Character Table for Point Group D94d

Character table for the D_94d point group

D94d E 2 S188 2 C94 2 S188^3 2 C47 2 S188^5 2 C94^3 2 S188^7 2 C47^2 2 S188^9 2 C94^5 2 S188^11 2 C47^3 2 S188^13 2 C94^7 2 S188^15 2 C47^4 2 S188^17 2 C94^9 2 S188^19 2 C47^5 2 S188^21 2 C94^11 2 S188^23 2 C47^6 2 S188^25 2 C94^13 2 S188^27 2 C47^7 2 S188^29 2 C94^15 2 S188^31 2 C47^8 2 S188^33 2 C94^17 2 S188^35 2 C47^9 2 S188^37 2 C94^19 2 S188^39 2 C47^10 2 S188^41 2 C94^21 2 S188^43 2 C47^11 2 S188^45 2 C94^23 2 S4 2 C47^12 2 S188^49 2 C94^25 2 S188^51 2 C47^13 2 S188^53 2 C94^27 2 S188^55 2 C47^14 2 S188^57 2 C94^29 2 S188^59 2 C47^15 2 S188^61 2 C94^31 2 S188^63 2 C47^16 2 S188^65 2 C94^33 2 S188^67 2 C47^17 2 S188^69 2 C94^35 2 S188^71 2 C47^18 2 S188^73 2 C94^37 2 S188^75 2 C47^19 2 S188^77 2 C94^39 2 S188^79 2 C47^20 2 S188^81 2 C94^41 2 S188^83 2 C47^21 2 S188^85 2 C94^43 2 S188^87 2 C47^22 2 S188^89 2 C94^45 2 S188^91 2 C47^23 2 S188^93 C2 94 C2' 94 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 ... ... ....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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99888 1.99553 1.98996 1.98215 1.97214 1.95992 1.94552 1.92894 1.91020 1.88934 1.86636 1.84130 1.81418 1.78504 1.75390 1.72080 1.68578 1.64888 1.61014 1.56960 1.52730 1.48330 1.43765 1.39038 1.34157 1.29126 1.23950 1.18636 1.13189 1.07616 1.01923 0.96116 0.90202 0.84187 0.78078 0.71882 0.65605 0.59255 0.52839 0.46364 0.39837 0.33266 0.26657 0.20019 0.13359 0.06683 0.00000 -0.06683 -0.13359 -0.20019 -0.26657 -0.33266 -0.39837 -0.46364 -0.52839 -0.59255 -0.65605 -0.71882 -0.78078 -0.84187 -0.90202 -0.96116 -1.01923 -1.07616 -1.13189 -1.18636 -1.23950 -1.29126 -1.34157 -1.39038 -1.43765 -1.48330 -1.52730 -1.56960 -1.61014 -1.64888 -1.68578 -1.72080 -1.75390 -1.78504 -1.81418 -1.84130 -1.86636 -1.88934 -1.91020 -1.92894 -1.94552 -1.95992 -1.97214 -1.98215 -1.98996 -1.99553 -1.99888 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 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 -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... E3 2.00000 1.98996 1.95992 1.91020 1.84130 1.75390 1.64888 1.52730 1.39038 1.23950 1.07616 0.90202 0.71882 0.52839 0.33266 0.13359 -0.06683 -0.26657 -0.46364 -0.65605 -0.84187 -1.01923 -1.18636 -1.34157 -1.48330 -1.61014 -1.72080 -1.81418 -1.88934 -1.94552 -1.98215 -1.99888 -1.99553 -1.97214 -1.92894 -1.86636 -1.78504 -1.68578 -1.56960 -1.43765 -1.29126 -1.13189 -0.96116 -0.78078 -0.59255 -0.39837 -0.20019 0.00000 0.20019 0.39837 0.59255 0.78078 0.96116 1.13189 1.29126 1.43765 1.56960 1.68578 1.78504 1.86636 1.92894 1.97214 1.99553 1.99888 1.98215 1.94552 1.88934 1.81418 1.72080 1.61014 1.48330 1.34157 1.18636 1.01923 0.84187 0.65605 0.46364 0.26657 0.06683 -0.13359 -0.33266 -0.52839 -0.71882 -0.90202 -1.07616 -1.23950 -1.39038 -1.52730 -1.64888 -1.75390 -1.84130 -1.91020 -1.95992 -1.98996 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 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 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....... E5 2.00000 1.97214 1.88934 1.75390 1.56960 1.34157 1.07616 0.78078 0.46364 0.13359 -0.20019 -0.52839 -0.84187 -1.13189 -1.39038 -1.61014 -1.78504 -1.91020 -1.98215 -1.99888 -1.95992 -1.86636 -1.72080 -1.52730 -1.29126 -1.01923 -0.71882 -0.39837 -0.06683 0.26657 0.59255 0.90202 1.18636 1.43765 1.64888 1.81418 1.92894 1.98996 1.99553 1.94552 1.84130 1.68578 1.48330 1.23950 0.96116 0.65605 0.33266 0.00000 -0.33266 -0.65605 -0.96116 -1.23950 -1.48330 -1.68578 -1.84130 -1.94552 -1.99553 -1.98996 -1.92894 -1.81418 -1.64888 -1.43765 -1.18636 -0.90202 -0.59255 -0.26657 0.06683 0.39837 0.71882 1.01923 1.29126 1.52730 1.72080 1.86636 1.95992 1.99888 1.98215 1.91020 1.78504 1.61014 1.39038 1.13189 0.84187 0.52839 0.20019 -0.13359 -0.46364 -0.78078 -1.07616 -1.34157 -1.56960 -1.75390 -1.88934 -1.97214 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 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 -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........... E7 2.00000 1.94552 1.78504 1.52730 1.18636 0.78078 0.33266 -0.13359 -0.59255 -1.01923 -1.39038 -1.68578 -1.88934 -1.98996 -1.98215 -1.86636 -1.64888 -1.34157 -0.96116 -0.52839 -0.06683 0.39837 0.84187 1.23950 1.56960 1.81418 1.95992 1.99888 1.92894 1.75390 1.48330 1.13189 0.71882 0.26657 -0.20019 -0.65605 -1.07616 -1.43765 -1.72080 -1.91020 -1.99553 -1.97214 -1.84130 -1.61014 -1.29126 -0.90202 -0.46364 0.00000 0.46364 0.90202 1.29126 1.61014 1.84130 1.97214 1.99553 1.91020 1.72080 1.43765 1.07616 0.65605 0.20019 -0.26657 -0.71882 -1.13189 -1.48330 -1.75390 -1.92894 -1.99888 -1.95992 -1.81418 -1.56960 -1.23950 -0.84187 -0.39837 0.06683 0.52839 0.96116 1.34157 1.64888 1.86636 1.98215 1.98996 1.88934 1.68578 1.39038 1.01923 0.59255 0.13359 -0.33266 -0.78078 -1.18636 -1.52730 -1.78504 -1.94552 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 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 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 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.91020 1.64888 1.23950 0.71882 0.13359 -0.46364 -1.01923 -1.48330 -1.81418 -1.98215 -1.97214 -1.78504 -1.43765 -0.96116 -0.39837 0.20019 0.78078 1.29126 1.68578 1.92894 1.99888 1.88934 1.61014 1.18636 0.65605 0.06683 -0.52839 -1.07616 -1.52730 -1.84130 -1.98996 -1.95992 -1.75390 -1.39038 -0.90202 -0.33266 0.26657 0.84187 1.34157 1.72080 1.94552 1.99553 1.86636 1.56960 1.13189 0.59255 0.00000 -0.59255 -1.13189 -1.56960 -1.86636 -1.99553 -1.94552 -1.72080 -1.34157 -0.84187 -0.26657 0.33266 0.90202 1.39038 1.75390 1.95992 1.98996 1.84130 1.52730 1.07616 0.52839 -0.06683 -0.65605 -1.18636 -1.61014 -1.88934 -1.99888 -1.92894 -1.68578 -1.29126 -0.78078 -0.20019 0.39837 0.96116 1.43765 1.78504 1.97214 1.98215 1.81418 1.48330 1.01923 0.46364 -0.13359 -0.71882 -1.23950 -1.64888 -1.91020 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E10 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 -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 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.86636 1.48330 0.90202 0.20019 -0.52839 -1.18636 -1.68578 -1.95992 -1.97214 -1.72080 -1.23950 -0.59255 0.13359 0.84187 1.43765 1.84130 1.99888 1.88934 1.52730 0.96116 0.26657 -0.46364 -1.13189 -1.64888 -1.94552 -1.98215 -1.75390 -1.29126 -0.65605 0.06683 0.78078 1.39038 1.81418 1.99553 1.91020 1.56960 1.01923 0.33266 -0.39837 -1.07616 -1.61014 -1.92894 -1.98996 -1.78504 -1.34157 -0.71882 0.00000 0.71882 1.34157 1.78504 1.98996 1.92894 1.61014 1.07616 0.39837 -0.33266 -1.01923 -1.56960 -1.91020 -1.99553 -1.81418 -1.39038 -0.78078 -0.06683 0.65605 1.29126 1.75390 1.98215 1.94552 1.64888 1.13189 0.46364 -0.26657 -0.96116 -1.52730 -1.88934 -1.99888 -1.84130 -1.43765 -0.84187 -0.13359 0.59255 1.23950 1.72080 1.97214 1.95992 1.68578 1.18636 0.52839 -0.20019 -0.90202 -1.48330 -1.86636 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E90 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 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....... ............. E91 2.00000 -1.98996 1.95992 -1.91020 1.84130 -1.75390 1.64888 -1.52730 1.39038 -1.23950 1.07616 -0.90202 0.71882 -0.52839 0.33266 -0.13359 -0.06683 0.26657 -0.46364 0.65605 -0.84187 1.01923 -1.18636 1.34157 -1.48330 1.61014 -1.72080 1.81418 -1.88934 1.94552 -1.98215 1.99888 -1.99553 1.97214 -1.92894 1.86636 -1.78504 1.68578 -1.56960 1.43765 -1.29126 1.13189 -0.96116 0.78078 -0.59255 0.39837 -0.20019 0.00000 0.20019 -0.39837 0.59255 -0.78078 0.96116 -1.13189 1.29126 -1.43765 1.56960 -1.68578 1.78504 -1.86636 1.92894 -1.97214 1.99553 -1.99888 1.98215 -1.94552 1.88934 -1.81418 1.72080 -1.61014 1.48330 -1.34157 1.18636 -1.01923 0.84187 -0.65605 0.46364 -0.26657 0.06683 0.13359 -0.33266 0.52839 -0.71882 0.90202 -1.07616 1.23950 -1.39038 1.52730 -1.64888 1.75390 -1.84130 1.91020 -1.95992 1.98996 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E92 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 -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... ............. E93 2.00000 -1.99888 1.99553 -1.98996 1.98215 -1.97214 1.95992 -1.94552 1.92894 -1.91020 1.88934 -1.86636 1.84130 -1.81418 1.78504 -1.75390 1.72080 -1.68578 1.64888 -1.61014 1.56960 -1.52730 1.48330 -1.43765 1.39038 -1.34157 1.29126 -1.23950 1.18636 -1.13189 1.07616 -1.01923 0.96116 -0.90202 0.84187 -0.78078 0.71882 -0.65605 0.59255 -0.52839 0.46364 -0.39837 0.33266 -0.26657 0.20019 -0.13359 0.06683 0.00000 -0.06683 0.13359 -0.20019 0.26657 -0.33266 0.39837 -0.46364 0.52839 -0.59255 0.65605 -0.71882 0.78078 -0.84187 0.90202 -0.96116 1.01923 -1.07616 1.13189 -1.18636 1.23950 -1.29126 1.34157 -1.39038 1.43765 -1.48330 1.52730 -1.56960 1.61014 -1.64888 1.68578 -1.72080 1.75390 -1.78504 1.81418 -1.84130 1.86636 -1.88934 1.91020 -1.92894 1.94552 -1.95992 1.97214 -1.98215 1.98996 -1.99553 1.99888 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.998883127461 = 2*cos(2*π/188) = 2*cos(π/94) 1.995533757246 = 2*cos(4*π/188) = 2*cos(π/47) 1.989955630177 = 2*cos(6*π/188) = 2*cos(3*π/94) 1.982154976310 = 2*cos(8*π/188) = 2*cos(2*π/47) 1.972140507980 = 2*cos(10*π/188) = 2*cos(5*π/94) 1.959923410073 = 2*cos(12*π/188) = 2*cos(3*π/47) 1.945517327530 = 2*cos(14*π/188) = 2*cos(7*π/94) 1.928938350109 = 2*cos(16*π/188) = 2*cos(4*π/47) 1.910204994414 = 2*cos(18*π/188) = 2*cos(9*π/94) 1.889338183216 = 2*cos(20*π/188) = 2*cos(5*π/47) 1.866361222083 = 2*cos(22*π/188) = 2*cos(11*π/94) 1.841299773353 = 2*cos(24*π/188) = 2*cos(6*π/47) 1.814181827469 = 2*cos(26*π/188) = 2*cos(13*π/94) 1.785037671720 = 2*cos(28*π/188) = 2*cos(7*π/47) 1.753899856413 = 2*cos(30*π/188) = 2*cos(15*π/94) 1.720803158520 = 2*cos(32*π/188) = 2*cos(8*π/47) 1.685784542834 = 2*cos(34*π/188) = 2*cos(17*π/94) 1.648883120684 = 2*cos(36*π/188) = 2*cos(9*π/47) 1.610140106255 = 2*cos(38*π/188) = 2*cos(19*π/94) 1.569598770557 = 2*cos(40*π/188) = 2*cos(10*π/47) 1.527304393095 = 2*cos(42*π/188) = 2*cos(21*π/94) 1.483304211296 = 2*cos(44*π/188) = 2*cos(11*π/47) 1.437647367756 = 2*cos(46*π/188) = 2*cos(23*π/94) 1.390384855349 = 2*cos(48*π/188) = 2*cos(12*π/47) 1.341569460278 = 2*cos(50*π/188) = 2*cos(25*π/94) 1.291255703118 = 2*cos(52*π/188) = 2*cos(13*π/47) 1.239499777920 = 2*cos(54*π/188) = 2*cos(27*π/94) 1.186359489459 = 2*cos(56*π/188) = 2*cos(14*π/47) 1.131894188661 = 2*cos(58*π/188) = 2*cos(29*π/94) 1.076164706327 = 2*cos(60*π/188) = 2*cos(15*π/47) 1.019233285184 = 2*cos(62*π/188) = 2*cos(31*π/94) 0.961163510373 = 2*cos(64*π/188) = 2*cos(16*π/47) 0.902020238432 = 2*cos(66*π/188) = 2*cos(33*π/94) 0.841869524857 = 2*cos(68*π/188) = 2*cos(17*π/47) 0.780778550327 = 2*cos(70*π/188) = 2*cos(35*π/94) 0.718815545675 = 2*cos(72*π/188) = 2*cos(18*π/47) 0.656049715679 = 2*cos(74*π/188) = 2*cos(37*π/94) 0.592551161771 = 2*cos(76*π/188) = 2*cos(19*π/47) 0.528390803743 = 2*cos(78*π/188) = 2*cos(39*π/94) 0.463640300535 = 2*cos(80*π/188) = 2*cos(20*π/47) 0.398371970208 = 2*cos(82*π/188) = 2*cos(41*π/94) 0.332658709166 = 2*cos(84*π/188) = 2*cos(21*π/47) 0.266573910748 = 2*cos(86*π/188) = 2*cos(43*π/94) 0.200191383248 = 2*cos(88*π/188) = 2*cos(22*π/47) 0.133585267490 = 2*cos(90*π/188) = 2*cos(45*π/94) 0.066829954015 = 2*cos(92*π/188) = 2*cos(23*π/47) 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 E85 m E86 l E87 k+m E88 j+l E89 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)} E90 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E91 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E92 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E93 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_94d point group is 376, and the order of the principal axis (S₁₈₈) is 188. The group has 97 irreducible representations. β The D_94d point group is isomorphic to C_188v and D₁₈₈. γ The D_94d point group is generated by two symmetry elements, S₁₈₈ 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_94d 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_94d point group was created by Gernot Katzer.

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

	D_92d
	D_93d
C₉₄ C_94v C_94h D₉₄ D_94h	D_94d	S₉₄
	D_95d
	D_96d

Character table for the D94d point group

Character table for the D_94d point group