Character Table for Point Group C113v

Character table for the C_113v point group

C113v E 2 C113 2 C113^2 2 C113^3 2 C113^4 2 C113^5 2 C113^6 2 C113^7 2 C113^8 2 C113^9 2 C113^10 2 C113^11 2 C113^12 2 C113^13 2 C113^14 2 C113^15 2 C113^16 2 C113^17 2 C113^18 2 C113^19 2 C113^20 2 C113^21 2 C113^22 2 C113^23 2 C113^24 2 C113^25 2 C113^26 2 C113^27 2 C113^28 2 C113^29 2 C113^30 2 C113^31 2 C113^32 2 C113^33 2 C113^34 2 C113^35 2 C113^36 2 C113^37 2 C113^38 2 C113^39 2 C113^40 2 C113^41 2 C113^42 2 C113^43 2 C113^44 2 C113^45 2 C113^46 2 C113^47 2 C113^48 2 C113^49 2 C113^50 2 C113^51 2 C113^52 2 C113^53 2 C113^54 2 C113^55 2 C113^56 113 sv <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 ... ..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 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. E1 2.00000 1.99691 1.98765 1.97224 1.95074 1.92320 1.88973 1.85041 1.80537 1.75475 1.69871 1.63742 1.57106 1.49985 1.42401 1.34376 1.25936 1.17107 1.07915 0.98391 0.88562 0.78459 0.68114 0.57558 0.46824 0.35946 0.24956 0.13890 0.02780 -0.08338 -0.19430 -0.30463 -0.41401 -0.52211 -0.62860 -0.73315 -0.83543 -0.93512 -1.03193 -1.12555 -1.21568 -1.30206 -1.38442 -1.46250 -1.53605 -1.60486 -1.66871 -1.72740 -1.78075 -1.82860 -1.87079 -1.90720 -1.93772 -1.96225 -1.98071 -1.99305 -1.99923 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.98765 1.95074 1.88973 1.80537 1.69871 1.57106 1.42401 1.25936 1.07915 0.88562 0.68114 0.46824 0.24956 0.02780 -0.19430 -0.41401 -0.62860 -0.83543 -1.03193 -1.21568 -1.38442 -1.53605 -1.66871 -1.78075 -1.87079 -1.93772 -1.98071 -1.99923 -1.99305 -1.96225 -1.90720 -1.82860 -1.72740 -1.60486 -1.46250 -1.30206 -1.12555 -0.93512 -0.73315 -0.52211 -0.30463 -0.08338 0.13890 0.35946 0.57558 0.78459 0.98391 1.17107 1.34376 1.49985 1.63742 1.75475 1.85041 1.92320 1.97224 1.99691 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.97224 1.88973 1.75475 1.57106 1.34376 1.07915 0.78459 0.46824 0.13890 -0.19430 -0.52211 -0.83543 -1.12555 -1.38442 -1.60486 -1.78075 -1.90720 -1.98071 -1.99923 -1.96225 -1.87079 -1.72740 -1.53605 -1.30206 -1.03193 -0.73315 -0.41401 -0.08338 0.24956 0.57558 0.88562 1.17107 1.42401 1.63742 1.80537 1.92320 1.98765 1.99691 1.95074 1.85041 1.69871 1.49985 1.25936 0.98391 0.68114 0.35946 0.02780 -0.30463 -0.62860 -0.93512 -1.21568 -1.46250 -1.66871 -1.82860 -1.93772 -1.99305 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.95074 1.80537 1.57106 1.25936 0.88562 0.46824 0.02780 -0.41401 -0.83543 -1.21568 -1.53605 -1.78075 -1.93772 -1.99923 -1.96225 -1.82860 -1.60486 -1.30206 -0.93512 -0.52211 -0.08338 0.35946 0.78459 1.17107 1.49985 1.75475 1.92320 1.99691 1.97224 1.85041 1.63742 1.34376 0.98391 0.57558 0.13890 -0.30463 -0.73315 -1.12555 -1.46250 -1.72740 -1.90720 -1.99305 -1.98071 -1.87079 -1.66871 -1.38442 -1.03193 -0.62860 -0.19430 0.24956 0.68114 1.07915 1.42401 1.69871 1.88973 1.98765 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.92320 1.69871 1.34376 0.88562 0.35946 -0.19430 -0.73315 -1.21568 -1.60486 -1.87079 -1.99305 -1.96225 -1.78075 -1.46250 -1.03193 -0.52211 0.02780 0.57558 1.07915 1.49985 1.80537 1.97224 1.98765 1.85041 1.57106 1.17107 0.68114 0.13890 -0.41401 -0.93512 -1.38442 -1.72740 -1.93772 -1.99923 -1.90720 -1.66871 -1.30206 -0.83543 -0.30463 0.24956 0.78459 1.25936 1.63742 1.88973 1.99691 1.95074 1.75475 1.42401 0.98391 0.46824 -0.08338 -0.62860 -1.12555 -1.53605 -1.82860 -1.98071 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.88973 1.57106 1.07915 0.46824 -0.19430 -0.83543 -1.38442 -1.78075 -1.98071 -1.96225 -1.72740 -1.30206 -0.73315 -0.08338 0.57558 1.17107 1.63742 1.92320 1.99691 1.85041 1.49985 0.98391 0.35946 -0.30463 -0.93512 -1.46250 -1.82860 -1.99305 -1.93772 -1.66871 -1.21568 -0.62860 0.02780 0.68114 1.25936 1.69871 1.95074 1.98765 1.80537 1.42401 0.88562 0.24956 -0.41401 -1.03193 -1.53605 -1.87079 -1.99923 -1.90720 -1.60486 -1.12555 -0.52211 0.13890 0.78459 1.34376 1.75475 1.97224 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.85041 1.42401 0.78459 0.02780 -0.73315 -1.38442 -1.82860 -1.99923 -1.87079 -1.46250 -0.83543 -0.08338 0.68114 1.34376 1.80537 1.99691 1.88973 1.49985 0.88562 0.13890 -0.62860 -1.30206 -1.78075 -1.99305 -1.90720 -1.53605 -0.93512 -0.19430 0.57558 1.25936 1.75475 1.98765 1.92320 1.57106 0.98391 0.24956 -0.52211 -1.21568 -1.72740 -1.98071 -1.93772 -1.60486 -1.03193 -0.30463 0.46824 1.17107 1.69871 1.97224 1.95074 1.63742 1.07915 0.35946 -0.41401 -1.12555 -1.66871 -1.96225 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.80537 1.25936 0.46824 -0.41401 -1.21568 -1.78075 -1.99923 -1.82860 -1.30206 -0.52211 0.35946 1.17107 1.75475 1.99691 1.85041 1.34376 0.57558 -0.30463 -1.12555 -1.72740 -1.99305 -1.87079 -1.38442 -0.62860 0.24956 1.07915 1.69871 1.98765 1.88973 1.42401 0.68114 -0.19430 -1.03193 -1.66871 -1.98071 -1.90720 -1.46250 -0.73315 0.13890 0.98391 1.63742 1.97224 1.92320 1.49985 0.78459 -0.08338 -0.93512 -1.60486 -1.96225 -1.93772 -1.53605 -0.83543 0.02780 0.88562 1.57106 1.95074 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.75475 1.07915 0.13890 -0.83543 -1.60486 -1.98071 -1.87079 -1.30206 -0.41401 0.57558 1.42401 1.92320 1.95074 1.49985 0.68114 -0.30463 -1.21568 -1.82860 -1.99305 -1.66871 -0.93512 0.02780 0.98391 1.69871 1.99691 1.80537 1.17107 0.24956 -0.73315 -1.53605 -1.96225 -1.90720 -1.38442 -0.52211 0.46824 1.34376 1.88973 1.97224 1.57106 0.78459 -0.19430 -1.12555 -1.78075 -1.99923 -1.72740 -1.03193 -0.08338 0.88562 1.63742 1.98765 1.85041 1.25936 0.35946 -0.62860 -1.46250 -1.93772 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.69871 0.88562 -0.19430 -1.21568 -1.87079 -1.96225 -1.46250 -0.52211 0.57558 1.49985 1.97224 1.85041 1.17107 0.13890 -0.93512 -1.72740 -1.99923 -1.66871 -0.83543 0.24956 1.25936 1.88973 1.95074 1.42401 0.46824 -0.62860 -1.53605 -1.98071 -1.82860 -1.12555 -0.08338 0.98391 1.75475 1.99691 1.63742 0.78459 -0.30463 -1.30206 -1.90720 -1.93772 -1.38442 -0.41401 0.68114 1.57106 1.98765 1.80537 1.07915 0.02780 -1.03193 -1.78075 -1.99305 -1.60486 -0.73315 0.35946 1.34376 1.92320 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.63742 0.68114 -0.52211 -1.53605 -1.99305 -1.72740 -0.83543 0.35946 1.42401 1.97224 1.80537 0.98391 -0.19430 -1.30206 -1.93772 -1.87079 -1.12555 0.02780 1.17107 1.88973 1.92320 1.25936 0.13890 -1.03193 -1.82860 -1.96225 -1.38442 -0.30463 0.88562 1.75475 1.98765 1.49985 0.46824 -0.73315 -1.66871 -1.99923 -1.60486 -0.62860 0.57558 1.57106 1.99691 1.69871 0.78459 -0.41401 -1.46250 -1.98071 -1.78075 -0.93512 0.24956 1.34376 1.95074 1.85041 1.07915 -0.08338 -1.21568 -1.90720 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.57106 0.46824 -0.83543 -1.78075 -1.96225 -1.30206 -0.08338 1.17107 1.92320 1.85041 0.98391 -0.30463 -1.46250 -1.99305 -1.66871 -0.62860 0.68114 1.69871 1.98765 1.42401 0.24956 -1.03193 -1.87079 -1.90720 -1.12555 0.13890 1.34376 1.97224 1.75475 0.78459 -0.52211 -1.60486 -1.99923 -1.53605 -0.41401 0.88562 1.80537 1.95074 1.25936 0.02780 -1.21568 -1.93772 -1.82860 -0.93512 0.35946 1.49985 1.99691 1.63742 0.57558 -0.73315 -1.72740 -1.98071 -1.38442 -0.19430 1.07915 1.88973 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.49985 0.24956 -1.12555 -1.93772 -1.78075 -0.73315 0.68114 1.75475 1.95074 1.17107 -0.19430 -1.46250 -1.99923 -1.53605 -0.30463 1.07915 1.92320 1.80537 0.78459 -0.62860 -1.72740 -1.96225 -1.21568 0.13890 1.42401 1.99691 1.57106 0.35946 -1.03193 -1.90720 -1.82860 -0.83543 0.57558 1.69871 1.97224 1.25936 -0.08338 -1.38442 -1.99305 -1.60486 -0.41401 0.98391 1.88973 1.85041 0.88562 -0.52211 -1.66871 -1.98071 -1.30206 0.02780 1.34376 1.98765 1.63742 0.46824 -0.93512 -1.87079 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.42401 0.02780 -1.38442 -1.99923 -1.46250 -0.08338 1.34376 1.99691 1.49985 0.13890 -1.30206 -1.99305 -1.53605 -0.19430 1.25936 1.98765 1.57106 0.24956 -1.21568 -1.98071 -1.60486 -0.30463 1.17107 1.97224 1.63742 0.35946 -1.12555 -1.96225 -1.66871 -0.41401 1.07915 1.95074 1.69871 0.46824 -1.03193 -1.93772 -1.72740 -0.52211 0.98391 1.92320 1.75475 0.57558 -0.93512 -1.90720 -1.78075 -0.62860 0.88562 1.88973 1.80537 0.68114 -0.83543 -1.87079 -1.82860 -0.73315 0.78459 1.85041 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 1.34376 -0.19430 -1.60486 -1.96225 -1.03193 0.57558 1.80537 1.85041 0.68114 -0.93512 -1.93772 -1.66871 -0.30463 1.25936 1.99691 1.42401 -0.08338 -1.53605 -1.98071 -1.12555 0.46824 1.75475 1.88973 0.78459 -0.83543 -1.90720 -1.72740 -0.41401 1.17107 1.98765 1.49985 0.02780 -1.46250 -1.99305 -1.21568 0.35946 1.69871 1.92320 0.88562 -0.73315 -1.87079 -1.78075 -0.52211 1.07915 1.97224 1.57106 0.13890 -1.38442 -1.99923 -1.30206 0.24956 1.63742 1.95074 0.98391 -0.62860 -1.82860 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 1.25936 -0.41401 -1.78075 -1.82860 -0.52211 1.17107 1.99691 1.34376 -0.30463 -1.72740 -1.87079 -0.62860 1.07915 1.98765 1.42401 -0.19430 -1.66871 -1.90720 -0.73315 0.98391 1.97224 1.49985 -0.08338 -1.60486 -1.93772 -0.83543 0.88562 1.95074 1.57106 0.02780 -1.53605 -1.96225 -0.93512 0.78459 1.92320 1.63742 0.13890 -1.46250 -1.98071 -1.03193 0.68114 1.88973 1.69871 0.24956 -1.38442 -1.99305 -1.12555 0.57558 1.85041 1.75475 0.35946 -1.30206 -1.99923 -1.21568 0.46824 1.80537 0.00000 ... ... ..... ....... ......... ........... ............. E17 2.00000 1.17107 -0.62860 -1.90720 -1.60486 0.02780 1.63742 1.88973 0.57558 -1.21568 -1.99923 -1.12555 0.68114 1.92320 1.57106 -0.08338 -1.66871 -1.87079 -0.52211 1.25936 1.99691 1.07915 -0.73315 -1.93772 -1.53605 0.13890 1.69871 1.85041 0.46824 -1.30206 -1.99305 -1.03193 0.78459 1.95074 1.49985 -0.19430 -1.72740 -1.82860 -0.41401 1.34376 1.98765 0.98391 -0.83543 -1.96225 -1.46250 0.24956 1.75475 1.80537 0.35946 -1.38442 -1.98071 -0.93512 0.88562 1.97224 1.42401 -0.30463 -1.78075 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 1.07915 -0.83543 -1.98071 -1.30206 0.57558 1.92320 1.49985 -0.30463 -1.82860 -1.66871 0.02780 1.69871 1.80537 0.24956 -1.53605 -1.90720 -0.52211 1.34376 1.97224 0.78459 -1.12555 -1.99923 -1.03193 0.88562 1.98765 1.25936 -0.62860 -1.93772 -1.46250 0.35946 1.85041 1.63742 -0.08338 -1.72740 -1.78075 -0.19430 1.57106 1.88973 0.46824 -1.38442 -1.96225 -0.73315 1.17107 1.99691 0.98391 -0.93512 -1.99305 -1.21568 0.68114 1.95074 1.42401 -0.41401 -1.87079 -1.60486 0.13890 1.75475 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 0.98391 -1.03193 -1.99923 -0.93512 1.07915 1.99691 0.88562 -1.12555 -1.99305 -0.83543 1.17107 1.98765 0.78459 -1.21568 -1.98071 -0.73315 1.25936 1.97224 0.68114 -1.30206 -1.96225 -0.62860 1.34376 1.95074 0.57558 -1.38442 -1.93772 -0.52211 1.42401 1.92320 0.46824 -1.46250 -1.90720 -0.41401 1.49985 1.88973 0.35946 -1.53605 -1.87079 -0.30463 1.57106 1.85041 0.24956 -1.60486 -1.82860 -0.19430 1.63742 1.80537 0.13890 -1.66871 -1.78075 -0.08338 1.69871 1.75475 0.02780 -1.72740 0.00000 ... ... ..... ....... ......... ........... ............. E20 2.00000 0.88562 -1.21568 -1.96225 -0.52211 1.49985 1.85041 0.13890 -1.72740 -1.66871 0.24956 1.88973 1.42401 -0.62860 -1.98071 -1.12555 0.98391 1.99691 0.78459 -1.30206 -1.93772 -0.41401 1.57106 1.80537 0.02780 -1.78075 -1.60486 0.35946 1.92320 1.34376 -0.73315 -1.99305 -1.03193 1.07915 1.98765 0.68114 -1.38442 -1.90720 -0.30463 1.63742 1.75475 -0.08338 -1.82860 -1.53605 0.46824 1.95074 1.25936 -0.83543 -1.99923 -0.93512 1.17107 1.97224 0.57558 -1.46250 -1.87079 -0.19430 1.69871 0.00000 ... ... ..... ....... ......... ........... ............. E21 2.00000 0.78459 -1.38442 -1.87079 -0.08338 1.80537 1.49985 -0.62860 -1.99305 -0.93512 1.25936 1.92320 0.24956 -1.72740 -1.60486 0.46824 1.97224 1.07915 -1.12555 -1.96225 -0.41401 1.63742 1.69871 -0.30463 -1.93772 -1.21568 0.98391 1.98765 0.57558 -1.53605 -1.78075 0.13890 1.88973 1.34376 -0.83543 -1.99923 -0.73315 1.42401 1.85041 0.02780 -1.82860 -1.46250 0.68114 1.99691 0.88562 -1.30206 -1.90720 -0.19430 1.75475 1.57106 -0.52211 -1.98071 -1.03193 1.17107 1.95074 0.35946 -1.66871 0.00000 ... ... ..... ....... ......... ........... ............. E22 2.00000 0.68114 -1.53605 -1.72740 0.35946 1.97224 0.98391 -1.30206 -1.87079 0.02780 1.88973 1.25936 -1.03193 -1.96225 -0.30463 1.75475 1.49985 -0.73315 -1.99923 -0.62860 1.57106 1.69871 -0.41401 -1.98071 -0.93512 1.34376 1.85041 -0.08338 -1.90720 -1.21568 1.07915 1.95074 0.24956 -1.78075 -1.46250 0.78459 1.99691 0.57558 -1.60486 -1.66871 0.46824 1.98765 0.88562 -1.38442 -1.82860 0.13890 1.92320 1.17107 -1.12555 -1.93772 -0.19430 1.80537 1.42401 -0.83543 -1.99305 -0.52211 1.63742 0.00000 ... ... ..... ....... ......... ........... ............. E23 2.00000 0.57558 -1.66871 -1.53605 0.78459 1.98765 0.35946 -1.78075 -1.38442 0.98391 1.95074 0.13890 -1.87079 -1.21568 1.17107 1.88973 -0.08338 -1.93772 -1.03193 1.34376 1.80537 -0.30463 -1.98071 -0.83543 1.49985 1.69871 -0.52211 -1.99923 -0.62860 1.63742 1.57106 -0.73315 -1.99305 -0.41401 1.75475 1.42401 -0.93512 -1.96225 -0.19430 1.85041 1.25936 -1.12555 -1.90720 0.02780 1.92320 1.07915 -1.30206 -1.82860 0.24956 1.97224 0.88562 -1.46250 -1.72740 0.46824 1.99691 0.68114 -1.60486 0.00000 ... ... ..... ....... ......... ........... ............. E24 2.00000 0.46824 -1.78075 -1.30206 1.17107 1.85041 -0.30463 -1.99305 -0.62860 1.69871 1.42401 -1.03193 -1.90720 0.13890 1.97224 0.78459 -1.60486 -1.53605 0.88562 1.95074 0.02780 -1.93772 -0.93512 1.49985 1.63742 -0.73315 -1.98071 -0.19430 1.88973 1.07915 -1.38442 -1.72740 0.57558 1.99691 0.35946 -1.82860 -1.21568 1.25936 1.80537 -0.41401 -1.99923 -0.52211 1.75475 1.34376 -1.12555 -1.87079 0.24956 1.98765 0.68114 -1.66871 -1.46250 0.98391 1.92320 -0.08338 -1.96225 -0.83543 1.57106 0.00000 ... ... ..... ....... ......... ........... ............. 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E26 2.00000 0.24956 -1.93772 -0.73315 1.75475 1.17107 -1.46250 -1.53605 1.07915 1.80537 -0.62860 -1.96225 0.13890 1.99691 0.35946 -1.90720 -0.83543 1.69871 1.25936 -1.38442 -1.60486 0.98391 1.85041 -0.52211 -1.98071 0.02780 1.98765 0.46824 -1.87079 -0.93512 1.63742 1.34376 -1.30206 -1.66871 0.88562 1.88973 -0.41401 -1.99305 -0.08338 1.97224 0.57558 -1.82860 -1.03193 1.57106 1.42401 -1.21568 -1.72740 0.78459 1.92320 -0.30463 -1.99923 -0.19430 1.95074 0.68114 -1.78075 -1.12555 1.49985 0.00000 ... ... ..... ....... ......... ........... ............. 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E51 2.00000 -1.90720 1.63742 -1.21568 0.68114 -0.08338 -0.52211 1.07915 -1.53605 1.85041 -1.99305 1.95074 -1.72740 1.34376 -0.83543 0.24956 0.35946 -0.93512 1.42401 -1.78075 1.97224 -1.98071 1.80537 -1.46250 0.98391 -0.41401 -0.19430 0.78459 -1.30206 1.69871 -1.93772 1.99691 -1.87079 1.57106 -1.12555 0.57558 0.02780 -0.62860 1.17107 -1.60486 1.88973 -1.99923 1.92320 -1.66871 1.25936 -0.73315 0.13890 0.46824 -1.03193 1.49985 -1.82860 1.98765 -1.96225 1.75475 -1.38442 0.88562 -0.30463 0.00000 ... ... ..... ....... ......... ........... ............. E52 2.00000 -1.93772 1.75475 -1.46250 1.07915 -0.62860 0.13890 0.35946 -0.83543 1.25936 -1.60486 1.85041 -1.98071 1.98765 -1.87079 1.63742 -1.30206 0.88562 -0.41401 -0.08338 0.57558 -1.03193 1.42401 -1.72740 1.92320 -1.99923 1.95074 -1.78075 1.49985 -1.12555 0.68114 -0.19430 -0.30463 0.78459 -1.21568 1.57106 -1.82860 1.97224 -1.99305 1.88973 -1.66871 1.34376 -0.93512 0.46824 0.02780 -0.52211 0.98391 -1.38442 1.69871 -1.90720 1.99691 -1.96225 1.80537 -1.53605 1.17107 -0.73315 0.24956 0.00000 ... ... ..... ....... ......... ........... ............. E53 2.00000 -1.96225 1.85041 -1.66871 1.42401 -1.12555 0.78459 -0.41401 0.02780 0.35946 -0.73315 1.07915 -1.38442 1.63742 -1.82860 1.95074 -1.99923 1.97224 -1.87079 1.69871 -1.46250 1.17107 -0.83543 0.46824 -0.08338 -0.30463 0.68114 -1.03193 1.34376 -1.60486 1.80537 -1.93772 1.99691 -1.98071 1.88973 -1.72740 1.49985 -1.21568 0.88562 -0.52211 0.13890 0.24956 -0.62860 0.98391 -1.30206 1.57106 -1.78075 1.92320 -1.99305 1.98765 -1.90720 1.75475 -1.53605 1.25936 -0.93512 0.57558 -0.19430 0.00000 ... ... ..... ....... ......... ........... ............. E54 2.00000 -1.98071 1.92320 -1.82860 1.69871 -1.53605 1.34376 -1.12555 0.88562 -0.62860 0.35946 -0.08338 -0.19430 0.46824 -0.73315 0.98391 -1.21568 1.42401 -1.60486 1.75475 -1.87079 1.95074 -1.99305 1.99691 -1.96225 1.88973 -1.78075 1.63742 -1.46250 1.25936 -1.03193 0.78459 -0.52211 0.24956 0.02780 -0.30463 0.57558 -0.83543 1.07915 -1.30206 1.49985 -1.66871 1.80537 -1.90720 1.97224 -1.99923 1.98765 -1.93772 1.85041 -1.72740 1.57106 -1.38442 1.17107 -0.93512 0.68114 -0.41401 0.13890 0.00000 ... ... ..... ....... ......... ........... ............. E55 2.00000 -1.99305 1.97224 -1.93772 1.88973 -1.82860 1.75475 -1.66871 1.57106 -1.46250 1.34376 -1.21568 1.07915 -0.93512 0.78459 -0.62860 0.46824 -0.30463 0.13890 0.02780 -0.19430 0.35946 -0.52211 0.68114 -0.83543 0.98391 -1.12555 1.25936 -1.38442 1.49985 -1.60486 1.69871 -1.78075 1.85041 -1.90720 1.95074 -1.98071 1.99691 -1.99923 1.98765 -1.96225 1.92320 -1.87079 1.80537 -1.72740 1.63742 -1.53605 1.42401 -1.30206 1.17107 -1.03193 0.88562 -0.73315 0.57558 -0.41401 0.24956 -0.08338 0.00000 ... ... ..... ....... ......... ........... ............. E56 2.00000 -1.99923 1.99691 -1.99305 1.98765 -1.98071 1.97224 -1.96225 1.95074 -1.93772 1.92320 -1.90720 1.88973 -1.87079 1.85041 -1.82860 1.80537 -1.78075 1.75475 -1.72740 1.69871 -1.66871 1.63742 -1.60486 1.57106 -1.53605 1.49985 -1.46250 1.42401 -1.38442 1.34376 -1.30206 1.25936 -1.21568 1.17107 -1.12555 1.07915 -1.03193 0.98391 -0.93512 0.88562 -0.83543 0.78459 -0.73315 0.68114 -0.62860 0.57558 -0.52211 0.46824 -0.41401 0.35946 -0.30463 0.24956 -0.19430 0.13890 -0.08338 0.02780 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.996909057308 = 2*cos(2*π/113) 1.987645783157 = 2*cos(4*π/113) 1.972238809799 = 2*cos(6*π/113) 1.950735759303 = 2*cos(8*π/113) 1.923203096368 = 2*cos(10*π/113) 1.889725922876 = 2*cos(12*π/113) 1.850407714853 = 2*cos(14*π/113) 1.805370002625 = 2*cos(16*π/113) 1.754751995181 = 2*cos(18*π/113) 1.698710149880 = 2*cos(20*π/113) 1.637417688856 = 2*cos(22*π/113) 1.571064063591 = 2*cos(24*π/113) 1.499854369340 = 2*cos(26*π/113) 1.424008711187 = 2*cos(28*π/113) 1.343761523714 = 2*cos(30*π/113) 1.259360846379 = 2*cos(32*π/113) 1.171067556839 = 2*cos(34*π/113) 1.079154564592 = 2*cos(36*π/113) 0.983905967429 = 2*cos(38*π/113) 0.885616173307 = 2*cos(40*π/113) 0.784588990345 = 2*cos(42*π/113) 0.681136687778 = 2*cos(44*π/113) 0.575579030742 = 2*cos(46*π/113) 0.468242291908 = 2*cos(48*π/113) 0.359458242984 = 2*cos(50*π/113) 0.249563129230 = 2*cos(52*π/113) 0.138896630145 = 2*cos(54*π/113) 0.027800809537 = 2*cos(56*π/113) -0.083380941781 = 2*cos(58*π/113) -0.194304967386 = 2*cos(60*π/113) -0.304628407472 = 2*cos(62*π/113) -0.414010258607 = 2*cos(64*π/113) -0.522112427760 = 2*cos(66*π/113) -0.628600777319 = 2*cos(68*π/113) -0.733146157900 = 2*cos(70*π/113) -0.835425425721 = 2*cos(72*π/113) -0.935122441427 = 2*cos(74*π/113) -1.031929047257 = 2*cos(76*π/113) -1.125546019539 = 2*cos(78*π/113) -1.215683993577 = 2*cos(80*π/113) -1.302064358059 = 2*cos(82*π/113) -1.384420116229 = 2*cos(84*π/113) -1.462496711157 = 2*cos(86*π/113) -1.536052812563 = 2*cos(88*π/113) -1.604861062754 = 2*cos(90*π/113) -1.668708779370 = 2*cos(92*π/113) -1.727398612779 = 2*cos(94*π/113) -1.780749156069 = 2*cos(96*π/113) -1.828595505768 = 2*cos(98*π/113) -1.870789771551 = 2*cos(100*π/113) -1.907201533361 = 2*cos(102*π/113) -1.937718244529 = 2*cos(104*π/113) -1.962245579649 = 2*cos(106*π/113) -1.980707726134 = 2*cos(108*π/113) -1.993047618548 = 2*cos(110*π/113) -1.999227114989 = 2*cos(112*π/113) 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_113v point group is 226, and the order of the principal axis (C₁₁₃) is 113. The group has 58 irreducible representations. β The C_113v point group is isomorphic to D₁₁₃. γ The C_113v point group is generated by two symmetry elements, C₁₁₃ and any σ_v. Also, the group may be generated from any two σ_v planes. δ The lowest nonvanishing multipole moment in C_113v is 2 (dipole moment). ε This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. ζ 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 just 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_113v point group was created by Gernot Katzer.

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

	C_111v
	C_112v
C₁₁₃	C_113v	C_113h D₁₁₃ D_113h D_113d
	C_114v
	C_115v

Character table for the C113v point group

Character table for the C_113v point group