Character table for the C76v point group

C76v    E        2 C76    2 C38    2 C76^3  2 C19    2 C76^5  2 C38^3  2 C76^7  2 C19^2  2 C76^9  2 C38^5  2 C76^11 2 C19^3  2 C76^13 2 C38^7  2 C76^15 2 C19^4  2 C76^17 2 C38^9  2 C4     2 C19^5  2 C76^21 2 C38^11 2 C76^23 2 C19^6  2 C76^25 2 C38^13 2 C76^27 2 C19^7  2 C76^29 2 C38^15 2 C76^31 2 C19^8  2 C76^33 2 C38^17 2 C76^35 2 C19^9  2 C76^37 C2       38 sv    38 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     ... ..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     ..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     ... ... ..... ....... ......... ........... .............
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     ... ... ..... ....... ......... ........... .............
E1      2.00000  1.99317  1.97272  1.93880  1.89163  1.83155  1.75895  1.67433  1.57828  1.47145  1.35456  1.22843  1.09390  0.95189  0.80339  0.64940  0.49097  0.32919  0.16516  0.00000 -0.16516 -0.32919 -0.49097 -0.64940 -0.80339 -0.95189 -1.09390 -1.22843 -1.35456 -1.47145 -1.57828 -1.67433 -1.75895 -1.83155 -1.89163 -1.93880 -1.97272 -1.99317 -2.00000  0.00000  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.97272  1.89163  1.75895  1.57828  1.35456  1.09390  0.80339  0.49097  0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 -2.00000 -1.97272 -1.89163 -1.75895 -1.57828 -1.35456 -1.09390 -0.80339 -0.49097 -0.16516  0.16516  0.49097  0.80339  1.09390  1.35456  1.57828  1.75895  1.89163  1.97272  2.00000  0.00000  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.93880  1.75895  1.47145  1.09390  0.64940  0.16516 -0.32919 -0.80339 -1.22843 -1.57828 -1.83155 -1.97272 -1.99317 -1.89163 -1.67433 -1.35456 -0.95189 -0.49097  0.00000  0.49097  0.95189  1.35456  1.67433  1.89163  1.99317  1.97272  1.83155  1.57828  1.22843  0.80339  0.32919 -0.16516 -0.64940 -1.09390 -1.47145 -1.75895 -1.93880 -2.00000  0.00000  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.89163  1.57828  1.09390  0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516  0.49097  1.09390  1.57828  1.89163  2.00000  1.89163  1.57828  1.09390  0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516  0.49097  1.09390  1.57828  1.89163  2.00000  0.00000  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.83155  1.35456  0.64940 -0.16516 -0.95189 -1.57828 -1.93880 -1.97272 -1.67433 -1.09390 -0.32919  0.49097  1.22843  1.75895  1.99317  1.89163  1.47145  0.80339  0.00000 -0.80339 -1.47145 -1.89163 -1.99317 -1.75895 -1.22843 -0.49097  0.32919  1.09390  1.67433  1.97272  1.93880  1.57828  0.95189  0.16516 -0.64940 -1.35456 -1.83155 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.75895  1.09390  0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097  0.49097  1.35456  1.89163  1.97272  1.57828  0.80339 -0.16516 -1.09390 -1.75895 -2.00000 -1.75895 -1.09390 -0.16516  0.80339  1.57828  1.97272  1.89163  1.35456  0.49097 -0.49097 -1.35456 -1.89163 -1.97272 -1.57828 -0.80339  0.16516  1.09390  1.75895  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.67433  0.80339 -0.32919 -1.35456 -1.93880 -1.89163 -1.22843 -0.16516  0.95189  1.75895  1.99317  1.57828  0.64940 -0.49097 -1.47145 -1.97272 -1.83155 -1.09390  0.00000  1.09390  1.83155  1.97272  1.47145  0.49097 -0.64940 -1.57828 -1.99317 -1.75895 -0.95189  0.16516  1.22843  1.89163  1.93880  1.35456  0.32919 -0.80339 -1.67433 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.57828  0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516  1.09390  1.89163  1.89163  1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339  0.49097  1.57828  2.00000  1.57828  0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516  1.09390  1.89163  1.89163  1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339  0.49097  1.57828  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.47145  0.16516 -1.22843 -1.97272 -1.67433 -0.49097  0.95189  1.89163  1.83155  0.80339 -0.64940 -1.75895 -1.93880 -1.09390  0.32919  1.57828  1.99317  1.35456  0.00000 -1.35456 -1.99317 -1.57828 -0.32919  1.09390  1.93880  1.75895  0.64940 -0.80339 -1.83155 -1.89163 -0.95189  0.49097  1.67433  1.97272  1.22843 -0.16516 -1.47145 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.35456 -0.16516 -1.57828 -1.97272 -1.09390  0.49097  1.75895  1.89163  0.80339 -0.80339 -1.89163 -1.75895 -0.49097  1.09390  1.97272  1.57828  0.16516 -1.35456 -2.00000 -1.35456  0.16516  1.57828  1.97272  1.09390 -0.49097 -1.75895 -1.89163 -0.80339  0.80339  1.89163  1.75895  0.49097 -1.09390 -1.97272 -1.57828 -0.16516  1.35456  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.22843 -0.49097 -1.83155 -1.75895 -0.32919  1.35456  1.99317  1.09390 -0.64940 -1.89163 -1.67433 -0.16516  1.47145  1.97272  0.95189 -0.80339 -1.93880 -1.57828  0.00000  1.57828  1.93880  0.80339 -0.95189 -1.97272 -1.47145  0.16516  1.67433  1.89163  0.64940 -1.09390 -1.99317 -1.35456  0.32919  1.75895  1.83155  0.49097 -1.22843 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  1.09390 -0.80339 -1.97272 -1.35456  0.49097  1.89163  1.57828 -0.16516 -1.75895 -1.75895 -0.16516  1.57828  1.89163  0.49097 -1.35456 -1.97272 -0.80339  1.09390  2.00000  1.09390 -0.80339 -1.97272 -1.35456  0.49097  1.89163  1.57828 -0.16516 -1.75895 -1.75895 -0.16516  1.57828  1.89163  0.49097 -1.35456 -1.97272 -0.80339  1.09390  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  0.95189 -1.09390 -1.99317 -0.80339  1.22843  1.97272  0.64940 -1.35456 -1.93880 -0.49097  1.47145  1.89163  0.32919 -1.57828 -1.83155 -0.16516  1.67433  1.75895  0.00000 -1.75895 -1.67433  0.16516  1.83155  1.57828 -0.32919 -1.89163 -1.47145  0.49097  1.93880  1.35456 -0.64940 -1.97272 -1.22843  0.80339  1.99317  1.09390 -0.95189 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  0.80339 -1.35456 -1.89163 -0.16516  1.75895  1.57828 -0.49097 -1.97272 -1.09390  1.09390  1.97272  0.49097 -1.57828 -1.75895  0.16516  1.89163  1.35456 -0.80339 -2.00000 -0.80339  1.35456  1.89163  0.16516 -1.75895 -1.57828  0.49097  1.97272  1.09390 -1.09390 -1.97272 -0.49097  1.57828  1.75895 -0.16516 -1.89163 -1.35456  0.80339  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  0.64940 -1.57828 -1.67433  0.49097  1.99317  0.80339 -1.47145 -1.75895  0.32919  1.97272  0.95189 -1.35456 -1.83155  0.16516  1.93880  1.09390 -1.22843 -1.89163  0.00000  1.89163  1.22843 -1.09390 -1.93880 -0.16516  1.83155  1.35456 -0.95189 -1.97272 -0.32919  1.75895  1.47145 -0.80339 -1.99317 -0.49097  1.67433  1.57828 -0.64940 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  0.49097 -1.75895 -1.35456  1.09390  1.89163 -0.16516 -1.97272 -0.80339  1.57828  1.57828 -0.80339 -1.97272 -0.16516  1.89163  1.09390 -1.35456 -1.75895  0.49097  2.00000  0.49097 -1.75895 -1.35456  1.09390  1.89163 -0.16516 -1.97272 -0.80339  1.57828  1.57828 -0.80339 -1.97272 -0.16516  1.89163  1.09390 -1.35456 -1.75895  0.49097  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.32919 -1.89163 -0.95189  1.57828  1.47145 -1.09390 -1.83155  0.49097  1.99317  0.16516 -1.93880 -0.80339  1.67433  1.35456 -1.22843 -1.75895  0.64940  1.97272  0.00000 -1.97272 -0.64940  1.75895  1.22843 -1.35456 -1.67433  0.80339  1.93880 -0.16516 -1.99317 -0.49097  1.83155  1.09390 -1.47145 -1.57828  0.95189  1.89163 -0.32919 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000  0.16516 -1.97272 -0.49097  1.89163  0.80339 -1.75895 -1.09390  1.57828  1.35456 -1.35456 -1.57828  1.09390  1.75895 -0.80339 -1.89163  0.49097  1.97272 -0.16516 -2.00000 -0.16516  1.97272  0.49097 -1.89163 -0.80339  1.75895  1.09390 -1.57828 -1.35456  1.35456  1.57828 -1.09390 -1.75895  0.80339  1.89163 -0.49097 -1.97272  0.16516  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  2.00000  0.00000 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000 -0.16516 -1.97272  0.49097  1.89163 -0.80339 -1.75895  1.09390  1.57828 -1.35456 -1.35456  1.57828  1.09390 -1.75895 -0.80339  1.89163  0.49097 -1.97272 -0.16516  2.00000 -0.16516 -1.97272  0.49097  1.89163 -0.80339 -1.75895  1.09390  1.57828 -1.35456 -1.35456  1.57828  1.09390 -1.75895 -0.80339  1.89163  0.49097 -1.97272 -0.16516  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000 -0.32919 -1.89163  0.95189  1.57828 -1.47145 -1.09390  1.83155  0.49097 -1.99317  0.16516  1.93880 -0.80339 -1.67433  1.35456  1.22843 -1.75895 -0.64940  1.97272  0.00000 -1.97272  0.64940  1.75895 -1.22843 -1.35456  1.67433  0.80339 -1.93880 -0.16516  1.99317 -0.49097 -1.83155  1.09390  1.47145 -1.57828 -0.95189  1.89163  0.32919 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000 -0.49097 -1.75895  1.35456  1.09390 -1.89163 -0.16516  1.97272 -0.80339 -1.57828  1.57828  0.80339 -1.97272  0.16516  1.89163 -1.09390 -1.35456  1.75895  0.49097 -2.00000  0.49097  1.75895 -1.35456 -1.09390  1.89163  0.16516 -1.97272  0.80339  1.57828 -1.57828 -0.80339  1.97272 -0.16516 -1.89163  1.09390  1.35456 -1.75895 -0.49097  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000 -0.64940 -1.57828  1.67433  0.49097 -1.99317  0.80339  1.47145 -1.75895 -0.32919  1.97272 -0.95189 -1.35456  1.83155  0.16516 -1.93880  1.09390  1.22843 -1.89163  0.00000  1.89163 -1.22843 -1.09390  1.93880 -0.16516 -1.83155  1.35456  0.95189 -1.97272  0.32919  1.75895 -1.47145 -0.80339  1.99317 -0.49097 -1.67433  1.57828  0.64940 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000 -0.80339 -1.35456  1.89163 -0.16516 -1.75895  1.57828  0.49097 -1.97272  1.09390  1.09390 -1.97272  0.49097  1.57828 -1.75895 -0.16516  1.89163 -1.35456 -0.80339  2.00000 -0.80339 -1.35456  1.89163 -0.16516 -1.75895  1.57828  0.49097 -1.97272  1.09390  1.09390 -1.97272  0.49097  1.57828 -1.75895 -0.16516  1.89163 -1.35456 -0.80339  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -0.95189 -1.09390  1.99317 -0.80339 -1.22843  1.97272 -0.64940 -1.35456  1.93880 -0.49097 -1.47145  1.89163 -0.32919 -1.57828  1.83155 -0.16516 -1.67433  1.75895  0.00000 -1.75895  1.67433  0.16516 -1.83155  1.57828  0.32919 -1.89163  1.47145  0.49097 -1.93880  1.35456  0.64940 -1.97272  1.22843  0.80339 -1.99317  1.09390  0.95189 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -1.09390 -0.80339  1.97272 -1.35456 -0.49097  1.89163 -1.57828 -0.16516  1.75895 -1.75895  0.16516  1.57828 -1.89163  0.49097  1.35456 -1.97272  0.80339  1.09390 -2.00000  1.09390  0.80339 -1.97272  1.35456  0.49097 -1.89163  1.57828  0.16516 -1.75895  1.75895 -0.16516 -1.57828  1.89163 -0.49097 -1.35456  1.97272 -0.80339 -1.09390  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -1.22843 -0.49097  1.83155 -1.75895  0.32919  1.35456 -1.99317  1.09390  0.64940 -1.89163  1.67433 -0.16516 -1.47145  1.97272 -0.95189 -0.80339  1.93880 -1.57828  0.00000  1.57828 -1.93880  0.80339  0.95189 -1.97272  1.47145  0.16516 -1.67433  1.89163 -0.64940 -1.09390  1.99317 -1.35456 -0.32919  1.75895 -1.83155  0.49097  1.22843 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -1.35456 -0.16516  1.57828 -1.97272  1.09390  0.49097 -1.75895  1.89163 -0.80339 -0.80339  1.89163 -1.75895  0.49097  1.09390 -1.97272  1.57828 -0.16516 -1.35456  2.00000 -1.35456 -0.16516  1.57828 -1.97272  1.09390  0.49097 -1.75895  1.89163 -0.80339 -0.80339  1.89163 -1.75895  0.49097  1.09390 -1.97272  1.57828 -0.16516 -1.35456  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -1.47145  0.16516  1.22843 -1.97272  1.67433 -0.49097 -0.95189  1.89163 -1.83155  0.80339  0.64940 -1.75895  1.93880 -1.09390 -0.32919  1.57828 -1.99317  1.35456  0.00000 -1.35456  1.99317 -1.57828  0.32919  1.09390 -1.93880  1.75895 -0.64940 -0.80339  1.83155 -1.89163  0.95189  0.49097 -1.67433  1.97272 -1.22843 -0.16516  1.47145 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -1.57828  0.49097  0.80339 -1.75895  1.97272 -1.35456  0.16516  1.09390 -1.89163  1.89163 -1.09390 -0.16516  1.35456 -1.97272  1.75895 -0.80339 -0.49097  1.57828 -2.00000  1.57828 -0.49097 -0.80339  1.75895 -1.97272  1.35456 -0.16516 -1.09390  1.89163 -1.89163  1.09390  0.16516 -1.35456  1.97272 -1.75895  0.80339  0.49097 -1.57828  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -1.67433  0.80339  0.32919 -1.35456  1.93880 -1.89163  1.22843 -0.16516 -0.95189  1.75895 -1.99317  1.57828 -0.64940 -0.49097  1.47145 -1.97272  1.83155 -1.09390  0.00000  1.09390 -1.83155  1.97272 -1.47145  0.49097  0.64940 -1.57828  1.99317 -1.75895  0.95189  0.16516 -1.22843  1.89163 -1.93880  1.35456 -0.32919 -0.80339  1.67433 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -1.75895  1.09390 -0.16516 -0.80339  1.57828 -1.97272  1.89163 -1.35456  0.49097  0.49097 -1.35456  1.89163 -1.97272  1.57828 -0.80339 -0.16516  1.09390 -1.75895  2.00000 -1.75895  1.09390 -0.16516 -0.80339  1.57828 -1.97272  1.89163 -1.35456  0.49097  0.49097 -1.35456  1.89163 -1.97272  1.57828 -0.80339 -0.16516  1.09390 -1.75895  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.83155  1.35456 -0.64940 -0.16516  0.95189 -1.57828  1.93880 -1.97272  1.67433 -1.09390  0.32919  0.49097 -1.22843  1.75895 -1.99317  1.89163 -1.47145  0.80339  0.00000 -0.80339  1.47145 -1.89163  1.99317 -1.75895  1.22843 -0.49097 -0.32919  1.09390 -1.67433  1.97272 -1.93880  1.57828 -0.95189  0.16516  0.64940 -1.35456  1.83155 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.89163  1.57828 -1.09390  0.49097  0.16516 -0.80339  1.35456 -1.75895  1.97272 -1.97272  1.75895 -1.35456  0.80339 -0.16516 -0.49097  1.09390 -1.57828  1.89163 -2.00000  1.89163 -1.57828  1.09390 -0.49097 -0.16516  0.80339 -1.35456  1.75895 -1.97272  1.97272 -1.75895  1.35456 -0.80339  0.16516  0.49097 -1.09390  1.57828 -1.89163  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.93880  1.75895 -1.47145  1.09390 -0.64940  0.16516  0.32919 -0.80339  1.22843 -1.57828  1.83155 -1.97272  1.99317 -1.89163  1.67433 -1.35456  0.95189 -0.49097  0.00000  0.49097 -0.95189  1.35456 -1.67433  1.89163 -1.99317  1.97272 -1.83155  1.57828 -1.22843  0.80339 -0.32919 -0.16516  0.64940 -1.09390  1.47145 -1.75895  1.93880 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E36     2.00000 -1.97272  1.89163 -1.75895  1.57828 -1.35456  1.09390 -0.80339  0.49097 -0.16516 -0.16516  0.49097 -0.80339  1.09390 -1.35456  1.57828 -1.75895  1.89163 -1.97272  2.00000 -1.97272  1.89163 -1.75895  1.57828 -1.35456  1.09390 -0.80339  0.49097 -0.16516 -0.16516  0.49097 -0.80339  1.09390 -1.35456  1.57828 -1.75895  1.89163 -1.97272  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E37     2.00000 -1.99317  1.97272 -1.93880  1.89163 -1.83155  1.75895 -1.67433  1.57828 -1.47145  1.35456 -1.22843  1.09390 -0.95189  0.80339 -0.64940  0.49097 -0.32919  0.16516  0.00000 -0.16516  0.32919 -0.49097  0.64940 -0.80339  0.95189 -1.09390  1.22843 -1.35456  1.47145 -1.57828  1.67433 -1.75895  1.83155 -1.89163  1.93880 -1.97272  1.99317 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.993168986013 = 2*cos(2*π/76) = 2*cos(π/38)
                               1.972722606805 = 2*cos(4*π/76) = 2*cos(π/19)
                               1.938800531879 = 2*cos(6*π/76) = 2*cos(3*π/38)
                               1.891634483401 = 2*cos(8*π/76) = 2*cos(2*π/19)
                               1.831546653310 = 2*cos(10*π/76) = 2*cos(5*π/38)
                               1.758947502413 = 2*cos(12*π/76) = 2*cos(3*π/19)
                               1.674332956525 = 2*cos(14*π/76) = 2*cos(7*π/38)
                               1.578281018793 = 2*cos(16*π/76) = 2*cos(4*π/19)
                               1.471447821346 = 2*cos(18*π/76) = 2*cos(9*π/38)
                               1.354563143251 = 2*cos(20*π/76) = 2*cos(5*π/19)
                               1.228425425379 = 2*cos(22*π/76) = 2*cos(11*π/38)
                               1.093896316245 = 2*cos(24*π/76) = 2*cos(6*π/19)
                               0.951894786074 = 2*cos(26*π/76) = 2*cos(13*π/38)
                               0.803390849306 = 2*cos(28*π/76) = 2*cos(7*π/19)
                               0.649398938409 = 2*cos(30*π/76) = 2*cos(15*π/38)
                               0.490970974282 = 2*cos(32*π/76) = 2*cos(8*π/19)
                               0.329189180561 = 2*cos(34*π/76) = 2*cos(17*π/38)
                               0.165158690945 = 2*cos(36*π/76) = 2*cos(9*π/19)



 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 C76v point group is 152, and the order of the principal axis (C76) is 76. The group has 41 irreducible representations.

    β  The C76v point group is isomorphic to D38d and D76.

    γ  The C76v point group is generated by two symmetry elements, C76 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 contains both the xz and the yz planes.

    ε  The lowest nonvanishing multipole moment in C76v 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 polygon inconstructible by the classical means of ruler and compass. Yet it becomes constructible
       if angle trisection is allowed, e.g., with neusis construction or origami. This is because the order of the principal axis is given
       by a product of any number of different Pierpont primes (...,5,7,13,17,19,37,73,97,109,163,...) times arbitrary powers of two and three.
       All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.

This Character Table for the C76v point group was created by Gernot Katzer.

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