2.00000 0.00000 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 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 -0.33266 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 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 0.46364 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E9 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 -0.59255 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E11 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 0.71882 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E12 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E13 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 -0.84187 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E14 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E15 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 0.96116 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E16 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E17 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E18 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E19 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E20 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E21 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E22 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E23 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E24 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E25 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E26 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E27 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E28 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 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E29 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E30 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 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E31 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E32 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 0.96116 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E33 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E34 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 -0.84187 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E35 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E36 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 0.71882 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E37 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E38 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 -0.59255 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E39 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E40 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 0.46364 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E41 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E42 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 -0.33266 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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E43 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 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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E44 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 0.20019 -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 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E45 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 -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 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E46 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 -0.06683 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 2.00000 0.00000 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 p+d+f+g+h+i+j+k+l+m z, z², z³, z⁴, z⁵, z⁶ A2 R R_z E1 R+p+d+f+g+h+i+j+k+l+m {R_x, R_y}, {x, y}, {xz, yz}, {xz², yz²}, {xz³, yz³}, {xz⁴, yz⁴}, {xz⁵, yz⁵} E2 d+f+g+h+i+j+k+l+m {x²−y², xy}, {z(x²−y²), xyz}, {z²(x²−y²), xyz²}, {z³(x²−y²), xyz³}, {z⁴(x²−y²), xyz⁴} E3 f+g+h+i+j+k+l+m {x(x²−3y²), y(3x²−y²)}, {xz(x²−3y²), yz(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4 g+h+i+j+k+l+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z((x²−y²)²−4x²y²), xyz(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5 h+i+j+k+l+m {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)}, {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6 i+j+k+l+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C_94v point group is 188, and the order of the principal axis (C₉₄) is 94. The group has 50 irreducible representations. β The C_94v point group is isomorphic to D_47d, D_47h and D₉₄. γ The C_94v point group is generated by two symmetry elements, C₉₄ and any σ_v (or, non-canonically, any σ_d). Also, the group may be generated from a σ_v plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ There are two different sets of symmetry planes containing the principal axis (z axis in standard orientation). By convention, the set denoted as σ_v has the xz plane as a member, while the yz plane is a member of the σ_d set. ε The lowest nonvanishing multipole moment in C_94v is 2 (dipole 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 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 C_94v point group was created by Gernot Katzer.

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

	C_92v
	C_93v
C₉₄	C_94v	C_94h D₉₄ D_94h D_94d S₉₄
	C_95v
	C_96v

Character table for the C94v point group

Character table for the C_94v point group