Character table for the C102v point group

C102v   E         2 C102    2 C51     2 C34     2 C51^2   2 C102^5  2 C17     2 C102^7  2 C51^4   2 C34^3   2 C51^5   2 C102^11 2 C17^2   2 C102^13 2 C51^7   2 C34^5   2 C51^8   2 C6      2 C17^3   2 C102^19 2 C51^10  2 C34^7   2 C51^11  2 C102^23 2 C17^4   2 C102^25 2 C51^13  2 C34^9   2 C51^14  2 C102^29 2 C17^5   2 C102^31 2 C51^16  2 C34^11  2 C3      2 C102^35 2 C17^6   2 C102^37 2 C51^19  2 C34^13  2 C51^20  2 C102^41 2 C17^7   2 C102^43 2 C51^22  2 C34^15  2 C51^23  2 C102^47 2 C17^8   2 C102^49 2 C51^25  C2        51 sv     51 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     ... ..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     ..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     ... ... ..... ....... ......... ........... .............
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     ... ... ..... ....... ......... ........... .............
E1       2.00000   1.99621   1.98484   1.96595   1.93959   1.90588   1.86494   1.81693   1.76202   1.70043   1.63239   1.55816   1.47802   1.39227   1.30124   1.20527   1.10473   1.00000   0.89148   0.77957   0.66471   0.54733   0.42787   0.30678   0.18454   0.06159  -0.06159  -0.18454  -0.30678  -0.42787  -0.54733  -0.66471  -0.77957  -0.89148  -1.00000  -1.10473  -1.20527  -1.30124  -1.39227  -1.47802  -1.55816  -1.63239  -1.70043  -1.76202  -1.81693  -1.86494  -1.90588  -1.93959  -1.96595  -1.98484  -1.99621  -2.00000   0.00000   0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2       2.00000   1.98484   1.93959   1.86494   1.76202   1.63239   1.47802   1.30124   1.10473   0.89148   0.66471   0.42787   0.18454  -0.06159  -0.30678  -0.54733  -0.77957  -1.00000  -1.20527  -1.39227  -1.55816  -1.70043  -1.81693  -1.90588  -1.96595  -1.99621  -1.99621  -1.96595  -1.90588  -1.81693  -1.70043  -1.55816  -1.39227  -1.20527  -1.00000  -0.77957  -0.54733  -0.30678  -0.06159   0.18454   0.42787   0.66471   0.89148   1.10473   1.30124   1.47802   1.63239   1.76202   1.86494   1.93959   1.98484   2.00000   0.00000   0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3       2.00000   1.96595   1.86494   1.70043   1.47802   1.20527   0.89148   0.54733   0.18454  -0.18454  -0.54733  -0.89148  -1.20527  -1.47802  -1.70043  -1.86494  -1.96595  -2.00000  -1.96595  -1.86494  -1.70043  -1.47802  -1.20527  -0.89148  -0.54733  -0.18454   0.18454   0.54733   0.89148   1.20527   1.47802   1.70043   1.86494   1.96595   2.00000   1.96595   1.86494   1.70043   1.47802   1.20527   0.89148   0.54733   0.18454  -0.18454  -0.54733  -0.89148  -1.20527  -1.47802  -1.70043  -1.86494  -1.96595  -2.00000   0.00000   0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4       2.00000   1.93959   1.76202   1.47802   1.10473   0.66471   0.18454  -0.30678  -0.77957  -1.20527  -1.55816  -1.81693  -1.96595  -1.99621  -1.90588  -1.70043  -1.39227  -1.00000  -0.54733  -0.06159   0.42787   0.89148   1.30124   1.63239   1.86494   1.98484   1.98484   1.86494   1.63239   1.30124   0.89148   0.42787  -0.06159  -0.54733  -1.00000  -1.39227  -1.70043  -1.90588  -1.99621  -1.96595  -1.81693  -1.55816  -1.20527  -0.77957  -0.30678   0.18454   0.66471   1.10473   1.47802   1.76202   1.93959   2.00000   0.00000   0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5       2.00000   1.90588   1.63239   1.20527   0.66471   0.06159  -0.54733  -1.10473  -1.55816  -1.86494  -1.99621  -1.93959  -1.70043  -1.30124  -0.77957  -0.18454   0.42787   1.00000   1.47802   1.81693   1.98484   1.96595   1.76202   1.39227   0.89148   0.30678  -0.30678  -0.89148  -1.39227  -1.76202  -1.96595  -1.98484  -1.81693  -1.47802  -1.00000  -0.42787   0.18454   0.77957   1.30124   1.70043   1.93959   1.99621   1.86494   1.55816   1.10473   0.54733  -0.06159  -0.66471  -1.20527  -1.63239  -1.90588  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6       2.00000   1.86494   1.47802   0.89148   0.18454  -0.54733  -1.20527  -1.70043  -1.96595  -1.96595  -1.70043  -1.20527  -0.54733   0.18454   0.89148   1.47802   1.86494   2.00000   1.86494   1.47802   0.89148   0.18454  -0.54733  -1.20527  -1.70043  -1.96595  -1.96595  -1.70043  -1.20527  -0.54733   0.18454   0.89148   1.47802   1.86494   2.00000   1.86494   1.47802   0.89148   0.18454  -0.54733  -1.20527  -1.70043  -1.96595  -1.96595  -1.70043  -1.20527  -0.54733   0.18454   0.89148   1.47802   1.86494   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... TT...........
E7       2.00000   1.81693   1.30124   0.54733  -0.30678  -1.10473  -1.70043  -1.98484  -1.90588  -1.47802  -0.77957   0.06159   0.89148   1.55816   1.93959   1.96595   1.63239   1.00000   0.18454  -0.66471  -1.39227  -1.86494  -1.99621  -1.76202  -1.20527  -0.42787   0.42787   1.20527   1.76202   1.99621   1.86494   1.39227   0.66471  -0.18454  -1.00000  -1.63239  -1.96595  -1.93959  -1.55816  -0.89148  -0.06159   0.77957   1.47802   1.90588   1.98484   1.70043   1.10473   0.30678  -0.54733  -1.30124  -1.81693  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E8       2.00000   1.76202   1.10473   0.18454  -0.77957  -1.55816  -1.96595  -1.90588  -1.39227  -0.54733   0.42787   1.30124   1.86494   1.98484   1.63239   0.89148  -0.06159  -1.00000  -1.70043  -1.99621  -1.81693  -1.20527  -0.30678   0.66471   1.47802   1.93959   1.93959   1.47802   0.66471  -0.30678  -1.20527  -1.81693  -1.99621  -1.70043  -1.00000  -0.06159   0.89148   1.63239   1.98484   1.86494   1.30124   0.42787  -0.54733  -1.39227  -1.90588  -1.96595  -1.55816  -0.77957   0.18454   1.10473   1.76202   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E9       2.00000   1.70043   0.89148  -0.18454  -1.20527  -1.86494  -1.96595  -1.47802  -0.54733   0.54733   1.47802   1.96595   1.86494   1.20527   0.18454  -0.89148  -1.70043  -2.00000  -1.70043  -0.89148   0.18454   1.20527   1.86494   1.96595   1.47802   0.54733  -0.54733  -1.47802  -1.96595  -1.86494  -1.20527  -0.18454   0.89148   1.70043   2.00000   1.70043   0.89148  -0.18454  -1.20527  -1.86494  -1.96595  -1.47802  -0.54733   0.54733   1.47802   1.96595   1.86494   1.20527   0.18454  -0.89148  -1.70043  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E10      2.00000   1.63239   0.66471  -0.54733  -1.55816  -1.99621  -1.70043  -0.77957   0.42787   1.47802   1.98484   1.76202   0.89148  -0.30678  -1.39227  -1.96595  -1.81693  -1.00000   0.18454   1.30124   1.93959   1.86494   1.10473  -0.06159  -1.20527  -1.90588  -1.90588  -1.20527  -0.06159   1.10473   1.86494   1.93959   1.30124   0.18454  -1.00000  -1.81693  -1.96595  -1.39227  -0.30678   0.89148   1.76202   1.98484   1.47802   0.42787  -0.77957  -1.70043  -1.99621  -1.55816  -0.54733   0.66471   1.63239   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E11      2.00000   1.55816   0.42787  -0.89148  -1.81693  -1.93959  -1.20527   0.06159   1.30124   1.96595   1.76202   0.77957  -0.54733  -1.63239  -1.99621  -1.47802  -0.30678   1.00000   1.86494   1.90588   1.10473  -0.18454  -1.39227  -1.98484  -1.70043  -0.66471   0.66471   1.70043   1.98484   1.39227   0.18454  -1.10473  -1.90588  -1.86494  -1.00000   0.30678   1.47802   1.99621   1.63239   0.54733  -0.77957  -1.76202  -1.96595  -1.30124  -0.06159   1.20527   1.93959   1.81693   0.89148  -0.42787  -1.55816  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E12      2.00000   1.47802   0.18454  -1.20527  -1.96595  -1.70043  -0.54733   0.89148   1.86494   1.86494   0.89148  -0.54733  -1.70043  -1.96595  -1.20527   0.18454   1.47802   2.00000   1.47802   0.18454  -1.20527  -1.96595  -1.70043  -0.54733   0.89148   1.86494   1.86494   0.89148  -0.54733  -1.70043  -1.96595  -1.20527   0.18454   1.47802   2.00000   1.47802   0.18454  -1.20527  -1.96595  -1.70043  -0.54733   0.89148   1.86494   1.86494   0.89148  -0.54733  -1.70043  -1.96595  -1.20527   0.18454   1.47802   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E13      2.00000   1.39227  -0.06159  -1.47802  -1.99621  -1.30124   0.18454   1.55816   1.98484   1.20527  -0.30678  -1.63239  -1.96595  -1.10473   0.42787   1.70043   1.93959   1.00000  -0.54733  -1.76202  -1.90588  -0.89148   0.66471   1.81693   1.86494   0.77957  -0.77957  -1.86494  -1.81693  -0.66471   0.89148   1.90588   1.76202   0.54733  -1.00000  -1.93959  -1.70043  -0.42787   1.10473   1.96595   1.63239   0.30678  -1.20527  -1.98484  -1.55816  -0.18454   1.30124   1.99621   1.47802   0.06159  -1.39227  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E14      2.00000   1.30124  -0.30678  -1.70043  -1.90588  -0.77957   0.89148   1.93959   1.63239   0.18454  -1.39227  -1.99621  -1.20527   0.42787   1.76202   1.86494   0.66471  -1.00000  -1.96595  -1.55816  -0.06159   1.47802   1.98484   1.10473  -0.54733  -1.81693  -1.81693  -0.54733   1.10473   1.98484   1.47802  -0.06159  -1.55816  -1.96595  -1.00000   0.66471   1.86494   1.76202   0.42787  -1.20527  -1.99621  -1.39227   0.18454   1.63239   1.93959   0.89148  -0.77957  -1.90588  -1.70043  -0.30678   1.30124   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E15      2.00000   1.20527  -0.54733  -1.86494  -1.70043  -0.18454   1.47802   1.96595   0.89148  -0.89148  -1.96595  -1.47802   0.18454   1.70043   1.86494   0.54733  -1.20527  -2.00000  -1.20527   0.54733   1.86494   1.70043   0.18454  -1.47802  -1.96595  -0.89148   0.89148   1.96595   1.47802  -0.18454  -1.70043  -1.86494  -0.54733   1.20527   2.00000   1.20527  -0.54733  -1.86494  -1.70043  -0.18454   1.47802   1.96595   0.89148  -0.89148  -1.96595  -1.47802   0.18454   1.70043   1.86494   0.54733  -1.20527  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E16      2.00000   1.10473  -0.77957  -1.96595  -1.39227   0.42787   1.86494   1.63239  -0.06159  -1.70043  -1.81693  -0.30678   1.47802   1.93959   0.66471  -1.20527  -1.99621  -1.00000   0.89148   1.98484   1.30124  -0.54733  -1.90588  -1.55816   0.18454   1.76202   1.76202   0.18454  -1.55816  -1.90588  -0.54733   1.30124   1.98484   0.89148  -1.00000  -1.99621  -1.20527   0.66471   1.93959   1.47802  -0.30678  -1.81693  -1.70043  -0.06159   1.63239   1.86494   0.42787  -1.39227  -1.96595  -0.77957   1.10473   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E17      2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000  -1.00000   1.00000   2.00000   1.00000  -1.00000  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E18      2.00000   0.89148  -1.20527  -1.96595  -0.54733   1.47802   1.86494   0.18454  -1.70043  -1.70043   0.18454   1.86494   1.47802  -0.54733  -1.96595  -1.20527   0.89148   2.00000   0.89148  -1.20527  -1.96595  -0.54733   1.47802   1.86494   0.18454  -1.70043  -1.70043   0.18454   1.86494   1.47802  -0.54733  -1.96595  -1.20527   0.89148   2.00000   0.89148  -1.20527  -1.96595  -0.54733   1.47802   1.86494   0.18454  -1.70043  -1.70043   0.18454   1.86494   1.47802  -0.54733  -1.96595  -1.20527   0.89148   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E19      2.00000   0.77957  -1.39227  -1.86494  -0.06159   1.81693   1.47802  -0.66471  -1.99621  -0.89148   1.30124   1.90588   0.18454  -1.76202  -1.55816   0.54733   1.98484   1.00000  -1.20527  -1.93959  -0.30678   1.70043   1.63239  -0.42787  -1.96595  -1.10473   1.10473   1.96595   0.42787  -1.63239  -1.70043   0.30678   1.93959   1.20527  -1.00000  -1.98484  -0.54733   1.55816   1.76202  -0.18454  -1.90588  -1.30124   0.89148   1.99621   0.66471  -1.47802  -1.81693   0.06159   1.86494   1.39227  -0.77957  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E20      2.00000   0.66471  -1.55816  -1.70043   0.42787   1.98484   0.89148  -1.39227  -1.81693   0.18454   1.93959   1.10473  -1.20527  -1.90588  -0.06159   1.86494   1.30124  -1.00000  -1.96595  -0.30678   1.76202   1.47802  -0.77957  -1.99621  -0.54733   1.63239   1.63239  -0.54733  -1.99621  -0.77957   1.47802   1.76202  -0.30678  -1.96595  -1.00000   1.30124   1.86494  -0.06159  -1.90588  -1.20527   1.10473   1.93959   0.18454  -1.81693  -1.39227   0.89148   1.98484   0.42787  -1.70043  -1.55816   0.66471   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E21      2.00000   0.54733  -1.70043  -1.47802   0.89148   1.96595   0.18454  -1.86494  -1.20527   1.20527   1.86494  -0.18454  -1.96595  -0.89148   1.47802   1.70043  -0.54733  -2.00000  -0.54733   1.70043   1.47802  -0.89148  -1.96595  -0.18454   1.86494   1.20527  -1.20527  -1.86494   0.18454   1.96595   0.89148  -1.47802  -1.70043   0.54733   2.00000   0.54733  -1.70043  -1.47802   0.89148   1.96595   0.18454  -1.86494  -1.20527   1.20527   1.86494  -0.18454  -1.96595  -0.89148   1.47802   1.70043  -0.54733  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E22      2.00000   0.42787  -1.81693  -1.20527   1.30124   1.76202  -0.54733  -1.99621  -0.30678   1.86494   1.10473  -1.39227  -1.70043   0.66471   1.98484   0.18454  -1.90588  -1.00000   1.47802   1.63239  -0.77957  -1.96595  -0.06159   1.93959   0.89148  -1.55816  -1.55816   0.89148   1.93959  -0.06159  -1.96595  -0.77957   1.63239   1.47802  -1.00000  -1.90588   0.18454   1.98484   0.66471  -1.70043  -1.39227   1.10473   1.86494  -0.30678  -1.99621  -0.54733   1.76202   1.30124  -1.20527  -1.81693   0.42787   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E23      2.00000   0.30678  -1.90588  -0.89148   1.63239   1.39227  -1.20527  -1.76202   0.66471   1.96595  -0.06159  -1.98484  -0.54733   1.81693   1.10473  -1.47802  -1.55816   1.00000   1.86494  -0.42787  -1.99621  -0.18454   1.93959   0.77957  -1.70043  -1.30124   1.30124   1.70043  -0.77957  -1.93959   0.18454   1.99621   0.42787  -1.86494  -1.00000   1.55816   1.47802  -1.10473  -1.81693   0.54733   1.98484   0.06159  -1.96595  -0.66471   1.76202   1.20527  -1.39227  -1.63239   0.89148   1.90588  -0.30678  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E24      2.00000   0.18454  -1.96595  -0.54733   1.86494   0.89148  -1.70043  -1.20527   1.47802   1.47802  -1.20527  -1.70043   0.89148   1.86494  -0.54733  -1.96595   0.18454   2.00000   0.18454  -1.96595  -0.54733   1.86494   0.89148  -1.70043  -1.20527   1.47802   1.47802  -1.20527  -1.70043   0.89148   1.86494  -0.54733  -1.96595   0.18454   2.00000   0.18454  -1.96595  -0.54733   1.86494   0.89148  -1.70043  -1.20527   1.47802   1.47802  -1.20527  -1.70043   0.89148   1.86494  -0.54733  -1.96595   0.18454   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E25      2.00000   0.06159  -1.99621  -0.18454   1.98484   0.30678  -1.96595  -0.42787   1.93959   0.54733  -1.90588  -0.66471   1.86494   0.77957  -1.81693  -0.89148   1.76202   1.00000  -1.70043  -1.10473   1.63239   1.20527  -1.55816  -1.30124   1.47802   1.39227  -1.39227  -1.47802   1.30124   1.55816  -1.20527  -1.63239   1.10473   1.70043  -1.00000  -1.76202   0.89148   1.81693  -0.77957  -1.86494   0.66471   1.90588  -0.54733  -1.93959   0.42787   1.96595  -0.30678  -1.98484   0.18454   1.99621  -0.06159  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E26      2.00000  -0.06159  -1.99621   0.18454   1.98484  -0.30678  -1.96595   0.42787   1.93959  -0.54733  -1.90588   0.66471   1.86494  -0.77957  -1.81693   0.89148   1.76202  -1.00000  -1.70043   1.10473   1.63239  -1.20527  -1.55816   1.30124   1.47802  -1.39227  -1.39227   1.47802   1.30124  -1.55816  -1.20527   1.63239   1.10473  -1.70043  -1.00000   1.76202   0.89148  -1.81693  -0.77957   1.86494   0.66471  -1.90588  -0.54733   1.93959   0.42787  -1.96595  -0.30678   1.98484   0.18454  -1.99621  -0.06159   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E27      2.00000  -0.18454  -1.96595   0.54733   1.86494  -0.89148  -1.70043   1.20527   1.47802  -1.47802  -1.20527   1.70043   0.89148  -1.86494  -0.54733   1.96595   0.18454  -2.00000   0.18454   1.96595  -0.54733  -1.86494   0.89148   1.70043  -1.20527  -1.47802   1.47802   1.20527  -1.70043  -0.89148   1.86494   0.54733  -1.96595  -0.18454   2.00000  -0.18454  -1.96595   0.54733   1.86494  -0.89148  -1.70043   1.20527   1.47802  -1.47802  -1.20527   1.70043   0.89148  -1.86494  -0.54733   1.96595   0.18454  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E28      2.00000  -0.30678  -1.90588   0.89148   1.63239  -1.39227  -1.20527   1.76202   0.66471  -1.96595  -0.06159   1.98484  -0.54733  -1.81693   1.10473   1.47802  -1.55816  -1.00000   1.86494   0.42787  -1.99621   0.18454   1.93959  -0.77957  -1.70043   1.30124   1.30124  -1.70043  -0.77957   1.93959   0.18454  -1.99621   0.42787   1.86494  -1.00000  -1.55816   1.47802   1.10473  -1.81693  -0.54733   1.98484  -0.06159  -1.96595   0.66471   1.76202  -1.20527  -1.39227   1.63239   0.89148  -1.90588  -0.30678   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E29      2.00000  -0.42787  -1.81693   1.20527   1.30124  -1.76202  -0.54733   1.99621  -0.30678  -1.86494   1.10473   1.39227  -1.70043  -0.66471   1.98484  -0.18454  -1.90588   1.00000   1.47802  -1.63239  -0.77957   1.96595  -0.06159  -1.93959   0.89148   1.55816  -1.55816  -0.89148   1.93959   0.06159  -1.96595   0.77957   1.63239  -1.47802  -1.00000   1.90588   0.18454  -1.98484   0.66471   1.70043  -1.39227  -1.10473   1.86494   0.30678  -1.99621   0.54733   1.76202  -1.30124  -1.20527   1.81693   0.42787  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E30      2.00000  -0.54733  -1.70043   1.47802   0.89148  -1.96595   0.18454   1.86494  -1.20527  -1.20527   1.86494   0.18454  -1.96595   0.89148   1.47802  -1.70043  -0.54733   2.00000  -0.54733  -1.70043   1.47802   0.89148  -1.96595   0.18454   1.86494  -1.20527  -1.20527   1.86494   0.18454  -1.96595   0.89148   1.47802  -1.70043  -0.54733   2.00000  -0.54733  -1.70043   1.47802   0.89148  -1.96595   0.18454   1.86494  -1.20527  -1.20527   1.86494   0.18454  -1.96595   0.89148   1.47802  -1.70043  -0.54733   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E31      2.00000  -0.66471  -1.55816   1.70043   0.42787  -1.98484   0.89148   1.39227  -1.81693  -0.18454   1.93959  -1.10473  -1.20527   1.90588  -0.06159  -1.86494   1.30124   1.00000  -1.96595   0.30678   1.76202  -1.47802  -0.77957   1.99621  -0.54733  -1.63239   1.63239   0.54733  -1.99621   0.77957   1.47802  -1.76202  -0.30678   1.96595  -1.00000  -1.30124   1.86494   0.06159  -1.90588   1.20527   1.10473  -1.93959   0.18454   1.81693  -1.39227  -0.89148   1.98484  -0.42787  -1.70043   1.55816   0.66471  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E32      2.00000  -0.77957  -1.39227   1.86494  -0.06159  -1.81693   1.47802   0.66471  -1.99621   0.89148   1.30124  -1.90588   0.18454   1.76202  -1.55816  -0.54733   1.98484  -1.00000  -1.20527   1.93959  -0.30678  -1.70043   1.63239   0.42787  -1.96595   1.10473   1.10473  -1.96595   0.42787   1.63239  -1.70043  -0.30678   1.93959  -1.20527  -1.00000   1.98484  -0.54733  -1.55816   1.76202   0.18454  -1.90588   1.30124   0.89148  -1.99621   0.66471   1.47802  -1.81693  -0.06159   1.86494  -1.39227  -0.77957   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E33      2.00000  -0.89148  -1.20527   1.96595  -0.54733  -1.47802   1.86494  -0.18454  -1.70043   1.70043   0.18454  -1.86494   1.47802   0.54733  -1.96595   1.20527   0.89148  -2.00000   0.89148   1.20527  -1.96595   0.54733   1.47802  -1.86494   0.18454   1.70043  -1.70043  -0.18454   1.86494  -1.47802  -0.54733   1.96595  -1.20527  -0.89148   2.00000  -0.89148  -1.20527   1.96595  -0.54733  -1.47802   1.86494  -0.18454  -1.70043   1.70043   0.18454  -1.86494   1.47802   0.54733  -1.96595   1.20527   0.89148  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E34      2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000  -1.00000  -1.00000   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E35      2.00000  -1.10473  -0.77957   1.96595  -1.39227  -0.42787   1.86494  -1.63239  -0.06159   1.70043  -1.81693   0.30678   1.47802  -1.93959   0.66471   1.20527  -1.99621   1.00000   0.89148  -1.98484   1.30124   0.54733  -1.90588   1.55816   0.18454  -1.76202   1.76202  -0.18454  -1.55816   1.90588  -0.54733  -1.30124   1.98484  -0.89148  -1.00000   1.99621  -1.20527  -0.66471   1.93959  -1.47802  -0.30678   1.81693  -1.70043   0.06159   1.63239  -1.86494   0.42787   1.39227  -1.96595   0.77957   1.10473  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E36      2.00000  -1.20527  -0.54733   1.86494  -1.70043   0.18454   1.47802  -1.96595   0.89148   0.89148  -1.96595   1.47802   0.18454  -1.70043   1.86494  -0.54733  -1.20527   2.00000  -1.20527  -0.54733   1.86494  -1.70043   0.18454   1.47802  -1.96595   0.89148   0.89148  -1.96595   1.47802   0.18454  -1.70043   1.86494  -0.54733  -1.20527   2.00000  -1.20527  -0.54733   1.86494  -1.70043   0.18454   1.47802  -1.96595   0.89148   0.89148  -1.96595   1.47802   0.18454  -1.70043   1.86494  -0.54733  -1.20527   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E37      2.00000  -1.30124  -0.30678   1.70043  -1.90588   0.77957   0.89148  -1.93959   1.63239  -0.18454  -1.39227   1.99621  -1.20527  -0.42787   1.76202  -1.86494   0.66471   1.00000  -1.96595   1.55816  -0.06159  -1.47802   1.98484  -1.10473  -0.54733   1.81693  -1.81693   0.54733   1.10473  -1.98484   1.47802   0.06159  -1.55816   1.96595  -1.00000  -0.66471   1.86494  -1.76202   0.42787   1.20527  -1.99621   1.39227   0.18454  -1.63239   1.93959  -0.89148  -0.77957   1.90588  -1.70043   0.30678   1.30124  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E38      2.00000  -1.39227  -0.06159   1.47802  -1.99621   1.30124   0.18454  -1.55816   1.98484  -1.20527  -0.30678   1.63239  -1.96595   1.10473   0.42787  -1.70043   1.93959  -1.00000  -0.54733   1.76202  -1.90588   0.89148   0.66471  -1.81693   1.86494  -0.77957  -0.77957   1.86494  -1.81693   0.66471   0.89148  -1.90588   1.76202  -0.54733  -1.00000   1.93959  -1.70043   0.42787   1.10473  -1.96595   1.63239  -0.30678  -1.20527   1.98484  -1.55816   0.18454   1.30124  -1.99621   1.47802  -0.06159  -1.39227   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E39      2.00000  -1.47802   0.18454   1.20527  -1.96595   1.70043  -0.54733  -0.89148   1.86494  -1.86494   0.89148   0.54733  -1.70043   1.96595  -1.20527  -0.18454   1.47802  -2.00000   1.47802  -0.18454  -1.20527   1.96595  -1.70043   0.54733   0.89148  -1.86494   1.86494  -0.89148  -0.54733   1.70043  -1.96595   1.20527   0.18454  -1.47802   2.00000  -1.47802   0.18454   1.20527  -1.96595   1.70043  -0.54733  -0.89148   1.86494  -1.86494   0.89148   0.54733  -1.70043   1.96595  -1.20527  -0.18454   1.47802  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E40      2.00000  -1.55816   0.42787   0.89148  -1.81693   1.93959  -1.20527  -0.06159   1.30124  -1.96595   1.76202  -0.77957  -0.54733   1.63239  -1.99621   1.47802  -0.30678  -1.00000   1.86494  -1.90588   1.10473   0.18454  -1.39227   1.98484  -1.70043   0.66471   0.66471  -1.70043   1.98484  -1.39227   0.18454   1.10473  -1.90588   1.86494  -1.00000  -0.30678   1.47802  -1.99621   1.63239  -0.54733  -0.77957   1.76202  -1.96595   1.30124  -0.06159  -1.20527   1.93959  -1.81693   0.89148   0.42787  -1.55816   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E41      2.00000  -1.63239   0.66471   0.54733  -1.55816   1.99621  -1.70043   0.77957   0.42787  -1.47802   1.98484  -1.76202   0.89148   0.30678  -1.39227   1.96595  -1.81693   1.00000   0.18454  -1.30124   1.93959  -1.86494   1.10473   0.06159  -1.20527   1.90588  -1.90588   1.20527  -0.06159  -1.10473   1.86494  -1.93959   1.30124  -0.18454  -1.00000   1.81693  -1.96595   1.39227  -0.30678  -0.89148   1.76202  -1.98484   1.47802  -0.42787  -0.77957   1.70043  -1.99621   1.55816  -0.54733  -0.66471   1.63239  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E42      2.00000  -1.70043   0.89148   0.18454  -1.20527   1.86494  -1.96595   1.47802  -0.54733  -0.54733   1.47802  -1.96595   1.86494  -1.20527   0.18454   0.89148  -1.70043   2.00000  -1.70043   0.89148   0.18454  -1.20527   1.86494  -1.96595   1.47802  -0.54733  -0.54733   1.47802  -1.96595   1.86494  -1.20527   0.18454   0.89148  -1.70043   2.00000  -1.70043   0.89148   0.18454  -1.20527   1.86494  -1.96595   1.47802  -0.54733  -0.54733   1.47802  -1.96595   1.86494  -1.20527   0.18454   0.89148  -1.70043   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E43      2.00000  -1.76202   1.10473  -0.18454  -0.77957   1.55816  -1.96595   1.90588  -1.39227   0.54733   0.42787  -1.30124   1.86494  -1.98484   1.63239  -0.89148  -0.06159   1.00000  -1.70043   1.99621  -1.81693   1.20527  -0.30678  -0.66471   1.47802  -1.93959   1.93959  -1.47802   0.66471   0.30678  -1.20527   1.81693  -1.99621   1.70043  -1.00000   0.06159   0.89148  -1.63239   1.98484  -1.86494   1.30124  -0.42787  -0.54733   1.39227  -1.90588   1.96595  -1.55816   0.77957   0.18454  -1.10473   1.76202  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E44      2.00000  -1.81693   1.30124  -0.54733  -0.30678   1.10473  -1.70043   1.98484  -1.90588   1.47802  -0.77957  -0.06159   0.89148  -1.55816   1.93959  -1.96595   1.63239  -1.00000   0.18454   0.66471  -1.39227   1.86494  -1.99621   1.76202  -1.20527   0.42787   0.42787  -1.20527   1.76202  -1.99621   1.86494  -1.39227   0.66471   0.18454  -1.00000   1.63239  -1.96595   1.93959  -1.55816   0.89148  -0.06159  -0.77957   1.47802  -1.90588   1.98484  -1.70043   1.10473  -0.30678  -0.54733   1.30124  -1.81693   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E45      2.00000  -1.86494   1.47802  -0.89148   0.18454   0.54733  -1.20527   1.70043  -1.96595   1.96595  -1.70043   1.20527  -0.54733  -0.18454   0.89148  -1.47802   1.86494  -2.00000   1.86494  -1.47802   0.89148  -0.18454  -0.54733   1.20527  -1.70043   1.96595  -1.96595   1.70043  -1.20527   0.54733   0.18454  -0.89148   1.47802  -1.86494   2.00000  -1.86494   1.47802  -0.89148   0.18454   0.54733  -1.20527   1.70043  -1.96595   1.96595  -1.70043   1.20527  -0.54733  -0.18454   0.89148  -1.47802   1.86494  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E46      2.00000  -1.90588   1.63239  -1.20527   0.66471  -0.06159  -0.54733   1.10473  -1.55816   1.86494  -1.99621   1.93959  -1.70043   1.30124  -0.77957   0.18454   0.42787  -1.00000   1.47802  -1.81693   1.98484  -1.96595   1.76202  -1.39227   0.89148  -0.30678  -0.30678   0.89148  -1.39227   1.76202  -1.96595   1.98484  -1.81693   1.47802  -1.00000   0.42787   0.18454  -0.77957   1.30124  -1.70043   1.93959  -1.99621   1.86494  -1.55816   1.10473  -0.54733  -0.06159   0.66471  -1.20527   1.63239  -1.90588   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E47      2.00000  -1.93959   1.76202  -1.47802   1.10473  -0.66471   0.18454   0.30678  -0.77957   1.20527  -1.55816   1.81693  -1.96595   1.99621  -1.90588   1.70043  -1.39227   1.00000  -0.54733   0.06159   0.42787  -0.89148   1.30124  -1.63239   1.86494  -1.98484   1.98484  -1.86494   1.63239  -1.30124   0.89148  -0.42787  -0.06159   0.54733  -1.00000   1.39227  -1.70043   1.90588  -1.99621   1.96595  -1.81693   1.55816  -1.20527   0.77957  -0.30678  -0.18454   0.66471  -1.10473   1.47802  -1.76202   1.93959  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E48      2.00000  -1.96595   1.86494  -1.70043   1.47802  -1.20527   0.89148  -0.54733   0.18454   0.18454  -0.54733   0.89148  -1.20527   1.47802  -1.70043   1.86494  -1.96595   2.00000  -1.96595   1.86494  -1.70043   1.47802  -1.20527   0.89148  -0.54733   0.18454   0.18454  -0.54733   0.89148  -1.20527   1.47802  -1.70043   1.86494  -1.96595   2.00000  -1.96595   1.86494  -1.70043   1.47802  -1.20527   0.89148  -0.54733   0.18454   0.18454  -0.54733   0.89148  -1.20527   1.47802  -1.70043   1.86494  -1.96595   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E49      2.00000  -1.98484   1.93959  -1.86494   1.76202  -1.63239   1.47802  -1.30124   1.10473  -0.89148   0.66471  -0.42787   0.18454   0.06159  -0.30678   0.54733  -0.77957   1.00000  -1.20527   1.39227  -1.55816   1.70043  -1.81693   1.90588  -1.96595   1.99621  -1.99621   1.96595  -1.90588   1.81693  -1.70043   1.55816  -1.39227   1.20527  -1.00000   0.77957  -0.54733   0.30678  -0.06159  -0.18454   0.42787  -0.66471   0.89148  -1.10473   1.30124  -1.47802   1.63239  -1.76202   1.86494  -1.93959   1.98484  -2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............
E50      2.00000  -1.99621   1.98484  -1.96595   1.93959  -1.90588   1.86494  -1.81693   1.76202  -1.70043   1.63239  -1.55816   1.47802  -1.39227   1.30124  -1.20527   1.10473  -1.00000   0.89148  -0.77957   0.66471  -0.54733   0.42787  -0.30678   0.18454  -0.06159  -0.06159   0.18454  -0.30678   0.42787  -0.54733   0.66471  -0.77957   0.89148  -1.00000   1.10473  -1.20527   1.30124  -1.39227   1.47802  -1.55816   1.63239  -1.70043   1.76202  -1.81693   1.86494  -1.90588   1.93959  -1.96595   1.98484  -1.99621   2.00000   0.00000   0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.996206657474 = 2*cos(2*π/102) = 2*cos(π/51) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8
                               1.984841019344 = 2*cos(4*π/102) = 2*cos(2*π/51) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8
                               1.965946199368 = 2*cos(6*π/102) = 2*cos(π/17) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8
                               1.939593872070 = 2*cos(8*π/102) = 2*cos(4*π/51) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8
                               1.905884000854 = 2*cos(10*π/102) = 2*cos(5*π/51) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8
                               1.864944458809 = 2*cos(12*π/102) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8
                               1.816930543639 = 2*cos(14*π/102) = 2*cos(7*π/51) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8
                               1.762024388572 = 2*cos(16*π/102) = 2*cos(8*π/51) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8
                               1.700434271459 = 2*cos(18*π/102) = 2*cos(3*π/17) = (1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8
                               1.632393824712 = 2*cos(20*π/102) = 2*cos(10*π/51) = (1−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17/8
                               1.558161149051 = 2*cos(22*π/102) = 2*cos(11*π/51) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 + √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8
                               1.478017834441 = 2*cos(24*π/102) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8
                               1.392267891926 = 2*cos(26*π/102) = 2*cos(13*π/51) = (−1−√17+√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17/8
                               1.301236600408 = 2*cos(28*π/102) = 2*cos(14*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8
                               1.205269272759 = 2*cos(30*π/102) = 2*cos(5*π/17) = (1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8
                               1.104729945921 = 2*cos(32*π/102) = 2*cos(16*π/51) = (1+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17)/16 + √6*√17+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17/8
                               0.891476711553 = 2*cos(36*π/102) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8
                               0.779571746585 = 2*cos(38*π/102) = 2*cos(19*π/51) = (−1−√17−√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17/8
                               0.664709598959 = 2*cos(40*π/102) = 2*cos(20*π/51) = (1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 − √6*√17−√17−√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17/8
                               0.547325980144 = 2*cos(42*π/102) = 2*cos(7*π/17) = (1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8
                               0.427866166413 = 2*cos(44*π/102) = 2*cos(22*π/51) = (1−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17)/16 + √6*√17−√17−√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17/8
                               0.306783309757 = 2*cos(46*π/102) = 2*cos(23*π/51) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/16 − √6*√17−√17+√34−2*√17−2*√17+3*√17+√34−2*√17+2*√34+2*√17/8
                               0.184536718927 = 2*cos(48*π/102) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8
                               0.061590117112 = 2*cos(50*π/102) = 2*cos(25*π/51) = (−1−√17−√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/16 + √6*√17+√17−√34+2*√17−2*√17−3*√17−√34+2*√17+2*√34−2*√17/8



 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 C102v point group is 204, and the order of the principal axis (C102) is 102. The group has 54 irreducible representations.

    β  The C102v point group is isomorphic to D51d, D51h and D102.

    γ  The C102v point group is generated by two symmetry elements, C102 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 C102v 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.

    θ  The point group corresponds to a constructible polygon, as the order of the principal axis is a product of any number
       of different Fermat primes (3,5,17,257,65537) times an arbitrary power of two. Therefore, all characters have an
       algebraic degree which is a power of two and can be expressed as radicals involving only square roots and integer numbers.

    ι  That a regular 17-gon can be constructed with compass and ruler was unknown to mathematicians until Gauss proved it in 1796.
       The first actual construction was performed thirty years later by Johannes Erchinger in 1825.
       The regular 51-gon can be derived from the regular 17-gon by overlaying it with a equilateral triangle.
       Further halving of angles yields regular polygons of order 102,204,408 etc.

This Character Table for the C102v point group was created by Gernot Katzer.

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