Character Table for Point Group D95

Character table for the D₉₅ point group

D95 E 2 C95 2 C95^2 2 C95^3 2 C95^4 2 C19 2 C95^6 2 C95^7 2 C95^8 2 C95^9 2 C19^2 2 C95^11 2 C95^12 2 C95^13 2 C95^14 2 C19^3 2 C95^16 2 C95^17 2 C95^18 2 C5 2 C19^4 2 C95^21 2 C95^22 2 C95^23 2 C95^24 2 C19^5 2 C95^26 2 C95^27 2 C95^28 2 C95^29 2 C19^6 2 C95^31 2 C95^32 2 C95^33 2 C95^34 2 C19^7 2 C95^36 2 C95^37 2 C5^2 2 C95^39 2 C19^8 2 C95^41 2 C95^42 2 C95^43 2 C95^44 2 C19^9 2 C95^46 2 C95^47 95 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 ... ... ....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 ..T ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99563 1.98253 1.96076 1.93042 1.89163 1.84458 1.78946 1.72651 1.65602 1.57828 1.49364 1.40247 1.30517 1.20216 1.09390 0.98085 0.86351 0.74239 0.61803 0.49097 0.36176 0.23097 0.09917 -0.03307 -0.16516 -0.29653 -0.42660 -0.55481 -0.68059 -0.80339 -0.92268 -1.03794 -1.14866 -1.25435 -1.35456 -1.44885 -1.53680 -1.61803 -1.69219 -1.75895 -1.81801 -1.86913 -1.91207 -1.94665 -1.97272 -1.99017 -1.99891 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.98253 1.93042 1.84458 1.72651 1.57828 1.40247 1.20216 0.98085 0.74239 0.49097 0.23097 -0.03307 -0.29653 -0.55481 -0.80339 -1.03794 -1.25435 -1.44885 -1.61803 -1.75895 -1.86913 -1.94665 -1.99017 -1.99891 -1.97272 -1.91207 -1.81801 -1.69219 -1.53680 -1.35456 -1.14866 -0.92268 -0.68059 -0.42660 -0.16516 0.09917 0.36176 0.61803 0.86351 1.09390 1.30517 1.49364 1.65602 1.78946 1.89163 1.96076 1.99563 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.96076 1.84458 1.65602 1.40247 1.09390 0.74239 0.36176 -0.03307 -0.42660 -0.80339 -1.14866 -1.44885 -1.69219 -1.86913 -1.97272 -1.99891 -1.94665 -1.81801 -1.61803 -1.35456 -1.03794 -0.68059 -0.29653 0.09917 0.49097 0.86351 1.20216 1.49364 1.72651 1.89163 1.98253 1.99563 1.93042 1.78946 1.57828 1.30517 0.98085 0.61803 0.23097 -0.16516 -0.55481 -0.92268 -1.25435 -1.53680 -1.75895 -1.91207 -1.99017 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.93042 1.72651 1.40247 0.98085 0.49097 -0.03307 -0.55481 -1.03794 -1.44885 -1.75895 -1.94665 -1.99891 -1.91207 -1.69219 -1.35456 -0.92268 -0.42660 0.09917 0.61803 1.09390 1.49364 1.78946 1.96076 1.99563 1.89163 1.65602 1.30517 0.86351 0.36176 -0.16516 -0.68059 -1.14866 -1.53680 -1.81801 -1.97272 -1.99017 -1.86913 -1.61803 -1.25435 -0.80339 -0.29653 0.23097 0.74239 1.20216 1.57828 1.84458 1.98253 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516 0.49097 1.09390 1.57828 1.89163 2.00000 1.89163 1.57828 1.09390 0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.84458 1.40247 0.74239 -0.03307 -0.80339 -1.44885 -1.86913 -1.99891 -1.81801 -1.35456 -0.68059 0.09917 0.86351 1.49364 1.89163 1.99563 1.78946 1.30517 0.61803 -0.16516 -0.92268 -1.53680 -1.91207 -1.99017 -1.75895 -1.25435 -0.55481 0.23097 0.98085 1.57828 1.93042 1.98253 1.72651 1.20216 0.49097 -0.29653 -1.03794 -1.61803 -1.94665 -1.97272 -1.69219 -1.14866 -0.42660 0.36176 1.09390 1.65602 1.96076 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.78946 1.20216 0.36176 -0.55481 -1.35456 -1.86913 -1.99017 -1.69219 -1.03794 -0.16516 0.74239 1.49364 1.93042 1.96076 1.57828 0.86351 -0.03307 -0.92268 -1.61803 -1.97272 -1.91207 -1.44885 -0.68059 0.23097 1.09390 1.72651 1.99563 1.84458 1.30517 0.49097 -0.42660 -1.25435 -1.81801 -1.99891 -1.75895 -1.14866 -0.29653 0.61803 1.40247 1.89163 1.98253 1.65602 0.98085 0.09917 -0.80339 -1.53680 -1.94665 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.72651 0.98085 -0.03307 -1.03794 -1.75895 -1.99891 -1.69219 -0.92268 0.09917 1.09390 1.78946 1.99563 1.65602 0.86351 -0.16516 -1.14866 -1.81801 -1.99017 -1.61803 -0.80339 0.23097 1.20216 1.84458 1.98253 1.57828 0.74239 -0.29653 -1.25435 -1.86913 -1.97272 -1.53680 -0.68059 0.36176 1.30517 1.89163 1.96076 1.49364 0.61803 -0.42660 -1.35456 -1.91207 -1.94665 -1.44885 -0.55481 0.49097 1.40247 1.93042 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.65602 0.74239 -0.42660 -1.44885 -1.97272 -1.81801 -1.03794 0.09917 1.20216 1.89163 1.93042 1.30517 0.23097 -0.92268 -1.75895 -1.99017 -1.53680 -0.55481 0.61803 1.57828 1.99563 1.72651 0.86351 -0.29653 -1.35456 -1.94665 -1.86913 -1.14866 -0.03307 1.09390 1.84458 1.96076 1.40247 0.36176 -0.80339 -1.69219 -1.99891 -1.61803 -0.68059 0.49097 1.49364 1.98253 1.78946 0.98085 -0.16516 -1.25435 -1.91207 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 1.89163 1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339 0.49097 1.57828 2.00000 1.57828 0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516 1.09390 1.89163 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.49364 0.23097 -1.14866 -1.94665 -1.75895 -0.68059 0.74239 1.78946 1.93042 1.09390 -0.29653 -1.53680 -1.99891 -1.44885 -0.16516 1.20216 1.96076 1.72651 0.61803 -0.80339 -1.81801 -1.91207 -1.03794 0.36176 1.57828 1.99563 1.40247 0.09917 -1.25435 -1.97272 -1.69219 -0.55481 0.86351 1.84458 1.89163 0.98085 -0.42660 -1.61803 -1.99017 -1.35456 -0.03307 1.30517 1.98253 1.65602 0.49097 -0.92268 -1.86913 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.40247 -0.03307 -1.44885 -1.99891 -1.35456 0.09917 1.49364 1.99563 1.30517 -0.16516 -1.53680 -1.99017 -1.25435 0.23097 1.57828 1.98253 1.20216 -0.29653 -1.61803 -1.97272 -1.14866 0.36176 1.65602 1.96076 1.09390 -0.42660 -1.69219 -1.94665 -1.03794 0.49097 1.72651 1.93042 0.98085 -0.55481 -1.75895 -1.91207 -0.92268 0.61803 1.78946 1.89163 0.86351 -0.68059 -1.81801 -1.86913 -0.80339 0.74239 1.84458 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.30517 -0.29653 -1.69219 -1.91207 -0.80339 0.86351 1.93042 1.65602 0.23097 -1.35456 -1.99891 -1.25435 0.36176 1.72651 1.89163 0.74239 -0.92268 -1.94665 -1.61803 -0.16516 1.40247 1.99563 1.20216 -0.42660 -1.75895 -1.86913 -0.68059 0.98085 1.96076 1.57828 0.09917 -1.44885 -1.99017 -1.14866 0.49097 1.78946 1.84458 0.61803 -1.03794 -1.97272 -1.53680 -0.03307 1.49364 1.98253 1.09390 -0.55481 -1.81801 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.20216 -0.55481 -1.86913 -1.69219 -0.16516 1.49364 1.96076 0.86351 -0.92268 -1.97272 -1.44885 0.23097 1.72651 1.84458 0.49097 -1.25435 -1.99891 -1.14866 0.61803 1.89163 1.65602 0.09917 -1.53680 -1.94665 -0.80339 0.98085 1.98253 1.40247 -0.29653 -1.75895 -1.81801 -0.42660 1.30517 1.99563 1.09390 -0.68059 -1.91207 -1.61803 -0.03307 1.57828 1.93042 0.74239 -1.03794 -1.99017 -1.35456 0.36176 1.78946 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 -1.75895 -0.16516 1.57828 1.89163 0.49097 -1.35456 -1.97272 -0.80339 1.09390 2.00000 1.09390 -0.80339 -1.97272 -1.35456 0.49097 1.89163 1.57828 -0.16516 -1.75895 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 0.98085 -1.03794 -1.99891 -0.92268 1.09390 1.99563 0.86351 -1.14866 -1.99017 -0.80339 1.20216 1.98253 0.74239 -1.25435 -1.97272 -0.68059 1.30517 1.96076 0.61803 -1.35456 -1.94665 -0.55481 1.40247 1.93042 0.49097 -1.44885 -1.91207 -0.42660 1.49364 1.89163 0.36176 -1.53680 -1.86913 -0.29653 1.57828 1.84458 0.23097 -1.61803 -1.81801 -0.16516 1.65602 1.78946 0.09917 -1.69219 -1.75895 -0.03307 1.72651 0.00000 ... ... ..... ....... ......... ........... ............. E17 2.00000 0.86351 -1.25435 -1.94665 -0.42660 1.57828 1.78946 -0.03307 -1.81801 -1.53680 0.49097 1.96076 1.20216 -0.92268 -1.99891 -0.80339 1.30517 1.93042 0.36176 -1.61803 -1.75895 0.09917 1.84458 1.49364 -0.55481 -1.97272 -1.14866 0.98085 1.99563 0.74239 -1.35456 -1.91207 -0.29653 1.65602 1.72651 -0.16516 -1.86913 -1.44885 0.61803 1.98253 1.09390 -1.03794 -1.99017 -0.68059 1.40247 1.89163 0.23097 -1.69219 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 0.74239 -1.44885 -1.81801 0.09917 1.89163 1.30517 -0.92268 -1.99017 -0.55481 1.57828 1.72651 -0.29653 -1.94665 -1.14866 1.09390 1.96076 0.36176 -1.69219 -1.61803 0.49097 1.98253 0.98085 -1.25435 -1.91207 -0.16516 1.78946 1.49364 -0.68059 -1.99891 -0.80339 1.40247 1.84458 -0.03307 -1.86913 -1.35456 0.86351 1.99563 0.61803 -1.53680 -1.75895 0.23097 1.93042 1.20216 -1.03794 -1.97272 -0.42660 1.65602 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 -1.61803 0.61803 2.00000 0.61803 -1.61803 0.00000 ... ... ..... ....... ......... ........... ............. E20 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 1.57828 -0.80339 -1.97272 -0.16516 1.89163 1.09390 -1.35456 -1.75895 0.49097 2.00000 0.49097 -1.75895 -1.35456 1.09390 1.89163 -0.16516 -1.97272 -0.80339 1.57828 0.00000 ... ... ..... ....... ......... ........... ............. E21 2.00000 0.36176 -1.86913 -1.03794 1.49364 1.57828 -0.92268 -1.91207 0.23097 1.99563 0.49097 -1.81801 -1.14866 1.40247 1.65602 -0.80339 -1.94665 0.09917 1.98253 0.61803 -1.75895 -1.25435 1.30517 1.72651 -0.68059 -1.97272 -0.03307 1.96076 0.74239 -1.69219 -1.35456 1.20216 1.78946 -0.55481 -1.99017 -0.16516 1.93042 0.86351 -1.61803 -1.44885 1.09390 1.84458 -0.42660 -1.99891 -0.29653 1.89163 0.98085 -1.53680 0.00000 ... ... ..... ....... ......... ........... ............. E22 2.00000 0.23097 -1.94665 -0.68059 1.78946 1.09390 -1.53680 -1.44885 1.20216 1.72651 -0.80339 -1.91207 0.36176 1.99563 0.09917 -1.97272 -0.55481 1.84458 0.98085 -1.61803 -1.35456 1.30517 1.65602 -0.92268 -1.86913 0.49097 1.98253 -0.03307 -1.99017 -0.42660 1.89163 0.86351 -1.69219 -1.25435 1.40247 1.57828 -1.03794 -1.81801 0.61803 1.96076 -0.16516 -1.99891 -0.29653 1.93042 0.74239 -1.75895 -1.14866 1.49364 0.00000 ... ... ..... ....... ......... ........... ............. E23 2.00000 0.09917 -1.99017 -0.29653 1.96076 0.49097 -1.91207 -0.68059 1.84458 0.86351 -1.75895 -1.03794 1.65602 1.20216 -1.53680 -1.35456 1.40247 1.49364 -1.25435 -1.61803 1.09390 1.72651 -0.92268 -1.81801 0.74239 1.89163 -0.55481 -1.94665 0.36176 1.98253 -0.16516 -1.99891 -0.03307 1.99563 0.23097 -1.97272 -0.42660 1.93042 0.61803 -1.86913 -0.80339 1.78946 0.98085 -1.69219 -1.14866 1.57828 1.30517 -1.44885 0.00000 ... ... ..... ....... ......... ........... ............. E24 2.00000 -0.03307 -1.99891 0.09917 1.99563 -0.16516 -1.99017 0.23097 1.98253 -0.29653 -1.97272 0.36176 1.96076 -0.42660 -1.94665 0.49097 1.93042 -0.55481 -1.91207 0.61803 1.89163 -0.68059 -1.86913 0.74239 1.84458 -0.80339 -1.81801 0.86351 1.78946 -0.92268 -1.75895 0.98085 1.72651 -1.03794 -1.69219 1.09390 1.65602 -1.14866 -1.61803 1.20216 1.57828 -1.25435 -1.53680 1.30517 1.49364 -1.35456 -1.44885 1.40247 0.00000 ... ... ..... ....... ......... ........... ............. E25 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 -1.35456 1.57828 1.09390 -1.75895 -0.80339 1.89163 0.49097 -1.97272 -0.16516 2.00000 -0.16516 -1.97272 0.49097 1.89163 -0.80339 -1.75895 1.09390 1.57828 -1.35456 0.00000 ... ... ..... ....... ......... ........... ............. E26 2.00000 -0.29653 -1.91207 0.86351 1.65602 -1.35456 -1.25435 1.72651 0.74239 -1.94665 -0.16516 1.99563 -0.42660 -1.86913 0.98085 1.57828 -1.44885 -1.14866 1.78946 0.61803 -1.97272 -0.03307 1.98253 -0.55481 -1.81801 1.09390 1.49364 -1.53680 -1.03794 1.84458 0.49097 -1.99017 0.09917 1.96076 -0.68059 -1.75895 1.20216 1.40247 -1.61803 -0.92268 1.89163 0.36176 -1.99891 0.23097 1.93042 -0.80339 -1.69219 1.30517 0.00000 ... ... ..... ....... ......... ........... ............. E27 2.00000 -0.42660 -1.81801 1.20216 1.30517 -1.75895 -0.55481 1.99563 -0.29653 -1.86913 1.09390 1.40247 -1.69219 -0.68059 1.98253 -0.16516 -1.91207 0.98085 1.49364 -1.61803 -0.80339 1.96076 -0.03307 -1.94665 0.86351 1.57828 -1.53680 -0.92268 1.93042 0.09917 -1.97272 0.74239 1.65602 -1.44885 -1.03794 1.89163 0.23097 -1.99017 0.61803 1.72651 -1.35456 -1.14866 1.84458 0.36176 -1.99891 0.49097 1.78946 -1.25435 0.00000 ... ... ..... ....... ......... ........... ............. E28 2.00000 -0.55481 -1.69219 1.49364 0.86351 -1.97272 0.23097 1.84458 -1.25435 -1.14866 1.89163 0.09917 -1.94665 0.98085 1.40247 -1.75895 -0.42660 1.99563 -0.68059 -1.61803 1.57828 0.74239 -1.99017 0.36176 1.78946 -1.35456 -1.03794 1.93042 -0.03307 -1.91207 1.09390 1.30517 -1.81801 -0.29653 1.98253 -0.80339 -1.53680 1.65602 0.61803 -1.99891 0.49097 1.72651 -1.44885 -0.92268 1.96076 -0.16516 -1.86913 1.20216 0.00000 ... ... ..... ....... ......... ........... ............. E29 2.00000 -0.68059 -1.53680 1.72651 0.36176 -1.97272 0.98085 1.30517 -1.86913 -0.03307 1.89163 -1.25435 -1.03794 1.96076 -0.29653 -1.75895 1.49364 0.74239 -1.99891 0.61803 1.57828 -1.69219 -0.42660 1.98253 -0.92268 -1.35456 1.84458 0.09917 -1.91207 1.20216 1.09390 -1.94665 0.23097 1.78946 -1.44885 -0.80339 1.99563 -0.55481 -1.61803 1.65602 0.49097 -1.99017 0.86351 1.40247 -1.81801 -0.16516 1.93042 -1.14866 0.00000 ... ... ..... ....... ......... ........... ............. E30 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 1.09390 -1.97272 0.49097 1.57828 -1.75895 -0.16516 1.89163 -1.35456 -0.80339 2.00000 -0.80339 -1.35456 1.89163 -0.16516 -1.75895 1.57828 0.49097 -1.97272 1.09390 0.00000 ... ... ..... ....... ......... ........... ............. E31 2.00000 -0.92268 -1.14866 1.98253 -0.68059 -1.35456 1.93042 -0.42660 -1.53680 1.84458 -0.16516 -1.69219 1.72651 0.09917 -1.81801 1.57828 0.36176 -1.91207 1.40247 0.61803 -1.97272 1.20216 0.86351 -1.99891 0.98085 1.09390 -1.99017 0.74239 1.30517 -1.94665 0.49097 1.49364 -1.86913 0.23097 1.65602 -1.75895 -0.03307 1.78946 -1.61803 -0.29653 1.89163 -1.44885 -0.55481 1.96076 -1.25435 -0.80339 1.99563 -1.03794 0.00000 ... ... ..... ....... ......... ........... ............. E32 2.00000 -1.03794 -0.92268 1.99563 -1.14866 -0.80339 1.98253 -1.25435 -0.68059 1.96076 -1.35456 -0.55481 1.93042 -1.44885 -0.42660 1.89163 -1.53680 -0.29653 1.84458 -1.61803 -0.16516 1.78946 -1.69219 -0.03307 1.72651 -1.75895 0.09917 1.65602 -1.81801 0.23097 1.57828 -1.86913 0.36176 1.49364 -1.91207 0.49097 1.40247 -1.94665 0.61803 1.30517 -1.97272 0.74239 1.20216 -1.99017 0.86351 1.09390 -1.99891 0.98085 0.00000 ... ... ..... ....... ......... ........... ............. E33 2.00000 -1.14866 -0.68059 1.93042 -1.53680 -0.16516 1.72651 -1.81801 0.36176 1.40247 -1.97272 0.86351 0.98085 -1.99017 1.30517 0.49097 -1.86913 1.65602 -0.03307 -1.61803 1.89163 -0.55481 -1.25435 1.99563 -1.03794 -0.80339 1.96076 -1.44885 -0.29653 1.78946 -1.75895 0.23097 1.49364 -1.94665 0.74239 1.09390 -1.99891 1.20216 0.61803 -1.91207 1.57828 0.09917 -1.69219 1.84458 -0.42660 -1.35456 1.98253 -0.92268 0.00000 ... ... ..... ....... ......... ........... ............. E34 2.00000 -1.25435 -0.42660 1.78946 -1.81801 0.49097 1.20216 -1.99891 1.30517 0.36176 -1.75895 1.84458 -0.55481 -1.14866 1.99563 -1.35456 -0.29653 1.72651 -1.86913 0.61803 1.09390 -1.99017 1.40247 0.23097 -1.69219 1.89163 -0.68059 -1.03794 1.98253 -1.44885 -0.16516 1.65602 -1.91207 0.74239 0.98085 -1.97272 1.49364 0.09917 -1.61803 1.93042 -0.80339 -0.92268 1.96076 -1.53680 -0.03307 1.57828 -1.94665 0.86351 0.00000 ... ... ..... ....... ......... ........... ............. E35 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 -0.80339 1.89163 -1.75895 0.49097 1.09390 -1.97272 1.57828 -0.16516 -1.35456 2.00000 -1.35456 -0.16516 1.57828 -1.97272 1.09390 0.49097 -1.75895 1.89163 -0.80339 0.00000 ... ... ..... ....... ......... ........... ............. E36 2.00000 -1.44885 0.09917 1.30517 -1.99017 1.57828 -0.29653 -1.14866 1.96076 -1.69219 0.49097 0.98085 -1.91207 1.78946 -0.68059 -0.80339 1.84458 -1.86913 0.86351 0.61803 -1.75895 1.93042 -1.03794 -0.42660 1.65602 -1.97272 1.20216 0.23097 -1.53680 1.99563 -1.35456 -0.03307 1.40247 -1.99891 1.49364 -0.16516 -1.25435 1.98253 -1.61803 0.36176 1.09390 -1.94665 1.72651 -0.55481 -0.92268 1.89163 -1.81801 0.74239 0.00000 ... ... ..... ....... ......... ........... ............. E37 2.00000 -1.53680 0.36176 0.98085 -1.86913 1.89163 -1.03794 -0.29653 1.49364 -1.99891 1.57828 -0.42660 -0.92268 1.84458 -1.91207 1.09390 0.23097 -1.44885 1.99563 -1.61803 0.49097 0.86351 -1.81801 1.93042 -1.14866 -0.16516 1.40247 -1.99017 1.65602 -0.55481 -0.80339 1.78946 -1.94665 1.20216 0.09917 -1.35456 1.98253 -1.69219 0.61803 0.74239 -1.75895 1.96076 -1.25435 -0.03307 1.30517 -1.97272 1.72651 -0.68059 0.00000 ... ... ..... ....... ......... ........... ............. E38 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.61803 -1.61803 2.00000 -1.61803 0.61803 0.00000 ... ... ..... ....... ......... ........... ............. E39 2.00000 -1.69219 0.86351 0.23097 -1.25435 1.89163 -1.94665 1.40247 -0.42660 -0.68059 1.57828 -1.99017 1.78946 -1.03794 -0.03307 1.09390 -1.81801 1.98253 -1.53680 0.61803 0.49097 -1.44885 1.96076 -1.86913 1.20216 -0.16516 -0.92268 1.72651 -1.99891 1.65602 -0.80339 -0.29653 1.30517 -1.91207 1.93042 -1.35456 0.36176 0.74239 -1.61803 1.99563 -1.75895 0.98085 0.09917 -1.14866 1.84458 -1.97272 1.49364 -0.55481 0.00000 ... ... ..... ....... ......... ........... ............. E40 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.49097 -1.35456 1.89163 -1.97272 1.57828 -0.80339 -0.16516 1.09390 -1.75895 2.00000 -1.75895 1.09390 -0.16516 -0.80339 1.57828 -1.97272 1.89163 -1.35456 0.49097 0.00000 ... ... ..... ....... ......... ........... ............. E41 2.00000 -1.81801 1.30517 -0.55481 -0.29653 1.09390 -1.69219 1.98253 -1.91207 1.49364 -0.80339 -0.03307 0.86351 -1.53680 1.93042 -1.97272 1.65602 -1.03794 0.23097 0.61803 -1.35456 1.84458 -1.99891 1.78946 -1.25435 0.49097 0.36176 -1.14866 1.72651 -1.99017 1.89163 -1.44885 0.74239 0.09917 -0.92268 1.57828 -1.94665 1.96076 -1.61803 0.98085 -0.16516 -0.68059 1.40247 -1.86913 1.99563 -1.75895 1.20216 -0.42660 0.00000 ... ... ..... ....... ......... ........... ............. E42 2.00000 -1.86913 1.49364 -0.92268 0.23097 0.49097 -1.14866 1.65602 -1.94665 1.98253 -1.75895 1.30517 -0.68059 -0.03307 0.74239 -1.35456 1.78946 -1.99017 1.93042 -1.61803 1.09390 -0.42660 -0.29653 0.98085 -1.53680 1.89163 -1.99891 1.84458 -1.44885 0.86351 -0.16516 -0.55481 1.20216 -1.69219 1.96076 -1.97272 1.72651 -1.25435 0.61803 0.09917 -0.80339 1.40247 -1.81801 1.99563 -1.91207 1.57828 -1.03794 0.36176 0.00000 ... ... ..... ....... ......... ........... ............. E43 2.00000 -1.91207 1.65602 -1.25435 0.74239 -0.16516 -0.42660 0.98085 -1.44885 1.78946 -1.97272 1.98253 -1.81801 1.49364 -1.03794 0.49097 0.09917 -0.68059 1.20216 -1.61803 1.89163 -1.99891 1.93042 -1.69219 1.30517 -0.80339 0.23097 0.36176 -0.92268 1.40247 -1.75895 1.96076 -1.99017 1.84458 -1.53680 1.09390 -0.55481 -0.03307 0.61803 -1.14866 1.57828 -1.86913 1.99563 -1.94665 1.72651 -1.35456 0.86351 -0.29653 0.00000 ... ... ..... ....... ......... ........... ............. E44 2.00000 -1.94665 1.78946 -1.53680 1.20216 -0.80339 0.36176 0.09917 -0.55481 0.98085 -1.35456 1.65602 -1.86913 1.98253 -1.99017 1.89163 -1.69219 1.40247 -1.03794 0.61803 -0.16516 -0.29653 0.74239 -1.14866 1.49364 -1.75895 1.93042 -1.99891 1.96076 -1.81801 1.57828 -1.25435 0.86351 -0.42660 -0.03307 0.49097 -0.92268 1.30517 -1.61803 1.84458 -1.97272 1.99563 -1.91207 1.72651 -1.44885 1.09390 -0.68059 0.23097 0.00000 ... ... ..... ....... ......... ........... ............. E45 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 -0.16516 0.49097 -0.80339 1.09390 -1.35456 1.57828 -1.75895 1.89163 -1.97272 2.00000 -1.97272 1.89163 -1.75895 1.57828 -1.35456 1.09390 -0.80339 0.49097 -0.16516 0.00000 ... ... ..... ....... ......... ........... ............. E46 2.00000 -1.99017 1.96076 -1.91207 1.84458 -1.75895 1.65602 -1.53680 1.40247 -1.25435 1.09390 -0.92268 0.74239 -0.55481 0.36176 -0.16516 -0.03307 0.23097 -0.42660 0.61803 -0.80339 0.98085 -1.14866 1.30517 -1.44885 1.57828 -1.69219 1.78946 -1.86913 1.93042 -1.97272 1.99563 -1.99891 1.98253 -1.94665 1.89163 -1.81801 1.72651 -1.61803 1.49364 -1.35456 1.20216 -1.03794 0.86351 -0.68059 0.49097 -0.29653 0.09917 0.00000 ... ... ..... ....... ......... ........... ............. E47 2.00000 -1.99891 1.99563 -1.99017 1.98253 -1.97272 1.96076 -1.94665 1.93042 -1.91207 1.89163 -1.86913 1.84458 -1.81801 1.78946 -1.75895 1.72651 -1.69219 1.65602 -1.61803 1.57828 -1.53680 1.49364 -1.44885 1.40247 -1.35456 1.30517 -1.25435 1.20216 -1.14866 1.09390 -1.03794 0.98085 -0.92268 0.86351 -0.80339 0.74239 -0.68059 0.61803 -0.55481 0.49097 -0.42660 0.36176 -0.29653 0.23097 -0.16516 0.09917 -0.03307 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995627254438 = 2*cos(2*π/95) 1.982528138654 = 2*cos(4*π/95) 1.960759931750 = 2*cos(6*π/95) 1.930417820555 = 2*cos(8*π/95) 1.891634483401 = 2*cos(10*π/95) = 2*cos(2*π/19) 1.844579509955 = 2*cos(12*π/95) 1.789458659642 = 2*cos(14*π/95) 1.726512961915 = 2*cos(16*π/95) 1.656017662296 = 2*cos(18*π/95) 1.578281018793 = 2*cos(20*π/95) = 2*cos(4*π/19) 1.493642953968 = 2*cos(22*π/95) 1.402473568545 = 2*cos(24*π/95) 1.305171523048 = 2*cos(26*π/95) 1.202162294566 = 2*cos(28*π/95) 1.093896316245 = 2*cos(30*π/95) = 2*cos(6*π/19) 0.980847007661 = 2*cos(32*π/95) 0.863508704677 = 2*cos(34*π/95) 0.742394497836 = 2*cos(36*π/95) 0.618033988750 = 2*cos(38*π/95) = 2*cos(2*π/5) = (√5−1)/2 0.490970974282 = 2*cos(40*π/95) = 2*cos(8*π/19) 0.361761068664 = 2*cos(42*π/95) 0.230969273939 = 2*cos(44*π/95) 0.099167509346 = 2*cos(46*π/95) -0.033067889533 = 2*cos(48*π/95) -0.165158690945 = 2*cos(50*π/95) = 2*cos(10*π/19) -0.296527295424 = 2*cos(52*π/95) -0.426599261487 = 2*cos(54*π/95) -0.554805817524 = 2*cos(56*π/95) -0.680586348883 = 2*cos(58*π/95) -0.803390849306 = 2*cos(60*π/95) = 2*cos(12*π/19) -0.922682325957 = 2*cos(62*π/95) -1.037939147562 = 2*cos(64*π/95) -1.148657325366 = 2*cos(66*π/95) -1.254352716947 = 2*cos(68*π/95) -1.354563143251 = 2*cos(70*π/95) = 2*cos(14*π/19) -1.448850409582 = 2*cos(72*π/95) -1.536802221714 = 2*cos(74*π/95) -1.618033988750 = 2*cos(76*π/95) = 2*cos(4*π/5) = −(√5+1)/2 -1.692190504842 = 2*cos(78*π/95) -1.758947502413 = 2*cos(80*π/95) = 2*cos(16*π/19) -1.818013070098 = 2*cos(82*π/95) -1.869128929199 = 2*cos(84*π/95) -1.912071563069 = 2*cos(86*π/95) -1.946653194496 = 2*cos(88*π/95) -1.972722606805 = 2*cos(90*π/95) = 2*cos(18*π/19) -1.990165805090 = 2*cos(92*π/95) -1.998906514682 = 2*cos(94*π/95) Symmetry of Rotations and Cartesian products A1 d+g+i+k+m z², z⁴, z⁶ A2 R+p+f+h+j+l R_z, z, z³, z⁵ 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 D₉₅ point group is 190, and the order of the principal axis (C₉₅) is 95. The group has 49 irreducible representations. β The D₉₅ point group is isomorphic to C_95v. γ The D₉₅ point group is generated by two symmetry elements, C₉₅ and a perpendicular C₂^′. Also, the group may be generated from two C₂^′ axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. ε The lowest nonvanishing multipole moment in D₉₅ is 4 (quadrupole moment). ζ This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. η The point group is chiral, as it does not contain any mirroring operation. 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. ι The point group corresponds to a polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three. While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots.

This Character Table for the D₉₅ point group was created by Gernot Katzer.

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

	D₉₃
	D₉₄
C₉₅ C_95v C_95h	D₉₅	D_95h D_95d
	D₉₆
	D₉₇

Character table for the D95 point group

Character table for the D₉₅ point group