Character table for the C91 point group

C91     E        2 C91    2 C91^2  2 C91^3  2 C91^4  2 C91^5  2 C91^6  2 C13    2 C91^8  2 C91^9  2 C91^10 2 C91^11 2 C91^12 2 C7     2 C13^2  2 C91^15 2 C91^16 2 C91^17 2 C91^18 2 C91^19 2 C91^20 2 C13^3  2 C91^22 2 C91^23 2 C91^24 2 C91^25 2 C7^2   2 C91^27 2 C13^4  2 C91^29 2 C91^30 2 C91^31 2 C91^32 2 C91^33 2 C91^34 2 C13^5  2 C91^36 2 C91^37 2 C91^38 2 C7^3   2 C91^40 2 C91^41 2 C13^6  2 C91^43 2 C91^44 2 C91^45    <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     ..T ..T ....T ......T ........T ..........T ............T
E1  *   2.00000  1.99523  1.98096  1.95725  1.92421  1.88200  1.83082  1.77091  1.70257  1.62611  1.54191  1.45035  1.35189  1.24698  1.13613  1.01987  0.89874  0.77333  0.64424  0.51208  0.37748  0.24107  0.10352 -0.03452 -0.17240 -0.30946 -0.44504 -0.57850 -0.70921 -0.83654 -0.95987 -1.07864 -1.19226 -1.30021 -1.40196 -1.49702 -1.58495 -1.66533 -1.73778 -1.80194 -1.85751 -1.90424 -1.94188 -1.97028 -1.98928 -1.99881     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2  *   2.00000  1.98096  1.92421  1.83082  1.70257  1.54191  1.35189  1.13613  0.89874  0.64424  0.37748  0.10352 -0.17240 -0.44504 -0.70921 -0.95987 -1.19226 -1.40196 -1.58495 -1.73778 -1.85751 -1.94188 -1.98928 -1.99881 -1.97028 -1.90424 -1.80194 -1.66533 -1.49702 -1.30021 -1.07864 -0.83654 -0.57850 -0.30946 -0.03452  0.24107  0.51208  0.77333  1.01987  1.24698  1.45035  1.62611  1.77091  1.88200  1.95725  1.99523     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3  *   2.00000  1.95725  1.83082  1.62611  1.35189  1.01987  0.64424  0.24107 -0.17240 -0.57850 -0.95987 -1.30021 -1.58495 -1.80194 -1.94188 -1.99881 -1.97028 -1.85751 -1.66533 -1.40196 -1.07864 -0.70921 -0.30946  0.10352  0.51208  0.89874  1.24698  1.54191  1.77091  1.92421  1.99523  1.98096  1.88200  1.70257  1.45035  1.13613  0.77333  0.37748 -0.03452 -0.44504 -0.83654 -1.19226 -1.49702 -1.73778 -1.90424 -1.98928     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4  *   2.00000  1.92421  1.70257  1.35189  0.89874  0.37748 -0.17240 -0.70921 -1.19226 -1.58495 -1.85751 -1.98928 -1.97028 -1.80194 -1.49702 -1.07864 -0.57850 -0.03452  0.51208  1.01987  1.45035  1.77091  1.95725  1.99523  1.88200  1.62611  1.24698  0.77333  0.24107 -0.30946 -0.83654 -1.30021 -1.66533 -1.90424 -1.99881 -1.94188 -1.73778 -1.40196 -0.95987 -0.44504  0.10352  0.64424  1.13613  1.54191  1.83082  1.98096     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5  *   2.00000  1.88200  1.54191  1.01987  0.37748 -0.30946 -0.95987 -1.49702 -1.85751 -1.99881 -1.90424 -1.58495 -1.07864 -0.44504  0.24107  0.89874  1.45035  1.83082  1.99523  1.92421  1.62611  1.13613  0.51208 -0.17240 -0.83654 -1.40196 -1.80194 -1.98928 -1.94188 -1.66533 -1.19226 -0.57850  0.10352  0.77333  1.35189  1.77091  1.98096  1.95725  1.70257  1.24698  0.64424 -0.03452 -0.70921 -1.30021 -1.73778 -1.97028     ... ... ..... ....... ......... TT......... ..TT.........
E6  *   2.00000  1.83082  1.35189  0.64424 -0.17240 -0.95987 -1.58495 -1.94188 -1.97028 -1.66533 -1.07864 -0.30946  0.51208  1.24698  1.77091  1.99523  1.88200  1.45035  0.77333 -0.03452 -0.83654 -1.49702 -1.90424 -1.98928 -1.73778 -1.19226 -0.44504  0.37748  1.13613  1.70257  1.98096  1.92421  1.54191  0.89874  0.10352 -0.70921 -1.40196 -1.85751 -1.99881 -1.80194 -1.30021 -0.57850  0.24107  1.01987  1.62611  1.95725     ... ... ..... ....... ......... ........... TT...........
E7  *   2.00000  1.77091  1.13613  0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921  0.24107  1.13613  1.77091  2.00000  1.77091  1.13613  0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921  0.24107  1.13613  1.77091  2.00000  1.77091  1.13613  0.24107 -0.70921 -1.49702 -1.94188 -1.94188 -1.49702 -0.70921  0.24107  1.13613  1.77091  2.00000  1.77091  1.13613  0.24107 -0.70921 -1.49702 -1.94188     ... ... ..... ....... ......... ........... .............
E8  *   2.00000  1.70257  0.89874 -0.17240 -1.19226 -1.85751 -1.97028 -1.49702 -0.57850  0.51208  1.45035  1.95725  1.88200  1.24698  0.24107 -0.83654 -1.66533 -1.99881 -1.73778 -0.95987  0.10352  1.13613  1.83082  1.98096  1.54191  0.64424 -0.44504 -1.40196 -1.94188 -1.90424 -1.30021 -0.30946  0.77333  1.62611  1.99523  1.77091  1.01987 -0.03452 -1.07864 -1.80194 -1.98928 -1.58495 -0.70921  0.37748  1.35189  1.92421     ... ... ..... ....... ......... ........... .............
E9  *   2.00000  1.62611  0.64424 -0.57850 -1.58495 -1.99881 -1.66533 -0.70921  0.51208  1.54191  1.99523  1.70257  0.77333 -0.44504 -1.49702 -1.98928 -1.73778 -0.83654  0.37748  1.45035  1.98096  1.77091  0.89874 -0.30946 -1.40196 -1.97028 -1.80194 -0.95987  0.24107  1.35189  1.95725  1.83082  1.01987 -0.17240 -1.30021 -1.94188 -1.85751 -1.07864  0.10352  1.24698  1.92421  1.88200  1.13613 -0.03452 -1.19226 -1.90424     ... ... ..... ....... ......... ........... .............
E10 *   2.00000  1.54191  0.37748 -0.95987 -1.85751 -1.90424 -1.07864  0.24107  1.45035  1.99523  1.62611  0.51208 -0.83654 -1.80194 -1.94188 -1.19226  0.10352  1.35189  1.98096  1.70257  0.64424 -0.70921 -1.73778 -1.97028 -1.30021 -0.03452  1.24698  1.95725  1.77091  0.77333 -0.57850 -1.66533 -1.98928 -1.40196 -0.17240  1.13613  1.92421  1.83082  0.89874 -0.44504 -1.58495 -1.99881 -1.49702 -0.30946  1.01987  1.88200     ... ... ..... ....... ......... ........... .............
E11 *   2.00000  1.45035  0.10352 -1.30021 -1.98928 -1.58495 -0.30946  1.13613  1.95725  1.70257  0.51208 -0.95987 -1.90424 -1.80194 -0.70921  0.77333  1.83082  1.88200  0.89874 -0.57850 -1.73778 -1.94188 -1.07864  0.37748  1.62611  1.98096  1.24698 -0.17240 -1.49702 -1.99881 -1.40196 -0.03452  1.35189  1.99523  1.54191  0.24107 -1.19226 -1.97028 -1.66533 -0.44504  1.01987  1.92421  1.77091  0.64424 -0.83654 -1.85751     ... ... ..... ....... ......... ........... .............
E12 *   2.00000  1.35189 -0.17240 -1.58495 -1.97028 -1.07864  0.51208  1.77091  1.88200  0.77333 -0.83654 -1.90424 -1.73778 -0.44504  1.13613  1.98096  1.54191  0.10352 -1.40196 -1.99881 -1.30021  0.24107  1.62611  1.95725  1.01987 -0.57850 -1.80194 -1.85751 -0.70921  0.89874  1.92421  1.70257  0.37748 -1.19226 -1.98928 -1.49702 -0.03452  1.45035  1.99523  1.24698 -0.30946 -1.66533 -1.94188 -0.95987  0.64424  1.83082     ... ... ..... ....... ......... ........... .............
E13 *   2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194 -1.80194 -0.44504  1.24698  2.00000  1.24698 -0.44504 -1.80194     ... ... ..... ....... ......... ........... .............
E14 *   2.00000  1.13613 -0.70921 -1.94188 -1.49702  0.24107  1.77091  1.77091  0.24107 -1.49702 -1.94188 -0.70921  1.13613  2.00000  1.13613 -0.70921 -1.94188 -1.49702  0.24107  1.77091  1.77091  0.24107 -1.49702 -1.94188 -0.70921  1.13613  2.00000  1.13613 -0.70921 -1.94188 -1.49702  0.24107  1.77091  1.77091  0.24107 -1.49702 -1.94188 -0.70921  1.13613  2.00000  1.13613 -0.70921 -1.94188 -1.49702  0.24107  1.77091     ... ... ..... ....... ......... ........... .............
E15 *   2.00000  1.01987 -0.95987 -1.99881 -1.07864  0.89874  1.99523  1.13613 -0.83654 -1.98928 -1.19226  0.77333  1.98096  1.24698 -0.70921 -1.97028 -1.30021  0.64424  1.95725  1.35189 -0.57850 -1.94188 -1.40196  0.51208  1.92421  1.45035 -0.44504 -1.90424 -1.49702  0.37748  1.88200  1.54191 -0.30946 -1.85751 -1.58495  0.24107  1.83082  1.62611 -0.17240 -1.80194 -1.66533  0.10352  1.77091  1.70257 -0.03452 -1.73778     ... ... ..... ....... ......... ........... .............
E16 *   2.00000  0.89874 -1.19226 -1.97028 -0.57850  1.45035  1.88200  0.24107 -1.66533 -1.73778  0.10352  1.83082  1.54191 -0.44504 -1.94188 -1.30021  0.77333  1.99523  1.01987 -1.07864 -1.98928 -0.70921  1.35189  1.92421  0.37748 -1.58495 -1.80194 -0.03452  1.77091  1.62611 -0.30946 -1.90424 -1.40196  0.64424  1.98096  1.13613 -0.95987 -1.99881 -0.83654  1.24698  1.95725  0.51208 -1.49702 -1.85751 -0.17240  1.70257     ... ... ..... ....... ......... ........... .............
E17 *   2.00000  0.77333 -1.40196 -1.85751 -0.03452  1.83082  1.45035 -0.70921 -1.99881 -0.83654  1.35189  1.88200  0.10352 -1.80194 -1.49702  0.64424  1.99523  0.89874 -1.30021 -1.90424 -0.17240  1.77091  1.54191 -0.57850 -1.98928 -0.95987  1.24698  1.92421  0.24107 -1.73778 -1.58495  0.51208  1.98096  1.01987 -1.19226 -1.94188 -0.30946  1.70257  1.62611 -0.44504 -1.97028 -1.07864  1.13613  1.95725  0.37748 -1.66533     ... ... ..... ....... ......... ........... .............
E18 *   2.00000  0.64424 -1.58495 -1.66533  0.51208  1.99523  0.77333 -1.49702 -1.73778  0.37748  1.98096  0.89874 -1.40196 -1.80194  0.24107  1.95725  1.01987 -1.30021 -1.85751  0.10352  1.92421  1.13613 -1.19226 -1.90424 -0.03452  1.88200  1.24698 -1.07864 -1.94188 -0.17240  1.83082  1.35189 -0.95987 -1.97028 -0.30946  1.77091  1.45035 -0.83654 -1.98928 -0.44504  1.70257  1.54191 -0.70921 -1.99881 -0.57850  1.62611     ... ... ..... ....... ......... ........... .............
E19 *   2.00000  0.51208 -1.73778 -1.40196  1.01987  1.92421 -0.03452 -1.94188 -0.95987  1.45035  1.70257 -0.57850 -1.99881 -0.44504  1.77091  1.35189 -1.07864 -1.90424  0.10352  1.95725  0.89874 -1.49702 -1.66533  0.64424  1.99523  0.37748 -1.80194 -1.30021  1.13613  1.88200 -0.17240 -1.97028 -0.83654  1.54191  1.62611 -0.70921 -1.98928 -0.30946  1.83082  1.24698 -1.19226 -1.85751  0.24107  1.98096  0.77333 -1.58495     ... ... ..... ....... ......... ........... .............
E20 *   2.00000  0.37748 -1.85751 -1.07864  1.45035  1.62611 -0.83654 -1.94188  0.10352  1.98096  0.64424 -1.73778 -1.30021  1.24698  1.77091 -0.57850 -1.98928 -0.17240  1.92421  0.89874 -1.58495 -1.49702  1.01987  1.88200 -0.30946 -1.99881 -0.44504  1.83082  1.13613 -1.40196 -1.66533  0.77333  1.95725 -0.03452 -1.97028 -0.70921  1.70257  1.35189 -1.19226 -1.80194  0.51208  1.99523  0.24107 -1.90424 -0.95987  1.54191     ... ... ..... ....... ......... ........... .............
E21 *   2.00000  0.24107 -1.94188 -0.70921  1.77091  1.13613 -1.49702 -1.49702  1.13613  1.77091 -0.70921 -1.94188  0.24107  2.00000  0.24107 -1.94188 -0.70921  1.77091  1.13613 -1.49702 -1.49702  1.13613  1.77091 -0.70921 -1.94188  0.24107  2.00000  0.24107 -1.94188 -0.70921  1.77091  1.13613 -1.49702 -1.49702  1.13613  1.77091 -0.70921 -1.94188  0.24107  2.00000  0.24107 -1.94188 -0.70921  1.77091  1.13613 -1.49702     ... ... ..... ....... ......... ........... .............
E22 *   2.00000  0.10352 -1.98928 -0.30946  1.95725  0.51208 -1.90424 -0.70921  1.83082  0.89874 -1.73778 -1.07864  1.62611  1.24698 -1.49702 -1.40196  1.35189  1.54191 -1.19226 -1.66533  1.01987  1.77091 -0.83654 -1.85751  0.64424  1.92421 -0.44504 -1.97028  0.24107  1.99523 -0.03452 -1.99881 -0.17240  1.98096  0.37748 -1.94188 -0.57850  1.88200  0.77333 -1.80194 -0.95987  1.70257  1.13613 -1.58495 -1.30021  1.45035     ... ... ..... ....... ......... ........... .............
E23 *   2.00000 -0.03452 -1.99881  0.10352  1.99523 -0.17240 -1.98928  0.24107  1.98096 -0.30946 -1.97028  0.37748  1.95725 -0.44504 -1.94188  0.51208  1.92421 -0.57850 -1.90424  0.64424  1.88200 -0.70921 -1.85751  0.77333  1.83082 -0.83654 -1.80194  0.89874  1.77091 -0.95987 -1.73778  1.01987  1.70257 -1.07864 -1.66533  1.13613  1.62611 -1.19226 -1.58495  1.24698  1.54191 -1.30021 -1.49702  1.35189  1.45035 -1.40196     ... ... ..... ....... ......... ........... .............
E24 *   2.00000 -0.17240 -1.97028  0.51208  1.88200 -0.83654 -1.73778  1.13613  1.54191 -1.40196 -1.30021  1.62611  1.01987 -1.80194 -0.70921  1.92421  0.37748 -1.98928 -0.03452  1.99523 -0.30946 -1.94188  0.64424  1.83082 -0.95987 -1.66533  1.24698  1.45035 -1.49702 -1.19226  1.70257  0.89874 -1.85751 -0.57850  1.95725  0.24107 -1.99881  0.10352  1.98096 -0.44504 -1.90424  0.77333  1.77091 -1.07864 -1.58495  1.35189     ... ... ..... ....... ......... ........... .............
E25 *   2.00000 -0.30946 -1.90424  0.89874  1.62611 -1.40196 -1.19226  1.77091  0.64424 -1.97028 -0.03452  1.98096 -0.57850 -1.80194  1.13613  1.45035 -1.58495 -0.95987  1.88200  0.37748 -1.99881  0.24107  1.92421 -0.83654 -1.66533  1.35189  1.24698 -1.73778 -0.70921  1.95725  0.10352 -1.98928  0.51208  1.83082 -1.07864 -1.49702  1.54191  1.01987 -1.85751 -0.44504  1.99523 -0.17240 -1.94188  0.77333  1.70257 -1.30021     ... ... ..... ....... ......... ........... .............
E26 *   2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698  1.24698 -1.80194 -0.44504  2.00000 -0.44504 -1.80194  1.24698     ... ... ..... ....... ......... ........... .............
E27 *   2.00000 -0.57850 -1.66533  1.54191  0.77333 -1.98928  0.37748  1.77091 -1.40196 -0.95987  1.95725 -0.17240 -1.85751  1.24698  1.13613 -1.90424 -0.03452  1.92421 -1.07864 -1.30021  1.83082  0.24107 -1.97028  0.89874  1.45035 -1.73778 -0.44504  1.99523 -0.70921 -1.58495  1.62611  0.64424 -1.99881  0.51208  1.70257 -1.49702 -0.83654  1.98096 -0.30946 -1.80194  1.35189  1.01987 -1.94188  0.10352  1.88200 -1.19226     ... ... ..... ....... ......... ........... .............
E28 *   2.00000 -0.70921 -1.49702  1.77091  0.24107 -1.94188  1.13613  1.13613 -1.94188  0.24107  1.77091 -1.49702 -0.70921  2.00000 -0.70921 -1.49702  1.77091  0.24107 -1.94188  1.13613  1.13613 -1.94188  0.24107  1.77091 -1.49702 -0.70921  2.00000 -0.70921 -1.49702  1.77091  0.24107 -1.94188  1.13613  1.13613 -1.94188  0.24107  1.77091 -1.49702 -0.70921  2.00000 -0.70921 -1.49702  1.77091  0.24107 -1.94188  1.13613     ... ... ..... ....... ......... ........... .............
E29 *   2.00000 -0.83654 -1.30021  1.92421 -0.30946 -1.66533  1.70257  0.24107 -1.90424  1.35189  0.77333 -1.99881  0.89874  1.24698 -1.94188  0.37748  1.62611 -1.73778 -0.17240  1.88200 -1.40196 -0.70921  1.99523 -0.95987 -1.19226  1.95725 -0.44504 -1.58495  1.77091  0.10352 -1.85751  1.45035  0.64424 -1.98928  1.01987  1.13613 -1.97028  0.51208  1.54191 -1.80194 -0.03452  1.83082 -1.49702 -0.57850  1.98096 -1.07864     ... ... ..... ....... ......... ........... .............
E30 *   2.00000 -0.95987 -1.07864  1.99523 -0.83654 -1.19226  1.98096 -0.70921 -1.30021  1.95725 -0.57850 -1.40196  1.92421 -0.44504 -1.49702  1.88200 -0.30946 -1.58495  1.83082 -0.17240 -1.66533  1.77091 -0.03452 -1.73778  1.70257  0.10352 -1.80194  1.62611  0.24107 -1.85751  1.54191  0.37748 -1.90424  1.45035  0.51208 -1.94188  1.35189  0.64424 -1.97028  1.24698  0.77333 -1.98928  1.13613  0.89874 -1.99881  1.01987     ... ... ..... ....... ......... ........... .............
E31 *   2.00000 -1.07864 -0.83654  1.98096 -1.30021 -0.57850  1.92421 -1.49702 -0.30946  1.83082 -1.66533 -0.03452  1.70257 -1.80194  0.24107  1.54191 -1.90424  0.51208  1.35189 -1.97028  0.77333  1.13613 -1.99881  1.01987  0.89874 -1.98928  1.24698  0.64424 -1.94188  1.45035  0.37748 -1.85751  1.62611  0.10352 -1.73778  1.77091 -0.17240 -1.58495  1.88200 -0.44504 -1.40196  1.95725 -0.70921 -1.19226  1.99523 -0.95987     ... ... ..... ....... ......... ........... .............
E32 *   2.00000 -1.19226 -0.57850  1.88200 -1.66533  0.10352  1.54191 -1.94188  0.77333  1.01987 -1.98928  1.35189  0.37748 -1.80194  1.77091 -0.30946 -1.40196  1.98096 -0.95987 -0.83654  1.95725 -1.49702 -0.17240  1.70257 -1.85751  0.51208  1.24698 -1.99881  1.13613  0.64424 -1.90424  1.62611 -0.03452 -1.58495  1.92421 -0.70921 -1.07864  1.99523 -1.30021 -0.44504  1.83082 -1.73778  0.24107  1.45035 -1.97028  0.89874     ... ... ..... ....... ......... ........... .............
E33 *   2.00000 -1.30021 -0.30946  1.70257 -1.90424  0.77333  0.89874 -1.94188  1.62611 -0.17240 -1.40196  1.99523 -1.19226 -0.44504  1.77091 -1.85751  0.64424  1.01987 -1.97028  1.54191 -0.03452 -1.49702  1.98096 -1.07864 -0.57850  1.83082 -1.80194  0.51208  1.13613 -1.98928  1.45035  0.10352 -1.58495  1.95725 -0.95987 -0.70921  1.88200 -1.73778  0.37748  1.24698 -1.99881  1.35189  0.24107 -1.66533  1.92421 -0.83654     ... ... ..... ....... ......... ........... .............
E34 *   2.00000 -1.40196 -0.03452  1.45035 -1.99881  1.35189  0.10352 -1.49702  1.99523 -1.30021 -0.17240  1.54191 -1.98928  1.24698  0.24107 -1.58495  1.98096 -1.19226 -0.30946  1.62611 -1.97028  1.13613  0.37748 -1.66533  1.95725 -1.07864 -0.44504  1.70257 -1.94188  1.01987  0.51208 -1.73778  1.92421 -0.95987 -0.57850  1.77091 -1.90424  0.89874  0.64424 -1.80194  1.88200 -0.83654 -0.70921  1.83082 -1.85751  0.77333     ... ... ..... ....... ......... ........... .............
E35 *   2.00000 -1.49702  0.24107  1.13613 -1.94188  1.77091 -0.70921 -0.70921  1.77091 -1.94188  1.13613  0.24107 -1.49702  2.00000 -1.49702  0.24107  1.13613 -1.94188  1.77091 -0.70921 -0.70921  1.77091 -1.94188  1.13613  0.24107 -1.49702  2.00000 -1.49702  0.24107  1.13613 -1.94188  1.77091 -0.70921 -0.70921  1.77091 -1.94188  1.13613  0.24107 -1.49702  2.00000 -1.49702  0.24107  1.13613 -1.94188  1.77091 -0.70921     ... ... ..... ....... ......... ........... .............
E36 *   2.00000 -1.58495  0.51208  0.77333 -1.73778  1.98096 -1.40196  0.24107  1.01987 -1.85751  1.92421 -1.19226 -0.03452  1.24698 -1.94188  1.83082 -0.95987 -0.30946  1.45035 -1.98928  1.70257 -0.70921 -0.57850  1.62611 -1.99881  1.54191 -0.44504 -0.83654  1.77091 -1.97028  1.35189 -0.17240 -1.07864  1.88200 -1.90424  1.13613  0.10352 -1.30021  1.95725 -1.80194  0.89874  0.37748 -1.49702  1.99523 -1.66533  0.64424     ... ... ..... ....... ......... ........... .............
E37 *   2.00000 -1.66533  0.77333  0.37748 -1.40196  1.95725 -1.85751  1.13613 -0.03452 -1.07864  1.83082 -1.97028  1.45035 -0.44504 -0.70921  1.62611 -1.99881  1.70257 -0.83654 -0.30946  1.35189 -1.94188  1.88200 -1.19226  0.10352  1.01987 -1.80194  1.98096 -1.49702  0.51208  0.64424 -1.58495  1.99523 -1.73778  0.89874  0.24107 -1.30021  1.92421 -1.90424  1.24698 -0.17240 -0.95987  1.77091 -1.98928  1.54191 -0.57850     ... ... ..... ....... ......... ........... .............
E38 *   2.00000 -1.73778  1.01987 -0.03452 -0.95987  1.70257 -1.99881  1.77091 -1.07864  0.10352  0.89874 -1.66533  1.99523 -1.80194  1.13613 -0.17240 -0.83654  1.62611 -1.98928  1.83082 -1.19226  0.24107  0.77333 -1.58495  1.98096 -1.85751  1.24698 -0.30946 -0.70921  1.54191 -1.97028  1.88200 -1.30021  0.37748  0.64424 -1.49702  1.95725 -1.90424  1.35189 -0.44504 -0.57850  1.45035 -1.94188  1.92421 -1.40196  0.51208     ... ... ..... ....... ......... ........... .............
E39 *   2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504 -0.44504  1.24698 -1.80194  2.00000 -1.80194  1.24698 -0.44504     ... ... ..... ....... ......... ........... .............
E40 *   2.00000 -1.85751  1.45035 -0.83654  0.10352  0.64424 -1.30021  1.77091 -1.98928  1.92421 -1.58495  1.01987 -0.30946 -0.44504  1.13613 -1.66533  1.95725 -1.97028  1.70257 -1.19226  0.51208  0.24107 -0.95987  1.54191 -1.90424  1.99523 -1.80194  1.35189 -0.70921 -0.03452  0.77333 -1.40196  1.83082 -1.99881  1.88200 -1.49702  0.89874 -0.17240 -0.57850  1.24698 -1.73778  1.98096 -1.94188  1.62611 -1.07864  0.37748     ... ... ..... ....... ......... ........... .............
E41 *   2.00000 -1.90424  1.62611 -1.19226  0.64424 -0.03452 -0.57850  1.13613 -1.58495  1.88200 -1.99881  1.92421 -1.66533  1.24698 -0.70921  0.10352  0.51208 -1.07864  1.54191 -1.85751  1.99523 -1.94188  1.70257 -1.30021  0.77333 -0.17240 -0.44504  1.01987 -1.49702  1.83082 -1.98928  1.95725 -1.73778  1.35189 -0.83654  0.24107  0.37748 -0.95987  1.45035 -1.80194  1.98096 -1.97028  1.77091 -1.40196  0.89874 -0.30946     ... ... ..... ....... ......... ........... .............
E42 *   2.00000 -1.94188  1.77091 -1.49702  1.13613 -0.70921  0.24107  0.24107 -0.70921  1.13613 -1.49702  1.77091 -1.94188  2.00000 -1.94188  1.77091 -1.49702  1.13613 -0.70921  0.24107  0.24107 -0.70921  1.13613 -1.49702  1.77091 -1.94188  2.00000 -1.94188  1.77091 -1.49702  1.13613 -0.70921  0.24107  0.24107 -0.70921  1.13613 -1.49702  1.77091 -1.94188  2.00000 -1.94188  1.77091 -1.49702  1.13613 -0.70921  0.24107     ... ... ..... ....... ......... ........... .............
E43 *   2.00000 -1.97028  1.88200 -1.73778  1.54191 -1.30021  1.01987 -0.70921  0.37748 -0.03452 -0.30946  0.64424 -0.95987  1.24698 -1.49702  1.70257 -1.85751  1.95725 -1.99881  1.98096 -1.90424  1.77091 -1.58495  1.35189 -1.07864  0.77333 -0.44504  0.10352  0.24107 -0.57850  0.89874 -1.19226  1.45035 -1.66533  1.83082 -1.94188  1.99523 -1.98928  1.92421 -1.80194  1.62611 -1.40196  1.13613 -0.83654  0.51208 -0.17240     ... ... ..... ....... ......... ........... .............
E44 *   2.00000 -1.98928  1.95725 -1.90424  1.83082 -1.73778  1.62611 -1.49702  1.35189 -1.19226  1.01987 -0.83654  0.64424 -0.44504  0.24107 -0.03452 -0.17240  0.37748 -0.57850  0.77333 -0.95987  1.13613 -1.30021  1.45035 -1.58495  1.70257 -1.80194  1.88200 -1.94188  1.98096 -1.99881  1.99523 -1.97028  1.92421 -1.85751  1.77091 -1.66533  1.54191 -1.40196  1.24698 -1.07864  0.89874 -0.70921  0.51208 -0.30946  0.10352     ... ... ..... ....... ......... ........... .............
E45 *   2.00000 -1.99881  1.99523 -1.98928  1.98096 -1.97028  1.95725 -1.94188  1.92421 -1.90424  1.88200 -1.85751  1.83082 -1.80194  1.77091 -1.73778  1.70257 -1.66533  1.62611 -1.58495  1.54191 -1.49702  1.45035 -1.40196  1.35189 -1.30021  1.24698 -1.19226  1.13613 -1.07864  1.01987 -0.95987  0.89874 -0.83654  0.77333 -0.70921  0.64424 -0.57850  0.51208 -0.44504  0.37748 -0.30946  0.24107 -0.17240  0.10352 -0.03452     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.995234544602 = 2*cos(2*π/91)
                               1.980960887975 = 2*cos(4*π/91)
                               1.957247050592 = 2*cos(6*π/91)
                               1.924206039687 = 2*cos(8*π/91)
                               1.881995310725 = 2*cos(10*π/91)
                               1.830816017051 = 2*cos(12*π/91)
                               1.770912051306 = 2*cos(14*π/91) = 2*cos(2*π/13)
                               1.702568883169 = 2*cos(16*π/91)
                               1.626112198957 = 2*cos(18*π/91)
                               1.541906349590 = 2*cos(20*π/91)
                               1.450352614287 = 2*cos(22*π/91)
                               1.351887288289 = 2*cos(24*π/91)
                               1.246979603717 = 2*cos(26*π/91) = 2*cos(2*π/7)
                               1.136129493462 = 2*cos(28*π/91) = 2*cos(4*π/13)
                               1.019865208780 = 2*cos(30*π/91)
                               0.898740801934 = 2*cos(32*π/91)
                               0.773333485883 = 2*cos(34*π/91)
                               0.644240883597 = 2*cos(36*π/91)
                               0.512078180115 = 2*cos(38*π/91)
                               0.377475190906 = 2*cos(40*π/91)
                               0.241073360510 = 2*cos(42*π/91) = 2*cos(6*π/13)
                               0.103522705768 = 2*cos(44*π/91)
                              -0.034521281811 = 2*cos(46*π/91)
                              -0.172400759761 = 2*cos(48*π/91)
                              -0.309458669581 = 2*cos(50*π/91)
                              -0.445041867913 = 2*cos(52*π/91) = 2*cos(4*π/7)
                              -0.578504239073 = 2*cos(54*π/91)
                              -0.709209774085 = 2*cos(56*π/91) = 2*cos(8*π/13)
                              -0.836535601551 = 2*cos(58*π/91)
                              -0.959874955920 = 2*cos(60*π/91)
                              -1.078640068999 = 2*cos(62*π/91)
                              -1.192264970939 = 2*cos(64*π/91)
                              -1.300208187338 = 2*cos(66*π/91)
                              -1.401955319613 = 2*cos(68*π/91)
                              -1.497021496342 = 2*cos(70*π/91) = 2*cos(10*π/13)
                              -1.584953683902 = 2*cos(72*π/91)
                              -1.665332845375 = 2*cos(74*π/91)
                              -1.737775937450 = 2*cos(76*π/91)
                              -1.801937735805 = 2*cos(78*π/91) = 2*cos(6*π/7)
                              -1.857512480251 = 2*cos(80*π/91)
                              -1.904235331822 = 2*cos(82*π/91)
                              -1.941883634852 = 2*cos(84*π/91) = 2*cos(12*π/13)
                              -1.970277978034 = 2*cos(86*π/91)
                              -1.989283049390 = 2*cos(88*π/91)
                              -1.998808281102 = 2*cos(90*π/91)



 Symmetry of Rotations and Cartesian products

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

 Notes:

    α  The order of the C91 point group is 91, and the order of the principal axis is 91.

    β  This is an Abelian point group (the commutative law holds between all symmetry operations).
       The C91 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.

    γ  Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters.
       These 90 cases have been combined into 45 two-dimensional representations that are no longer irreducible but have real-valued characters.
       Accordingly, 45 pairs of left and right rotations have been combined into one two-membered pseudo-class each.

    δ  The 45 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.

    ε  The point group is chiral, as it does not contain any mirroring operation.

    ζ  Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6.
       These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1.
       All characters are algebraic integers of a degree less than half the order of the principal axis (and often much less).
       For this group, however, none of the characters can be expressed by a closed algebraic form using real numbers only.

This Character Table for the C91 point group was created by Gernot Katzer.

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