Character table for the C53h point group

C53h     E        2 C53    2 C53^2  2 C53^3  2 C53^4  2 C53^5  2 C53^6  2 C53^7  2 C53^8  2 C53^9  2 C53^10 2 C53^11 2 C53^12 2 C53^13 2 C53^14 2 C53^15 2 C53^16 2 C53^17 2 C53^18 2 C53^19 2 C53^20 2 C53^21 2 C53^22 2 C53^23 2 C53^24 2 C53^25 2 C53^26 sh       2 S53    2 S53^3  2 S53^5  2 S53^7  2 S53^9  2 S53^11 2 S53^13 2 S53^15 2 S53^17 2 S53^19 2 S53^21 2 S53^23 2 S53^25 2 S53^27 2 S53^29 2 S53^31 2 S53^33 2 S53^35 2 S53^37 2 S53^39 2 S53^41 2 S53^43 2 S53^45 2 S53^47 2 S53^49 2 S53^51   <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A'      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  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
A"      1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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  1.98596  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  2.00000  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     ... TT. ..... ....TT. ......... ........TT. .............
E1"  *  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 -2.00000 -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     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2'  *  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  2.00000  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     ... ... TT... ....... ....TT... ........... ........TT...
E2"  *  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 -2.00000 -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     ... ... ..... ..TT... ......... ......TT... .............
E3'  *  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  2.00000  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     ... ... ..... TT..... ......... ....TT..... .............
E3"  *  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 -2.00000 -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     ... ... ..... ....... ..TT..... ........... ......TT.....
E4'  *  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  2.00000  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     ... ... ..... ....... TT....... ........... ....TT.......
E4"  *  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 -2.00000 -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     ... ... ..... ....... ......... ..TT....... .............
E5'  *  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  2.00000  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     ... ... ..... ....... ......... TT......... .............
E5"  *  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 -2.00000 -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     ... ... ..... ....... ......... ........... ..TT.........
E6'  *  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  2.00000  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     ... ... ..... ....... ......... ........... TT...........
E6"  *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E7'  *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E7"  *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E8'  *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E8"  *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E9'  *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E9"  *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E10' *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E10" *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E11' *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E11" *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E12' *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E12" *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E13' *  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  2.00000  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     ... ... ..... ....... ......... ........... .............
E13" *  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 -2.00000 -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     ... ... ..... ....... ......... ........... .............
E14' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E14" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E15' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E15" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E16' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E16" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E17' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E17" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E18' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E18" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E19' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E19" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E20' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E20" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E21' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E21" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E22' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E22" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E23' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E23" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E24' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E24" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E25' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E25" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............
E26' *  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  2.00000 -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     ... ... ..... ....... ......... ........... .............
E26" *  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 -2.00000  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     ... ... ..... ....... ......... ........... .............

 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

A'   R+d+g+i+k+m  Rz, z2, z4, z6 
A"   p+f+h+j+l    z, z3, z5 
E1'  p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E1"  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2'  d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E2"  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3'  f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E3"  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4'  g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E4"  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E5'  h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E5"  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6'  i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E6"  j+l 
E7'  j+l 
E7"  k+m 
E8'  k+m 
E8"  l 
E9'  l 
E9"  m 
E10' m 

 Notes:

    α  The order of the C53h point group is 106, and the order of the principal axis (S53) is 106. The group has 54 irreducible representations.

    β  The C53h point group could also be named S53, as it contains the S53 axis as its only symmetry element.
       Another rare designation is C106i because the S53 axis is identical to a roto-inversion axis of order 106.

    γ  The C53h point group is isomorphic to C106 and S106.

    δ  The C53h point group is generated by one single symmetry element, S53. Therefore, it is a cyclic group.
       The canonical choice, however, is to use redundant generators: C53 and σh.

    ε  The lowest nonvanishing multipole moment in C53h is 4 (quadrupole moment).

    ζ  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The C53h group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition).
       In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional.

    η  Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters.
       These 104 cases have been combined into 52 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 52 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    θ  The 52 reducible “E” representations almost behave like true irreducible representations.
       Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table.
       This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula.

    ι  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 C53h point group was created by Gernot Katzer.

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