Character table for the C106v point group

C106v   E         2 C106    2 C53     2 C106^3  2 C53^2   2 C106^5  2 C53^3   2 C106^7  2 C53^4   2 C106^9  2 C53^5   2 C106^11 2 C53^6   2 C106^13 2 C53^7   2 C106^15 2 C53^8   2 C106^17 2 C53^9   2 C106^19 2 C53^10  2 C106^21 2 C53^11  2 C106^23 2 C53^12  2 C106^25 2 C53^13  2 C106^27 2 C53^14  2 C106^29 2 C53^15  2 C106^31 2 C53^16  2 C106^33 2 C53^17  2 C106^35 2 C53^18  2 C106^37 2 C53^19  2 C106^39 2 C53^20  2 C106^41 2 C53^21  2 C106^43 2 C53^22  2 C106^45 2 C53^23  2 C106^47 2 C53^24  2 C106^49 2 C53^25  2 C106^51 2 C53^26  C2        53 sv     53 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     ... ..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     ..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     ... ... ..... ....... ......... ........... .............
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     ... ... ..... ....... ......... ........... .............
E1       2.00000   1.99649   1.98596   1.96846   1.94405   1.91280   1.87484   1.83029   1.77931   1.72209   1.65881   1.58971   1.51502   1.43501   1.34997   1.26018   1.16596   1.06765   0.96558   0.86013   0.75166   0.64054   0.52717   0.41196   0.29529   0.17759   0.05927  -0.05927  -0.17759  -0.29529  -0.41196  -0.52717  -0.64054  -0.75166  -0.86013  -0.96558  -1.06765  -1.16596  -1.26018  -1.34997  -1.43501  -1.51502  -1.58971  -1.65881  -1.72209  -1.77931  -1.83029  -1.87484  -1.91280  -1.94405  -1.96846  -1.98596  -1.99649  -2.00000   0.00000   0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2       2.00000   1.98596   1.94405   1.87484   1.77931   1.65881   1.51502   1.34997   1.16596   0.96558   0.75166   0.52717   0.29529   0.05927  -0.17759  -0.41196  -0.64054  -0.86013  -1.06765  -1.26018  -1.43501  -1.58971  -1.72209  -1.83029  -1.91280  -1.96846  -1.99649  -1.99649  -1.96846  -1.91280  -1.83029  -1.72209  -1.58971  -1.43501  -1.26018  -1.06765  -0.86013  -0.64054  -0.41196  -0.17759   0.05927   0.29529   0.52717   0.75166   0.96558   1.16596   1.34997   1.51502   1.65881   1.77931   1.87484   1.94405   1.98596   2.00000   0.00000   0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3       2.00000   1.96846   1.87484   1.72209   1.51502   1.26018   0.96558   0.64054   0.29529  -0.05927  -0.41196  -0.75166  -1.06765  -1.34997  -1.58971  -1.77931  -1.91280  -1.98596  -1.99649  -1.94405  -1.83029  -1.65881  -1.43501  -1.16596  -0.86013  -0.52717  -0.17759   0.17759   0.52717   0.86013   1.16596   1.43501   1.65881   1.83029   1.94405   1.99649   1.98596   1.91280   1.77931   1.58971   1.34997   1.06765   0.75166   0.41196   0.05927  -0.29529  -0.64054  -0.96558  -1.26018  -1.51502  -1.72209  -1.87484  -1.96846  -2.00000   0.00000   0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4       2.00000   1.94405   1.77931   1.51502   1.16596   0.75166   0.29529  -0.17759  -0.64054  -1.06765  -1.43501  -1.72209  -1.91280  -1.99649  -1.96846  -1.83029  -1.58971  -1.26018  -0.86013  -0.41196   0.05927   0.52717   0.96558   1.34997   1.65881   1.87484   1.98596   1.98596   1.87484   1.65881   1.34997   0.96558   0.52717   0.05927  -0.41196  -0.86013  -1.26018  -1.58971  -1.83029  -1.96846  -1.99649  -1.91280  -1.72209  -1.43501  -1.06765  -0.64054  -0.17759   0.29529   0.75166   1.16596   1.51502   1.77931   1.94405   2.00000   0.00000   0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5       2.00000   1.91280   1.65881   1.26018   0.75166   0.17759  -0.41196  -0.96558  -1.43501  -1.77931  -1.96846  -1.98596  -1.83029  -1.51502  -1.06765  -0.52717   0.05927   0.64054   1.16596   1.58971   1.87484   1.99649   1.94405   1.72209   1.34997   0.86013   0.29529  -0.29529  -0.86013  -1.34997  -1.72209  -1.94405  -1.99649  -1.87484  -1.58971  -1.16596  -0.64054  -0.05927   0.52717   1.06765   1.51502   1.83029   1.98596   1.96846   1.77931   1.43501   0.96558   0.41196  -0.17759  -0.75166  -1.26018  -1.65881  -1.91280  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6       2.00000   1.87484   1.51502   0.96558   0.29529  -0.41196  -1.06765  -1.58971  -1.91280  -1.99649  -1.83029  -1.43501  -0.86013  -0.17759   0.52717   1.16596   1.65881   1.94405   1.98596   1.77931   1.34997   0.75166   0.05927  -0.64054  -1.26018  -1.72209  -1.96846  -1.96846  -1.72209  -1.26018  -0.64054   0.05927   0.75166   1.34997   1.77931   1.98596   1.94405   1.65881   1.16596   0.52717  -0.17759  -0.86013  -1.43501  -1.83029  -1.99649  -1.91280  -1.58971  -1.06765  -0.41196   0.29529   0.96558   1.51502   1.87484   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... TT...........
E7       2.00000   1.83029   1.34997   0.64054  -0.17759  -0.96558  -1.58971  -1.94405  -1.96846  -1.65881  -1.06765  -0.29529   0.52717   1.26018   1.77931   1.99649   1.87484   1.43501   0.75166  -0.05927  -0.86013  -1.51502  -1.91280  -1.98596  -1.72209  -1.16596  -0.41196   0.41196   1.16596   1.72209   1.98596   1.91280   1.51502   0.86013   0.05927  -0.75166  -1.43501  -1.87484  -1.99649  -1.77931  -1.26018  -0.52717   0.29529   1.06765   1.65881   1.96846   1.94405   1.58971   0.96558   0.17759  -0.64054  -1.34997  -1.83029  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E8       2.00000   1.77931   1.16596   0.29529  -0.64054  -1.43501  -1.91280  -1.96846  -1.58971  -0.86013   0.05927   0.96558   1.65881   1.98596   1.87484   1.34997   0.52717  -0.41196  -1.26018  -1.83029  -1.99649  -1.72209  -1.06765  -0.17759   0.75166   1.51502   1.94405   1.94405   1.51502   0.75166  -0.17759  -1.06765  -1.72209  -1.99649  -1.83029  -1.26018  -0.41196   0.52717   1.34997   1.87484   1.98596   1.65881   0.96558   0.05927  -0.86013  -1.58971  -1.96846  -1.91280  -1.43501  -0.64054   0.29529   1.16596   1.77931   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.72209   0.96558  -0.05927  -1.06765  -1.77931  -1.99649  -1.65881  -0.86013   0.17759   1.16596   1.83029   1.98596   1.58971   0.75166  -0.29529  -1.26018  -1.87484  -1.96846  -1.51502  -0.64054   0.41196   1.34997   1.91280   1.94405   1.43501   0.52717  -0.52717  -1.43501  -1.94405  -1.91280  -1.34997  -0.41196   0.64054   1.51502   1.96846   1.87484   1.26018   0.29529  -0.75166  -1.58971  -1.98596  -1.83029  -1.16596  -0.17759   0.86013   1.65881   1.99649   1.77931   1.06765   0.05927  -0.96558  -1.72209  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E10      2.00000   1.65881   0.75166  -0.41196  -1.43501  -1.96846  -1.83029  -1.06765   0.05927   1.16596   1.87484   1.94405   1.34997   0.29529  -0.86013  -1.72209  -1.99649  -1.58971  -0.64054   0.52717   1.51502   1.98596   1.77931   0.96558  -0.17759  -1.26018  -1.91280  -1.91280  -1.26018  -0.17759   0.96558   1.77931   1.98596   1.51502   0.52717  -0.64054  -1.58971  -1.99649  -1.72209  -0.86013   0.29529   1.34997   1.94405   1.87484   1.16596   0.05927  -1.06765  -1.83029  -1.96846  -1.43501  -0.41196   0.75166   1.65881   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.58971   0.52717  -0.75166  -1.72209  -1.98596  -1.43501  -0.29529   0.96558   1.83029   1.94405   1.26018   0.05927  -1.16596  -1.91280  -1.87484  -1.06765   0.17759   1.34997   1.96846   1.77931   0.86013  -0.41196  -1.51502  -1.99649  -1.65881  -0.64054   0.64054   1.65881   1.99649   1.51502   0.41196  -0.86013  -1.77931  -1.96846  -1.34997  -0.17759   1.06765   1.87484   1.91280   1.16596  -0.05927  -1.26018  -1.94405  -1.83029  -0.96558   0.29529   1.43501   1.98596   1.72209   0.75166  -0.52717  -1.58971  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E12      2.00000   1.51502   0.29529  -1.06765  -1.91280  -1.83029  -0.86013   0.52717   1.65881   1.98596   1.34997   0.05927  -1.26018  -1.96846  -1.72209  -0.64054   0.75166   1.77931   1.94405   1.16596  -0.17759  -1.43501  -1.99649  -1.58971  -0.41196   0.96558   1.87484   1.87484   0.96558  -0.41196  -1.58971  -1.99649  -1.43501  -0.17759   1.16596   1.94405   1.77931   0.75166  -0.64054  -1.72209  -1.96846  -1.26018   0.05927   1.34997   1.98596   1.65881   0.52717  -0.86013  -1.83029  -1.91280  -1.06765   0.29529   1.51502   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.43501   0.05927  -1.34997  -1.99649  -1.51502  -0.17759   1.26018   1.98596   1.58971   0.29529  -1.16596  -1.96846  -1.65881  -0.41196   1.06765   1.94405   1.72209   0.52717  -0.96558  -1.91280  -1.77931  -0.64054   0.86013   1.87484   1.83029   0.75166  -0.75166  -1.83029  -1.87484  -0.86013   0.64054   1.77931   1.91280   0.96558  -0.52717  -1.72209  -1.94405  -1.06765   0.41196   1.65881   1.96846   1.16596  -0.29529  -1.58971  -1.98596  -1.26018   0.17759   1.51502   1.99649   1.34997  -0.05927  -1.43501  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E14      2.00000   1.34997  -0.17759  -1.58971  -1.96846  -1.06765   0.52717   1.77931   1.87484   0.75166  -0.86013  -1.91280  -1.72209  -0.41196   1.16596   1.98596   1.51502   0.05927  -1.43501  -1.99649  -1.26018   0.29529   1.65881   1.94405   0.96558  -0.64054  -1.83029  -1.83029  -0.64054   0.96558   1.94405   1.65881   0.29529  -1.26018  -1.99649  -1.43501   0.05927   1.51502   1.98596   1.16596  -0.41196  -1.72209  -1.91280  -0.86013   0.75166   1.87484   1.77931   0.52717  -1.06765  -1.96846  -1.58971  -0.17759   1.34997   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.26018  -0.41196  -1.77931  -1.83029  -0.52717   1.16596   1.99649   1.34997  -0.29529  -1.72209  -1.87484  -0.64054   1.06765   1.98596   1.43501  -0.17759  -1.65881  -1.91280  -0.75166   0.96558   1.96846   1.51502  -0.05927  -1.58971  -1.94405  -0.86013   0.86013   1.94405   1.58971   0.05927  -1.51502  -1.96846  -0.96558   0.75166   1.91280   1.65881   0.17759  -1.43501  -1.98596  -1.06765   0.64054   1.87484   1.72209   0.29529  -1.34997  -1.99649  -1.16596   0.52717   1.83029   1.77931   0.41196  -1.26018  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E16      2.00000   1.16596  -0.64054  -1.91280  -1.58971   0.05927   1.65881   1.87484   0.52717  -1.26018  -1.99649  -1.06765   0.75166   1.94405   1.51502  -0.17759  -1.72209  -1.83029  -0.41196   1.34997   1.98596   0.96558  -0.86013  -1.96846  -1.43501   0.29529   1.77931   1.77931   0.29529  -1.43501  -1.96846  -0.86013   0.96558   1.98596   1.34997  -0.41196  -1.83029  -1.72209  -0.17759   1.51502   1.94405   0.75166  -1.06765  -1.99649  -1.26018   0.52717   1.87484   1.65881   0.05927  -1.58971  -1.91280  -0.64054   1.16596   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.06765  -0.86013  -1.98596  -1.26018   0.64054   1.94405   1.43501  -0.41196  -1.87484  -1.58971   0.17759   1.77931   1.72209   0.05927  -1.65881  -1.83029  -0.29529   1.51502   1.91280   0.52717  -1.34997  -1.96846  -0.75166   1.16596   1.99649   0.96558  -0.96558  -1.99649  -1.16596   0.75166   1.96846   1.34997  -0.52717  -1.91280  -1.51502   0.29529   1.83029   1.65881  -0.05927  -1.72209  -1.77931  -0.17759   1.58971   1.87484   0.41196  -1.43501  -1.94405  -0.64054   1.26018   1.98596   0.86013  -1.06765  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E18      2.00000   0.96558  -1.06765  -1.99649  -0.86013   1.16596   1.98596   0.75166  -1.26018  -1.96846  -0.64054   1.34997   1.94405   0.52717  -1.43501  -1.91280  -0.41196   1.51502   1.87484   0.29529  -1.58971  -1.83029  -0.17759   1.65881   1.77931   0.05927  -1.72209  -1.72209   0.05927   1.77931   1.65881  -0.17759  -1.83029  -1.58971   0.29529   1.87484   1.51502  -0.41196  -1.91280  -1.43501   0.52717   1.94405   1.34997  -0.64054  -1.96846  -1.26018   0.75166   1.98596   1.16596  -0.86013  -1.99649  -1.06765   0.96558   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E19      2.00000   0.86013  -1.26018  -1.94405  -0.41196   1.58971   1.77931  -0.05927  -1.83029  -1.51502   0.52717   1.96846   1.16596  -0.96558  -1.99649  -0.75166   1.34997   1.91280   0.29529  -1.65881  -1.72209   0.17759   1.87484   1.43501  -0.64054  -1.98596  -1.06765   1.06765   1.98596   0.64054  -1.43501  -1.87484  -0.17759   1.72209   1.65881  -0.29529  -1.91280  -1.34997   0.75166   1.99649   0.96558  -1.16596  -1.96846  -0.52717   1.51502   1.83029   0.05927  -1.77931  -1.58971   0.41196   1.94405   1.26018  -0.86013  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E20      2.00000   0.75166  -1.43501  -1.83029   0.05927   1.87484   1.34997  -0.86013  -1.99649  -0.64054   1.51502   1.77931  -0.17759  -1.91280  -1.26018   0.96558   1.98596   0.52717  -1.58971  -1.72209   0.29529   1.94405   1.16596  -1.06765  -1.96846  -0.41196   1.65881   1.65881  -0.41196  -1.96846  -1.06765   1.16596   1.94405   0.29529  -1.72209  -1.58971   0.52717   1.98596   0.96558  -1.26018  -1.91280  -0.17759   1.77931   1.51502  -0.64054  -1.99649  -0.86013   1.34997   1.87484   0.05927  -1.83029  -1.43501   0.75166   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E21      2.00000   0.64054  -1.58971  -1.65881   0.52717   1.99649   0.75166  -1.51502  -1.72209   0.41196   1.98596   0.86013  -1.43501  -1.77931   0.29529   1.96846   0.96558  -1.34997  -1.83029   0.17759   1.94405   1.06765  -1.26018  -1.87484   0.05927   1.91280   1.16596  -1.16596  -1.91280  -0.05927   1.87484   1.26018  -1.06765  -1.94405  -0.17759   1.83029   1.34997  -0.96558  -1.96846  -0.29529   1.77931   1.43501  -0.86013  -1.98596  -0.41196   1.72209   1.51502  -0.75166  -1.99649  -0.52717   1.65881   1.58971  -0.64054  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E22      2.00000   0.52717  -1.72209  -1.43501   0.96558   1.94405   0.05927  -1.91280  -1.06765   1.34997   1.77931  -0.41196  -1.99649  -0.64054   1.65881   1.51502  -0.86013  -1.96846  -0.17759   1.87484   1.16596  -1.26018  -1.83029   0.29529   1.98596   0.75166  -1.58971  -1.58971   0.75166   1.98596   0.29529  -1.83029  -1.26018   1.16596   1.87484  -0.17759  -1.96846  -0.86013   1.51502   1.65881  -0.64054  -1.99649  -0.41196   1.77931   1.34997  -1.06765  -1.91280   0.05927   1.94405   0.96558  -1.43501  -1.72209   0.52717   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E23      2.00000   0.41196  -1.83029  -1.16596   1.34997   1.72209  -0.64054  -1.98596  -0.17759   1.91280   0.96558  -1.51502  -1.58971   0.86013   1.94405  -0.05927  -1.96846  -0.75166   1.65881   1.43501  -1.06765  -1.87484   0.29529   1.99649   0.52717  -1.77931  -1.26018   1.26018   1.77931  -0.52717  -1.99649  -0.29529   1.87484   1.06765  -1.43501  -1.65881   0.75166   1.96846   0.05927  -1.94405  -0.86013   1.58971   1.51502  -0.96558  -1.91280   0.17759   1.98596   0.64054  -1.72209  -1.34997   1.16596   1.83029  -0.41196  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E24      2.00000   0.29529  -1.91280  -0.86013   1.65881   1.34997  -1.26018  -1.72209   0.75166   1.94405  -0.17759  -1.99649  -0.41196   1.87484   0.96558  -1.58971  -1.43501   1.16596   1.77931  -0.64054  -1.96846   0.05927   1.98596   0.52717  -1.83029  -1.06765   1.51502   1.51502  -1.06765  -1.83029   0.52717   1.98596   0.05927  -1.96846  -0.64054   1.77931   1.16596  -1.43501  -1.58971   0.96558   1.87484  -0.41196  -1.99649  -0.17759   1.94405   0.75166  -1.72209  -1.26018   1.34997   1.65881  -0.86013  -1.91280   0.29529   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.17759  -1.96846  -0.52717   1.87484   0.86013  -1.72209  -1.16596   1.51502   1.43501  -1.26018  -1.65881   0.96558   1.83029  -0.64054  -1.94405   0.29529   1.99649   0.05927  -1.98596  -0.41196   1.91280   0.75166  -1.77931  -1.06765   1.58971   1.34997  -1.34997  -1.58971   1.06765   1.77931  -0.75166  -1.91280   0.41196   1.98596  -0.05927  -1.99649  -0.29529   1.94405   0.64054  -1.83029  -0.96558   1.65881   1.26018  -1.43501  -1.51502   1.16596   1.72209  -0.86013  -1.87484   0.52717   1.96846  -0.17759  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E26      2.00000   0.05927  -1.99649  -0.17759   1.98596   0.29529  -1.96846  -0.41196   1.94405   0.52717  -1.91280  -0.64054   1.87484   0.75166  -1.83029  -0.86013   1.77931   0.96558  -1.72209  -1.06765   1.65881   1.16596  -1.58971  -1.26018   1.51502   1.34997  -1.43501  -1.43501   1.34997   1.51502  -1.26018  -1.58971   1.16596   1.65881  -1.06765  -1.72209   0.96558   1.77931  -0.86013  -1.83029   0.75166   1.87484  -0.64054  -1.91280   0.52717   1.94405  -0.41196  -1.96846   0.29529   1.98596  -0.17759  -1.99649   0.05927   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E27      2.00000  -0.05927  -1.99649   0.17759   1.98596  -0.29529  -1.96846   0.41196   1.94405  -0.52717  -1.91280   0.64054   1.87484  -0.75166  -1.83029   0.86013   1.77931  -0.96558  -1.72209   1.06765   1.65881  -1.16596  -1.58971   1.26018   1.51502  -1.34997  -1.43501   1.43501   1.34997  -1.51502  -1.26018   1.58971   1.16596  -1.65881  -1.06765   1.72209   0.96558  -1.77931  -0.86013   1.83029   0.75166  -1.87484  -0.64054   1.91280   0.52717  -1.94405  -0.41196   1.96846   0.29529  -1.98596  -0.17759   1.99649   0.05927  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E28      2.00000  -0.17759  -1.96846   0.52717   1.87484  -0.86013  -1.72209   1.16596   1.51502  -1.43501  -1.26018   1.65881   0.96558  -1.83029  -0.64054   1.94405   0.29529  -1.99649   0.05927   1.98596  -0.41196  -1.91280   0.75166   1.77931  -1.06765  -1.58971   1.34997   1.34997  -1.58971  -1.06765   1.77931   0.75166  -1.91280  -0.41196   1.98596   0.05927  -1.99649   0.29529   1.94405  -0.64054  -1.83029   0.96558   1.65881  -1.26018  -1.43501   1.51502   1.16596  -1.72209  -0.86013   1.87484   0.52717  -1.96846  -0.17759   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E29      2.00000  -0.29529  -1.91280   0.86013   1.65881  -1.34997  -1.26018   1.72209   0.75166  -1.94405  -0.17759   1.99649  -0.41196  -1.87484   0.96558   1.58971  -1.43501  -1.16596   1.77931   0.64054  -1.96846  -0.05927   1.98596  -0.52717  -1.83029   1.06765   1.51502  -1.51502  -1.06765   1.83029   0.52717  -1.98596   0.05927   1.96846  -0.64054  -1.77931   1.16596   1.43501  -1.58971  -0.96558   1.87484   0.41196  -1.99649   0.17759   1.94405  -0.75166  -1.72209   1.26018   1.34997  -1.65881  -0.86013   1.91280   0.29529  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E30      2.00000  -0.41196  -1.83029   1.16596   1.34997  -1.72209  -0.64054   1.98596  -0.17759  -1.91280   0.96558   1.51502  -1.58971  -0.86013   1.94405   0.05927  -1.96846   0.75166   1.65881  -1.43501  -1.06765   1.87484   0.29529  -1.99649   0.52717   1.77931  -1.26018  -1.26018   1.77931   0.52717  -1.99649   0.29529   1.87484  -1.06765  -1.43501   1.65881   0.75166  -1.96846   0.05927   1.94405  -0.86013  -1.58971   1.51502   0.96558  -1.91280  -0.17759   1.98596  -0.64054  -1.72209   1.34997   1.16596  -1.83029  -0.41196   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E31      2.00000  -0.52717  -1.72209   1.43501   0.96558  -1.94405   0.05927   1.91280  -1.06765  -1.34997   1.77931   0.41196  -1.99649   0.64054   1.65881  -1.51502  -0.86013   1.96846  -0.17759  -1.87484   1.16596   1.26018  -1.83029  -0.29529   1.98596  -0.75166  -1.58971   1.58971   0.75166  -1.98596   0.29529   1.83029  -1.26018  -1.16596   1.87484   0.17759  -1.96846   0.86013   1.51502  -1.65881  -0.64054   1.99649  -0.41196  -1.77931   1.34997   1.06765  -1.91280  -0.05927   1.94405  -0.96558  -1.43501   1.72209   0.52717  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E32      2.00000  -0.64054  -1.58971   1.65881   0.52717  -1.99649   0.75166   1.51502  -1.72209  -0.41196   1.98596  -0.86013  -1.43501   1.77931   0.29529  -1.96846   0.96558   1.34997  -1.83029  -0.17759   1.94405  -1.06765  -1.26018   1.87484   0.05927  -1.91280   1.16596   1.16596  -1.91280   0.05927   1.87484  -1.26018  -1.06765   1.94405  -0.17759  -1.83029   1.34997   0.96558  -1.96846   0.29529   1.77931  -1.43501  -0.86013   1.98596  -0.41196  -1.72209   1.51502   0.75166  -1.99649   0.52717   1.65881  -1.58971  -0.64054   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E33      2.00000  -0.75166  -1.43501   1.83029   0.05927  -1.87484   1.34997   0.86013  -1.99649   0.64054   1.51502  -1.77931  -0.17759   1.91280  -1.26018  -0.96558   1.98596  -0.52717  -1.58971   1.72209   0.29529  -1.94405   1.16596   1.06765  -1.96846   0.41196   1.65881  -1.65881  -0.41196   1.96846  -1.06765  -1.16596   1.94405  -0.29529  -1.72209   1.58971   0.52717  -1.98596   0.96558   1.26018  -1.91280   0.17759   1.77931  -1.51502  -0.64054   1.99649  -0.86013  -1.34997   1.87484  -0.05927  -1.83029   1.43501   0.75166  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E34      2.00000  -0.86013  -1.26018   1.94405  -0.41196  -1.58971   1.77931   0.05927  -1.83029   1.51502   0.52717  -1.96846   1.16596   0.96558  -1.99649   0.75166   1.34997  -1.91280   0.29529   1.65881  -1.72209  -0.17759   1.87484  -1.43501  -0.64054   1.98596  -1.06765  -1.06765   1.98596  -0.64054  -1.43501   1.87484  -0.17759  -1.72209   1.65881   0.29529  -1.91280   1.34997   0.75166  -1.99649   0.96558   1.16596  -1.96846   0.52717   1.51502  -1.83029   0.05927   1.77931  -1.58971  -0.41196   1.94405  -1.26018  -0.86013   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E35      2.00000  -0.96558  -1.06765   1.99649  -0.86013  -1.16596   1.98596  -0.75166  -1.26018   1.96846  -0.64054  -1.34997   1.94405  -0.52717  -1.43501   1.91280  -0.41196  -1.51502   1.87484  -0.29529  -1.58971   1.83029  -0.17759  -1.65881   1.77931  -0.05927  -1.72209   1.72209   0.05927  -1.77931   1.65881   0.17759  -1.83029   1.58971   0.29529  -1.87484   1.51502   0.41196  -1.91280   1.43501   0.52717  -1.94405   1.34997   0.64054  -1.96846   1.26018   0.75166  -1.98596   1.16596   0.86013  -1.99649   1.06765   0.96558  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E36      2.00000  -1.06765  -0.86013   1.98596  -1.26018  -0.64054   1.94405  -1.43501  -0.41196   1.87484  -1.58971  -0.17759   1.77931  -1.72209   0.05927   1.65881  -1.83029   0.29529   1.51502  -1.91280   0.52717   1.34997  -1.96846   0.75166   1.16596  -1.99649   0.96558   0.96558  -1.99649   1.16596   0.75166  -1.96846   1.34997   0.52717  -1.91280   1.51502   0.29529  -1.83029   1.65881   0.05927  -1.72209   1.77931  -0.17759  -1.58971   1.87484  -0.41196  -1.43501   1.94405  -0.64054  -1.26018   1.98596  -0.86013  -1.06765   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E37      2.00000  -1.16596  -0.64054   1.91280  -1.58971  -0.05927   1.65881  -1.87484   0.52717   1.26018  -1.99649   1.06765   0.75166  -1.94405   1.51502   0.17759  -1.72209   1.83029  -0.41196  -1.34997   1.98596  -0.96558  -0.86013   1.96846  -1.43501  -0.29529   1.77931  -1.77931   0.29529   1.43501  -1.96846   0.86013   0.96558  -1.98596   1.34997   0.41196  -1.83029   1.72209  -0.17759  -1.51502   1.94405  -0.75166  -1.06765   1.99649  -1.26018  -0.52717   1.87484  -1.65881   0.05927   1.58971  -1.91280   0.64054   1.16596  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E38      2.00000  -1.26018  -0.41196   1.77931  -1.83029   0.52717   1.16596  -1.99649   1.34997   0.29529  -1.72209   1.87484  -0.64054  -1.06765   1.98596  -1.43501  -0.17759   1.65881  -1.91280   0.75166   0.96558  -1.96846   1.51502   0.05927  -1.58971   1.94405  -0.86013  -0.86013   1.94405  -1.58971   0.05927   1.51502  -1.96846   0.96558   0.75166  -1.91280   1.65881  -0.17759  -1.43501   1.98596  -1.06765  -0.64054   1.87484  -1.72209   0.29529   1.34997  -1.99649   1.16596   0.52717  -1.83029   1.77931  -0.41196  -1.26018   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E39      2.00000  -1.34997  -0.17759   1.58971  -1.96846   1.06765   0.52717  -1.77931   1.87484  -0.75166  -0.86013   1.91280  -1.72209   0.41196   1.16596  -1.98596   1.51502  -0.05927  -1.43501   1.99649  -1.26018  -0.29529   1.65881  -1.94405   0.96558   0.64054  -1.83029   1.83029  -0.64054  -0.96558   1.94405  -1.65881   0.29529   1.26018  -1.99649   1.43501   0.05927  -1.51502   1.98596  -1.16596  -0.41196   1.72209  -1.91280   0.86013   0.75166  -1.87484   1.77931  -0.52717  -1.06765   1.96846  -1.58971   0.17759   1.34997  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E40      2.00000  -1.43501   0.05927   1.34997  -1.99649   1.51502  -0.17759  -1.26018   1.98596  -1.58971   0.29529   1.16596  -1.96846   1.65881  -0.41196  -1.06765   1.94405  -1.72209   0.52717   0.96558  -1.91280   1.77931  -0.64054  -0.86013   1.87484  -1.83029   0.75166   0.75166  -1.83029   1.87484  -0.86013  -0.64054   1.77931  -1.91280   0.96558   0.52717  -1.72209   1.94405  -1.06765  -0.41196   1.65881  -1.96846   1.16596   0.29529  -1.58971   1.98596  -1.26018  -0.17759   1.51502  -1.99649   1.34997   0.05927  -1.43501   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E41      2.00000  -1.51502   0.29529   1.06765  -1.91280   1.83029  -0.86013  -0.52717   1.65881  -1.98596   1.34997  -0.05927  -1.26018   1.96846  -1.72209   0.64054   0.75166  -1.77931   1.94405  -1.16596  -0.17759   1.43501  -1.99649   1.58971  -0.41196  -0.96558   1.87484  -1.87484   0.96558   0.41196  -1.58971   1.99649  -1.43501   0.17759   1.16596  -1.94405   1.77931  -0.75166  -0.64054   1.72209  -1.96846   1.26018   0.05927  -1.34997   1.98596  -1.65881   0.52717   0.86013  -1.83029   1.91280  -1.06765  -0.29529   1.51502  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E42      2.00000  -1.58971   0.52717   0.75166  -1.72209   1.98596  -1.43501   0.29529   0.96558  -1.83029   1.94405  -1.26018   0.05927   1.16596  -1.91280   1.87484  -1.06765  -0.17759   1.34997  -1.96846   1.77931  -0.86013  -0.41196   1.51502  -1.99649   1.65881  -0.64054  -0.64054   1.65881  -1.99649   1.51502  -0.41196  -0.86013   1.77931  -1.96846   1.34997  -0.17759  -1.06765   1.87484  -1.91280   1.16596   0.05927  -1.26018   1.94405  -1.83029   0.96558   0.29529  -1.43501   1.98596  -1.72209   0.75166   0.52717  -1.58971   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E43      2.00000  -1.65881   0.75166   0.41196  -1.43501   1.96846  -1.83029   1.06765   0.05927  -1.16596   1.87484  -1.94405   1.34997  -0.29529  -0.86013   1.72209  -1.99649   1.58971  -0.64054  -0.52717   1.51502  -1.98596   1.77931  -0.96558  -0.17759   1.26018  -1.91280   1.91280  -1.26018   0.17759   0.96558  -1.77931   1.98596  -1.51502   0.52717   0.64054  -1.58971   1.99649  -1.72209   0.86013   0.29529  -1.34997   1.94405  -1.87484   1.16596  -0.05927  -1.06765   1.83029  -1.96846   1.43501  -0.41196  -0.75166   1.65881  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E44      2.00000  -1.72209   0.96558   0.05927  -1.06765   1.77931  -1.99649   1.65881  -0.86013  -0.17759   1.16596  -1.83029   1.98596  -1.58971   0.75166   0.29529  -1.26018   1.87484  -1.96846   1.51502  -0.64054  -0.41196   1.34997  -1.91280   1.94405  -1.43501   0.52717   0.52717  -1.43501   1.94405  -1.91280   1.34997  -0.41196  -0.64054   1.51502  -1.96846   1.87484  -1.26018   0.29529   0.75166  -1.58971   1.98596  -1.83029   1.16596  -0.17759  -0.86013   1.65881  -1.99649   1.77931  -1.06765   0.05927   0.96558  -1.72209   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E45      2.00000  -1.77931   1.16596  -0.29529  -0.64054   1.43501  -1.91280   1.96846  -1.58971   0.86013   0.05927  -0.96558   1.65881  -1.98596   1.87484  -1.34997   0.52717   0.41196  -1.26018   1.83029  -1.99649   1.72209  -1.06765   0.17759   0.75166  -1.51502   1.94405  -1.94405   1.51502  -0.75166  -0.17759   1.06765  -1.72209   1.99649  -1.83029   1.26018  -0.41196  -0.52717   1.34997  -1.87484   1.98596  -1.65881   0.96558  -0.05927  -0.86013   1.58971  -1.96846   1.91280  -1.43501   0.64054   0.29529  -1.16596   1.77931  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E46      2.00000  -1.83029   1.34997  -0.64054  -0.17759   0.96558  -1.58971   1.94405  -1.96846   1.65881  -1.06765   0.29529   0.52717  -1.26018   1.77931  -1.99649   1.87484  -1.43501   0.75166   0.05927  -0.86013   1.51502  -1.91280   1.98596  -1.72209   1.16596  -0.41196  -0.41196   1.16596  -1.72209   1.98596  -1.91280   1.51502  -0.86013   0.05927   0.75166  -1.43501   1.87484  -1.99649   1.77931  -1.26018   0.52717   0.29529  -1.06765   1.65881  -1.96846   1.94405  -1.58971   0.96558  -0.17759  -0.64054   1.34997  -1.83029   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E47      2.00000  -1.87484   1.51502  -0.96558   0.29529   0.41196  -1.06765   1.58971  -1.91280   1.99649  -1.83029   1.43501  -0.86013   0.17759   0.52717  -1.16596   1.65881  -1.94405   1.98596  -1.77931   1.34997  -0.75166   0.05927   0.64054  -1.26018   1.72209  -1.96846   1.96846  -1.72209   1.26018  -0.64054  -0.05927   0.75166  -1.34997   1.77931  -1.98596   1.94405  -1.65881   1.16596  -0.52717  -0.17759   0.86013  -1.43501   1.83029  -1.99649   1.91280  -1.58971   1.06765  -0.41196  -0.29529   0.96558  -1.51502   1.87484  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E48      2.00000  -1.91280   1.65881  -1.26018   0.75166  -0.17759  -0.41196   0.96558  -1.43501   1.77931  -1.96846   1.98596  -1.83029   1.51502  -1.06765   0.52717   0.05927  -0.64054   1.16596  -1.58971   1.87484  -1.99649   1.94405  -1.72209   1.34997  -0.86013   0.29529   0.29529  -0.86013   1.34997  -1.72209   1.94405  -1.99649   1.87484  -1.58971   1.16596  -0.64054   0.05927   0.52717  -1.06765   1.51502  -1.83029   1.98596  -1.96846   1.77931  -1.43501   0.96558  -0.41196  -0.17759   0.75166  -1.26018   1.65881  -1.91280   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E49      2.00000  -1.94405   1.77931  -1.51502   1.16596  -0.75166   0.29529   0.17759  -0.64054   1.06765  -1.43501   1.72209  -1.91280   1.99649  -1.96846   1.83029  -1.58971   1.26018  -0.86013   0.41196   0.05927  -0.52717   0.96558  -1.34997   1.65881  -1.87484   1.98596  -1.98596   1.87484  -1.65881   1.34997  -0.96558   0.52717  -0.05927  -0.41196   0.86013  -1.26018   1.58971  -1.83029   1.96846  -1.99649   1.91280  -1.72209   1.43501  -1.06765   0.64054  -0.17759  -0.29529   0.75166  -1.16596   1.51502  -1.77931   1.94405  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E50      2.00000  -1.96846   1.87484  -1.72209   1.51502  -1.26018   0.96558  -0.64054   0.29529   0.05927  -0.41196   0.75166  -1.06765   1.34997  -1.58971   1.77931  -1.91280   1.98596  -1.99649   1.94405  -1.83029   1.65881  -1.43501   1.16596  -0.86013   0.52717  -0.17759  -0.17759   0.52717  -0.86013   1.16596  -1.43501   1.65881  -1.83029   1.94405  -1.99649   1.98596  -1.91280   1.77931  -1.58971   1.34997  -1.06765   0.75166  -0.41196   0.05927   0.29529  -0.64054   0.96558  -1.26018   1.51502  -1.72209   1.87484  -1.96846   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E51      2.00000  -1.98596   1.94405  -1.87484   1.77931  -1.65881   1.51502  -1.34997   1.16596  -0.96558   0.75166  -0.52717   0.29529  -0.05927  -0.17759   0.41196  -0.64054   0.86013  -1.06765   1.26018  -1.43501   1.58971  -1.72209   1.83029  -1.91280   1.96846  -1.99649   1.99649  -1.96846   1.91280  -1.83029   1.72209  -1.58971   1.43501  -1.26018   1.06765  -0.86013   0.64054  -0.41196   0.17759   0.05927  -0.29529   0.52717  -0.75166   0.96558  -1.16596   1.34997  -1.51502   1.65881  -1.77931   1.87484  -1.94405   1.98596  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E52      2.00000  -1.99649   1.98596  -1.96846   1.94405  -1.91280   1.87484  -1.83029   1.77931  -1.72209   1.65881  -1.58971   1.51502  -1.43501   1.34997  -1.26018   1.16596  -1.06765   0.96558  -0.86013   0.75166  -0.64054   0.52717  -0.41196   0.29529  -0.17759   0.05927   0.05927  -0.17759   0.29529  -0.41196   0.52717  -0.64054   0.75166  -0.86013   0.96558  -1.06765   1.16596  -1.26018   1.34997  -1.43501   1.51502  -1.58971   1.65881  -1.72209   1.77931  -1.83029   1.87484  -1.91280   1.94405  -1.96846   1.98596  -1.99649   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.996487463529 = 2*cos(2*π/106) = 2*cos(π/53)
                               1.985962192027 = 2*cos(4*π/106) = 2*cos(2*π/53)
                               1.968461155895 = 2*cos(6*π/106) = 2*cos(3*π/53)
                               1.944045828161 = 2*cos(8*π/106) = 2*cos(4*π/53)
                               1.912801968553 = 2*cos(10*π/106) = 2*cos(5*π/53)
                               1.874839322268 = 2*cos(12*π/106) = 2*cos(6*π/53)
                               1.830291234486 = 2*cos(14*π/106) = 2*cos(7*π/53)
                               1.779314181989 = 2*cos(16*π/106) = 2*cos(8*π/53)
                               1.722087223535 = 2*cos(18*π/106) = 2*cos(9*π/53)
                               1.658811370900 = 2*cos(20*π/106) = 2*cos(10*π/53)
                               1.589708882827 = 2*cos(22*π/106) = 2*cos(11*π/53)
                               1.515022484323 = 2*cos(24*π/106) = 2*cos(12*π/53)
                               1.435014514089 = 2*cos(26*π/106) = 2*cos(13*π/53)
                               1.349966003036 = 2*cos(28*π/106) = 2*cos(14*π/53)
                               1.260175687163 = 2*cos(30*π/106) = 2*cos(15*π/53)
                               1.165958958229 = 2*cos(32*π/106) = 2*cos(16*π/53)
                               1.067646755930 = 2*cos(34*π/106) = 2*cos(17*π/53)
                               0.965584405461 = 2*cos(36*π/106) = 2*cos(18*π/53)
                               0.860130404553 = 2*cos(38*π/106) = 2*cos(19*π/53)
                               0.751655164228 = 2*cos(40*π/106) = 2*cos(20*π/53)
                               0.640539707726 = 2*cos(42*π/106) = 2*cos(21*π/53)
                               0.527174332138 = 2*cos(44*π/106) = 2*cos(22*π/53)
                               0.411957237482 = 2*cos(46*π/106) = 2*cos(23*π/53)
                               0.295293128005 = 2*cos(48*π/106) = 2*cos(24*π/53)
                               0.177591790646 = 2*cos(50*π/106) = 2*cos(25*π/53)
                               0.059266655645 = 2*cos(52*π/106) = 2*cos(26*π/53)



 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                      Rz 
E1   R+p+d+f+g+h+i+j+k+l+m  {Rx, Ry}, {x, y}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} 
E2   d+f+g+h+i+j+k+l+m      {x2y2, xy}, {z(x2y2), xyz}, {z2(x2y2), xyz2}, {z3(x2y2), xyz3}, {z4(x2y2), xyz4} 
E3   f+g+h+i+j+k+l+m        {x(x2−3y2), y(3x2y2)}, {xz(x2−3y2), yz(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4   g+h+i+j+k+l+m          {(x2y2)2−4x2y2, xy(x2y2)}, {z((x2y2)2−4x2y2), xyz(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+i+j+k+l+m            {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+j+k+l+m              {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+k+l+m 
E8   k+l+m 
E9   l+m 
E10  m 

 Notes:

    α  The order of the C106v point group is 212, and the order of the principal axis (C106) is 106. The group has 56 irreducible representations.

    β  The C106v point group is isomorphic to D53d, D53h and D106.

    γ  The C106v point group is generated by two symmetry elements, C106 and any σv (or, non-canonically, any σd).
       Also, the group may be generated from a σv plus a σd (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 σv has the xz plane as a member, while the yz plane is a member of the σd set.

    ε  The lowest nonvanishing multipole moment in C106v 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 C106v point group was created by Gernot Katzer.

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