Character table for the D87 point group

D87     E        2 C87    2 C87^2  2 C29    2 C87^4  2 C87^5  2 C29^2  2 C87^7  2 C87^8  2 C29^3  2 C87^10 2 C87^11 2 C29^4  2 C87^13 2 C87^14 2 C29^5  2 C87^16 2 C87^17 2 C29^6  2 C87^19 2 C87^20 2 C29^7  2 C87^22 2 C87^23 2 C29^8  2 C87^25 2 C87^26 2 C29^9  2 C87^28 2 C3     2 C29^10 2 C87^31 2 C87^32 2 C29^11 2 C87^34 2 C87^35 2 C29^12 2 C87^37 2 C87^38 2 C29^13 2 C87^40 2 C87^41 2 C29^14 2 C87^43 87 C2'      <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     ... ... ....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     ..T ..T ..... ......T ......... ..........T .............
E1      2.00000  1.99479  1.97917  1.95324  1.91713  1.87102  1.81515  1.74982  1.67537  1.59219  1.50070  1.40139  1.29477  1.18141  1.06188  0.93682  0.80687  0.67272  0.53506  0.39461  0.25210  0.10828 -0.03611 -0.18031 -0.32356 -0.46513 -0.60428 -0.74028 -0.87241 -1.00000 -1.12237 -1.23890 -1.34896 -1.45199 -1.54745 -1.63484 -1.71371 -1.78365 -1.84429 -1.89531 -1.93645 -1.96749 -1.98828 -1.99870  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.97917  1.91713  1.81515  1.67537  1.50070  1.29477  1.06188  0.80687  0.53506  0.25210 -0.03611 -0.32356 -0.60428 -0.87241 -1.12237 -1.34896 -1.54745 -1.71371 -1.84429 -1.93645 -1.98828 -1.99870 -1.96749 -1.89531 -1.78365 -1.63484 -1.45199 -1.23890 -1.00000 -0.74028 -0.46513 -0.18031  0.10828  0.39461  0.67272  0.93682  1.18141  1.40139  1.59219  1.74982  1.87102  1.95324  1.99479  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.95324  1.81515  1.59219  1.29477  0.93682  0.53506  0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828 -1.98828 -1.89531 -1.71371 -1.45199 -1.12237 -0.74028 -0.32356  0.10828  0.53506  0.93682  1.29477  1.59219  1.81515  1.95324  2.00000  1.95324  1.81515  1.59219  1.29477  0.93682  0.53506  0.10828 -0.32356 -0.74028 -1.12237 -1.45199 -1.71371 -1.89531 -1.98828  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.91713  1.67537  1.29477  0.80687  0.25210 -0.32356 -0.87241 -1.34896 -1.71371 -1.93645 -1.99870 -1.89531 -1.63484 -1.23890 -0.74028 -0.18031  0.39461  0.93682  1.40139  1.74982  1.95324  1.99479  1.87102  1.59219  1.18141  0.67272  0.10828 -0.46513 -1.00000 -1.45199 -1.78365 -1.96749 -1.98828 -1.84429 -1.54745 -1.12237 -0.60428 -0.03611  0.53506  1.06188  1.50070  1.81515  1.97917  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.87102  1.50070  0.93682  0.25210 -0.46513 -1.12237 -1.63484 -1.93645 -1.98828 -1.78365 -1.34896 -0.74028 -0.03611  0.67272  1.29477  1.74982  1.97917  1.95324  1.67537  1.18141  0.53506 -0.18031 -0.87241 -1.45199 -1.84429 -1.99870 -1.89531 -1.54745 -1.00000 -0.32356  0.39461  1.06188  1.59219  1.91713  1.99479  1.81515  1.40139  0.80687  0.10828 -0.60428 -1.23890 -1.71371 -1.96749  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.81515  1.29477  0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028  0.10828  0.93682  1.59219  1.95324  1.95324  1.59219  0.93682  0.10828 -0.74028 -1.45199 -1.89531 -1.98828 -1.71371 -1.12237 -0.32356  0.53506  1.29477  1.81515  2.00000  1.81515  1.29477  0.53506 -0.32356 -1.12237 -1.71371 -1.98828 -1.89531 -1.45199 -0.74028  0.10828  0.93682  1.59219  1.95324  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.74982  1.06188  0.10828 -0.87241 -1.63484 -1.98828 -1.84429 -1.23890 -0.32356  0.67272  1.50070  1.95324  1.91713  1.40139  0.53506 -0.46513 -1.34896 -1.89531 -1.96749 -1.54745 -0.74028  0.25210  1.18141  1.81515  1.99479  1.67537  0.93682 -0.03611 -1.00000 -1.71371 -1.99870 -1.78365 -1.12237 -0.18031  0.80687  1.59219  1.97917  1.87102  1.29477  0.39461 -0.60428 -1.45199 -1.93645  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.67537  0.80687 -0.32356 -1.34896 -1.93645 -1.89531 -1.23890 -0.18031  0.93682  1.74982  1.99479  1.59219  0.67272 -0.46513 -1.45199 -1.96749 -1.84429 -1.12237 -0.03611  1.06188  1.81515  1.97917  1.50070  0.53506 -0.60428 -1.54745 -1.98828 -1.78365 -1.00000  0.10828  1.18141  1.87102  1.95324  1.40139  0.39461 -0.74028 -1.63484 -1.99870 -1.71371 -0.87241  0.25210  1.29477  1.91713  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.59219  0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356  0.93682  1.81515  1.95324  1.29477  0.10828 -1.12237 -1.89531 -1.89531 -1.12237  0.10828  1.29477  1.95324  1.81515  0.93682 -0.32356 -1.45199 -1.98828 -1.71371 -0.74028  0.53506  1.59219  2.00000  1.59219  0.53506 -0.74028 -1.71371 -1.98828 -1.45199 -0.32356  0.93682  1.81515  1.95324  1.29477  0.10828 -1.12237 -1.89531  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.50070  0.25210 -1.12237 -1.93645 -1.78365 -0.74028  0.67272  1.74982  1.95324  1.18141 -0.18031 -1.45199 -1.99870 -1.54745 -0.32356  1.06188  1.91713  1.81515  0.80687 -0.60428 -1.71371 -1.96749 -1.23890  0.10828  1.40139  1.99479  1.59219  0.39461 -1.00000 -1.89531 -1.84429 -0.87241  0.53506  1.67537  1.97917  1.29477 -0.03611 -1.34896 -1.98828 -1.63484 -0.46513  0.93682  1.87102  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.40139 -0.03611 -1.45199 -1.99870 -1.34896  0.10828  1.50070  1.99479  1.29477 -0.18031 -1.54745 -1.98828 -1.23890  0.25210  1.59219  1.97917  1.18141 -0.32356 -1.63484 -1.96749 -1.12237  0.39461  1.67537  1.95324  1.06188 -0.46513 -1.71371 -1.93645 -1.00000  0.53506  1.74982  1.91713  0.93682 -0.60428 -1.78365 -1.89531 -0.87241  0.67272  1.81515  1.87102  0.80687 -0.74028 -1.84429  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  1.29477 -0.32356 -1.71371 -1.89531 -0.74028  0.93682  1.95324  1.59219  0.10828 -1.45199 -1.98828 -1.12237  0.53506  1.81515  1.81515  0.53506 -1.12237 -1.98828 -1.45199  0.10828  1.59219  1.95324  0.93682 -0.74028 -1.89531 -1.71371 -0.32356  1.29477  2.00000  1.29477 -0.32356 -1.71371 -1.89531 -0.74028  0.93682  1.95324  1.59219  0.10828 -1.45199 -1.98828 -1.12237  0.53506  1.81515  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  1.18141 -0.60428 -1.89531 -1.63484 -0.03611  1.59219  1.91713  0.67272 -1.12237 -1.99870 -1.23890  0.53506  1.87102  1.67537  0.10828 -1.54745 -1.93645 -0.74028  1.06188  1.99479  1.29477 -0.46513 -1.84429 -1.71371 -0.18031  1.50070  1.95324  0.80687 -1.00000 -1.98828 -1.34896  0.39461  1.81515  1.74982  0.25210 -1.45199 -1.96749 -0.87241  0.93682  1.97917  1.40139 -0.32356 -1.78365  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  1.06188 -0.87241 -1.98828 -1.23890  0.67272  1.95324  1.40139 -0.46513 -1.89531 -1.54745  0.25210  1.81515  1.67537 -0.03611 -1.71371 -1.78365 -0.18031  1.59219  1.87102  0.39461 -1.45199 -1.93645 -0.60428  1.29477  1.97917  0.80687 -1.12237 -1.99870 -1.00000  0.93682  1.99479  1.18141 -0.74028 -1.96749 -1.34896  0.53506  1.91713  1.50070 -0.32356 -1.84429 -1.63484  0.10828  1.74982  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  0.93682 -1.12237 -1.98828 -0.74028  1.29477  1.95324  0.53506 -1.45199 -1.89531 -0.32356  1.59219  1.81515  0.10828 -1.71371 -1.71371  0.10828  1.81515  1.59219 -0.32356 -1.89531 -1.45199  0.53506  1.95324  1.29477 -0.74028 -1.98828 -1.12237  0.93682  2.00000  0.93682 -1.12237 -1.98828 -0.74028  1.29477  1.95324  0.53506 -1.45199 -1.89531 -0.32356  1.59219  1.81515  0.10828 -1.71371  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  0.80687 -1.34896 -1.89531 -0.18031  1.74982  1.59219 -0.46513 -1.96749 -1.12237  1.06188  1.97917  0.53506 -1.54745 -1.78365  0.10828  1.87102  1.40139 -0.74028 -1.99870 -0.87241  1.29477  1.91713  0.25210 -1.71371 -1.63484  0.39461  1.95324  1.18141 -1.00000 -1.98828 -0.60428  1.50070  1.81515 -0.03611 -1.84429 -1.45199  0.67272  1.99479  0.93682 -1.23890 -1.93645 -0.32356  1.67537  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.67272 -1.54745 -1.71371  0.39461  1.97917  0.93682 -1.34896 -1.84429  0.10828  1.91713  1.18141 -1.12237 -1.93645 -0.18031  1.81515  1.40139 -0.87241 -1.98828 -0.46513  1.67537  1.59219 -0.60428 -1.99870 -0.74028  1.50070  1.74982 -0.32356 -1.96749 -1.00000  1.29477  1.87102 -0.03611 -1.89531 -1.23890  1.06188  1.95324  0.25210 -1.78365 -1.45199  0.80687  1.99479  0.53506 -1.63484  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000  0.53506 -1.71371 -1.45199  0.93682  1.95324  0.10828 -1.89531 -1.12237  1.29477  1.81515 -0.32356 -1.98828 -0.74028  1.59219  1.59219 -0.74028 -1.98828 -0.32356  1.81515  1.29477 -1.12237 -1.89531  0.10828  1.95324  0.93682 -1.45199 -1.71371  0.53506  2.00000  0.53506 -1.71371 -1.45199  0.93682  1.95324  0.10828 -1.89531 -1.12237  1.29477  1.81515 -0.32356 -1.98828 -0.74028  1.59219  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000  0.39461 -1.84429 -1.12237  1.40139  1.67537 -0.74028 -1.96749 -0.03611  1.95324  0.80687 -1.63484 -1.45199  1.06188  1.87102 -0.32356 -1.99870 -0.46513  1.81515  1.18141 -1.34896 -1.71371  0.67272  1.97917  0.10828 -1.93645 -0.87241  1.59219  1.50070 -1.00000 -1.89531  0.25210  1.99479  0.53506 -1.78365 -1.23890  1.29477  1.74982 -0.60428 -1.98828 -0.18031  1.91713  0.93682 -1.54745  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000  0.25210 -1.93645 -0.74028  1.74982  1.18141 -1.45199 -1.54745  1.06188  1.81515 -0.60428 -1.96749  0.10828  1.99479  0.39461 -1.89531 -0.87241  1.67537  1.29477 -1.34896 -1.63484  0.93682  1.87102 -0.46513 -1.98828 -0.03611  1.97917  0.53506 -1.84429 -1.00000  1.59219  1.40139 -1.23890 -1.71371  0.80687  1.91713 -0.32356 -1.99870 -0.18031  1.95324  0.67272 -1.78365 -1.12237  1.50070  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000  0.10828 -1.98828 -0.32356  1.95324  0.53506 -1.89531 -0.74028  1.81515  0.93682 -1.71371 -1.12237  1.59219  1.29477 -1.45199 -1.45199  1.29477  1.59219 -1.12237 -1.71371  0.93682  1.81515 -0.74028 -1.89531  0.53506  1.95324 -0.32356 -1.98828  0.10828  2.00000  0.10828 -1.98828 -0.32356  1.95324  0.53506 -1.89531 -0.74028  1.81515  0.93682 -1.71371 -1.12237  1.59219  1.29477 -1.45199  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000 -0.03611 -1.99870  0.10828  1.99479 -0.18031 -1.98828  0.25210  1.97917 -0.32356 -1.96749  0.39461  1.95324 -0.46513 -1.93645  0.53506  1.91713 -0.60428 -1.89531  0.67272  1.87102 -0.74028 -1.84429  0.80687  1.81515 -0.87241 -1.78365  0.93682  1.74982 -1.00000 -1.71371  1.06188  1.67537 -1.12237 -1.63484  1.18141  1.59219 -1.23890 -1.54745  1.29477  1.50070 -1.34896 -1.45199  1.40139  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000 -0.18031 -1.96749  0.53506  1.87102 -0.87241 -1.71371  1.18141  1.50070 -1.45199 -1.23890  1.67537  0.93682 -1.84429 -0.60428  1.95324  0.25210 -1.99870  0.10828  1.97917 -0.46513 -1.89531  0.80687  1.74982 -1.12237 -1.54745  1.40139  1.29477 -1.63484 -1.00000  1.81515  0.67272 -1.93645 -0.32356  1.99479 -0.03611 -1.98828  0.39461  1.91713 -0.74028 -1.78365  1.06188  1.59219 -1.34896  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000 -0.32356 -1.89531  0.93682  1.59219 -1.45199 -1.12237  1.81515  0.53506 -1.98828  0.10828  1.95324 -0.74028 -1.71371  1.29477  1.29477 -1.71371 -0.74028  1.95324  0.10828 -1.98828  0.53506  1.81515 -1.12237 -1.45199  1.59219  0.93682 -1.89531 -0.32356  2.00000 -0.32356 -1.89531  0.93682  1.59219 -1.45199 -1.12237  1.81515  0.53506 -1.98828  0.10828  1.95324 -0.74028 -1.71371  1.29477  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -0.46513 -1.78365  1.29477  1.18141 -1.84429 -0.32356  1.99479 -0.60428 -1.71371  1.40139  1.06188 -1.89531 -0.18031  1.97917 -0.74028 -1.63484  1.50070  0.93682 -1.93645 -0.03611  1.95324 -0.87241 -1.54745  1.59219  0.80687 -1.96749  0.10828  1.91713 -1.00000 -1.45199  1.67537  0.67272 -1.98828  0.25210  1.87102 -1.12237 -1.34896  1.74982  0.53506 -1.99870  0.39461  1.81515 -1.23890  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -0.60428 -1.63484  1.59219  0.67272 -1.99870  0.53506  1.67537 -1.54745 -0.74028  1.99479 -0.46513 -1.71371  1.50070  0.80687 -1.98828  0.39461  1.74982 -1.45199 -0.87241  1.97917 -0.32356 -1.78365  1.40139  0.93682 -1.96749  0.25210  1.81515 -1.34896 -1.00000  1.95324 -0.18031 -1.84429  1.29477  1.06188 -1.93645  0.10828  1.87102 -1.23890 -1.12237  1.91713 -0.03611 -1.89531  1.18141  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -0.74028 -1.45199  1.81515  0.10828 -1.89531  1.29477  0.93682 -1.98828  0.53506  1.59219 -1.71371 -0.32356  1.95324 -1.12237 -1.12237  1.95324 -0.32356 -1.71371  1.59219  0.53506 -1.98828  0.93682  1.29477 -1.89531  0.10828  1.81515 -1.45199 -0.74028  2.00000 -0.74028 -1.45199  1.81515  0.10828 -1.89531  1.29477  0.93682 -1.98828  0.53506  1.59219 -1.71371 -0.32356  1.95324 -1.12237  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -0.87241 -1.23890  1.95324 -0.46513 -1.54745  1.81515 -0.03611 -1.78365  1.59219  0.39461 -1.93645  1.29477  0.80687 -1.99870  0.93682  1.18141 -1.96749  0.53506  1.50070 -1.84429  0.10828  1.74982 -1.63484 -0.32356  1.91713 -1.34896 -0.74028  1.99479 -1.00000 -1.12237  1.97917 -0.60428 -1.45199  1.87102 -0.18031 -1.71371  1.67537  0.25210 -1.89531  1.40139  0.67272 -1.98828  1.06188  0.00000     ... ... ..... ....... ......... ........... .............
E29     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  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -1.12237 -0.74028  1.95324 -1.45199 -0.32356  1.81515 -1.71371  0.10828  1.59219 -1.89531  0.53506  1.29477 -1.98828  0.93682  0.93682 -1.98828  1.29477  0.53506 -1.89531  1.59219  0.10828 -1.71371  1.81515 -0.32356 -1.45199  1.95324 -0.74028 -1.12237  2.00000 -1.12237 -0.74028  1.95324 -1.45199 -0.32356  1.81515 -1.71371  0.10828  1.59219 -1.89531  0.53506  1.29477 -1.98828  0.93682  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -1.23890 -0.46513  1.81515 -1.78365  0.39461  1.29477 -1.99870  1.18141  0.53506 -1.84429  1.74982 -0.32356 -1.34896  1.99479 -1.12237 -0.60428  1.87102 -1.71371  0.25210  1.40139 -1.98828  1.06188  0.67272 -1.89531  1.67537 -0.18031 -1.45199  1.97917 -1.00000 -0.74028  1.91713 -1.63484  0.10828  1.50070 -1.96749  0.93682  0.80687 -1.93645  1.59219 -0.03611 -1.54745  1.95324 -0.87241  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -1.34896 -0.18031  1.59219 -1.96749  1.06188  0.53506 -1.78365  1.87102 -0.74028 -0.87241  1.91713 -1.71371  0.39461  1.18141 -1.98828  1.50070 -0.03611 -1.45199  1.99479 -1.23890 -0.32356  1.67537 -1.93645  0.93682  0.67272 -1.84429  1.81515 -0.60428 -1.00000  1.95324 -1.63484  0.25210  1.29477 -1.99870  1.40139  0.10828 -1.54745  1.97917 -1.12237 -0.46513  1.74982 -1.89531  0.80687  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.45199  0.10828  1.29477 -1.98828  1.59219 -0.32356 -1.12237  1.95324 -1.71371  0.53506  0.93682 -1.89531  1.81515 -0.74028 -0.74028  1.81515 -1.89531  0.93682  0.53506 -1.71371  1.95324 -1.12237 -0.32356  1.59219 -1.98828  1.29477  0.10828 -1.45199  2.00000 -1.45199  0.10828  1.29477 -1.98828  1.59219 -0.32356 -1.12237  1.95324 -1.71371  0.53506  0.93682 -1.89531  1.81515 -0.74028  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.54745  0.39461  0.93682 -1.84429  1.91713 -1.12237 -0.18031  1.40139 -1.98828  1.67537 -0.60428 -0.74028  1.74982 -1.96749  1.29477 -0.03611 -1.23890  1.95324 -1.78365  0.80687  0.53506 -1.63484  1.99479 -1.45199  0.25210  1.06188 -1.89531  1.87102 -1.00000 -0.32356  1.50070 -1.99870  1.59219 -0.46513 -0.87241  1.81515 -1.93645  1.18141  0.10828 -1.34896  1.97917 -1.71371  0.67272  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.63484  0.67272  0.53506 -1.54745  1.99479 -1.71371  0.80687  0.39461 -1.45199  1.97917 -1.78365  0.93682  0.25210 -1.34896  1.95324 -1.84429  1.06188  0.10828 -1.23890  1.91713 -1.89531  1.18141 -0.03611 -1.12237  1.87102 -1.93645  1.29477 -0.18031 -1.00000  1.81515 -1.96749  1.40139 -0.32356 -0.87241  1.74982 -1.98828  1.50070 -0.46513 -0.74028  1.67537 -1.99870  1.59219 -0.60428  0.00000     ... ... ..... ....... ......... ........... .............
E36     2.00000 -1.71371  0.93682  0.10828 -1.12237  1.81515 -1.98828  1.59219 -0.74028 -0.32356  1.29477 -1.89531  1.95324 -1.45199  0.53506  0.53506 -1.45199  1.95324 -1.89531  1.29477 -0.32356 -0.74028  1.59219 -1.98828  1.81515 -1.12237  0.10828  0.93682 -1.71371  2.00000 -1.71371  0.93682  0.10828 -1.12237  1.81515 -1.98828  1.59219 -0.74028 -0.32356  1.29477 -1.89531  1.95324 -1.45199  0.53506  0.00000     ... ... ..... ....... ......... ........... .............
E37     2.00000 -1.78365  1.18141 -0.32356 -0.60428  1.40139 -1.89531  1.97917 -1.63484  0.93682 -0.03611 -0.87241  1.59219 -1.96749  1.91713 -1.45199  0.67272  0.25210 -1.12237  1.74982 -1.99870  1.81515 -1.23890  0.39461  0.53506 -1.34896  1.87102 -1.98828  1.67537 -1.00000  0.10828  0.80687 -1.54745  1.95324 -1.93645  1.50070 -0.74028 -0.18031  1.06188 -1.71371  1.99479 -1.84429  1.29477 -0.46513  0.00000     ... ... ..... ....... ......... ........... .............
E38     2.00000 -1.84429  1.40139 -0.74028 -0.03611  0.80687 -1.45199  1.87102 -1.99870  1.81515 -1.34896  0.67272  0.10828 -0.87241  1.50070 -1.89531  1.99479 -1.78365  1.29477 -0.60428 -0.18031  0.93682 -1.54745  1.91713 -1.98828  1.74982 -1.23890  0.53506  0.25210 -1.00000  1.59219 -1.93645  1.97917 -1.71371  1.18141 -0.46513 -0.32356  1.06188 -1.63484  1.95324 -1.96749  1.67537 -1.12237  0.39461  0.00000     ... ... ..... ....... ......... ........... .............
E39     2.00000 -1.89531  1.59219 -1.12237  0.53506  0.10828 -0.74028  1.29477 -1.71371  1.95324 -1.98828  1.81515 -1.45199  0.93682 -0.32356 -0.32356  0.93682 -1.45199  1.81515 -1.98828  1.95324 -1.71371  1.29477 -0.74028  0.10828  0.53506 -1.12237  1.59219 -1.89531  2.00000 -1.89531  1.59219 -1.12237  0.53506  0.10828 -0.74028  1.29477 -1.71371  1.95324 -1.98828  1.81515 -1.45199  0.93682 -0.32356  0.00000     ... ... ..... ....... ......... ........... .............
E40     2.00000 -1.93645  1.74982 -1.45199  1.06188 -0.60428  0.10828  0.39461 -0.87241  1.29477 -1.63484  1.87102 -1.98828  1.97917 -1.84429  1.59219 -1.23890  0.80687 -0.32356 -0.18031  0.67272 -1.12237  1.50070 -1.78365  1.95324 -1.99870  1.91713 -1.71371  1.40139 -1.00000  0.53506 -0.03611 -0.46513  0.93682 -1.34896  1.67537 -1.89531  1.99479 -1.96749  1.81515 -1.54745  1.18141 -0.74028  0.25210  0.00000     ... ... ..... ....... ......... ........... .............
E41     2.00000 -1.96749  1.87102 -1.71371  1.50070 -1.23890  0.93682 -0.60428  0.25210  0.10828 -0.46513  0.80687 -1.12237  1.40139 -1.63484  1.81515 -1.93645  1.99479 -1.98828  1.91713 -1.78365  1.59219 -1.34896  1.06188 -0.74028  0.39461 -0.03611 -0.32356  0.67272 -1.00000  1.29477 -1.54745  1.74982 -1.89531  1.97917 -1.99870  1.95324 -1.84429  1.67537 -1.45199  1.18141 -0.87241  0.53506 -0.18031  0.00000     ... ... ..... ....... ......... ........... .............
E42     2.00000 -1.98828  1.95324 -1.89531  1.81515 -1.71371  1.59219 -1.45199  1.29477 -1.12237  0.93682 -0.74028  0.53506 -0.32356  0.10828  0.10828 -0.32356  0.53506 -0.74028  0.93682 -1.12237  1.29477 -1.45199  1.59219 -1.71371  1.81515 -1.89531  1.95324 -1.98828  2.00000 -1.98828  1.95324 -1.89531  1.81515 -1.71371  1.59219 -1.45199  1.29477 -1.12237  0.93682 -0.74028  0.53506 -0.32356  0.10828  0.00000     ... ... ..... ....... ......... ........... .............
E43     2.00000 -1.99870  1.99479 -1.98828  1.97917 -1.96749  1.95324 -1.93645  1.91713 -1.89531  1.87102 -1.84429  1.81515 -1.78365  1.74982 -1.71371  1.67537 -1.63484  1.59219 -1.54745  1.50070 -1.45199  1.40139 -1.34896  1.29477 -1.23890  1.18141 -1.12237  1.06188 -1.00000  0.93682 -0.87241  0.80687 -0.74028  0.67272 -0.60428  0.53506 -0.46513  0.39461 -0.32356  0.25210 -0.18031  0.10828 -0.03611  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.994786463036 = 2*cos(2*π/87)
                               1.979173033111 = 2*cos(4*π/87)
                               1.953241111420 = 2*cos(6*π/87) = 2*cos(2*π/29)
                               1.917125894995 = 2*cos(8*π/87)
                               1.871015671851 = 2*cos(10*π/87)
                               1.815150839342 = 2*cos(12*π/87) = 2*cos(4*π/29)
                               1.749822650836 = 2*cos(14*π/87)
                               1.675371697260 = 2*cos(16*π/87)
                               1.592186131411 = 2*cos(18*π/87) = 2*cos(6*π/29)
                               1.500699644313 = 2*cos(20*π/87)
                               1.401389204147 = 2*cos(22*π/87)
                               1.294772569564 = 2*cos(24*π/87) = 2*cos(8*π/29)
                               1.181405590329 = 2*cos(26*π/87)
                               1.061879309380 = 2*cos(28*π/87)
                               0.936816881400 = 2*cos(30*π/87) = 2*cos(10*π/29)
                               0.806870323980 = 2*cos(32*π/87)
                               0.672717118300 = 2*cos(34*π/87)
                               0.535056677058 = 2*cos(36*π/87) = 2*cos(12*π/29)
                               0.394606698053 = 2*cos(38*π/87)
                               0.252099422441 = 2*cos(40*π/87)
                               0.108277817171 = 2*cos(42*π/87) = 2*cos(14*π/29)
                              -0.036108298501 = 2*cos(44*π/87)
                              -0.180306162224 = 2*cos(46*π/87)
                              -0.323563993106 = 2*cos(48*π/87) = 2*cos(16*π/29)
                              -0.465134911149 = 2*cos(50*π/87)
                              -0.604280831139 = 2*cos(52*π/87)
                              -0.740276310680 = 2*cos(54*π/87) = 2*cos(18*π/29)
                              -0.872412332311 = 2*cos(56*π/87)
                              -1.122374130725 = 2*cos(60*π/87) = 2*cos(20*π/29)
                              -1.238896722431 = 2*cos(62*π/87)
                              -1.348960280281 = 2*cos(64*π/87)
                              -1.451990983846 = 2*cos(66*π/87) = 2*cos(22*π/29)
                              -1.547451678746 = 2*cos(68*π/87)
                              -1.634844677118 = 2*cos(70*π/87)
                              -1.713714352335 = 2*cos(72*π/87) = 2*cos(24*π/29)
                              -1.783649514431 = 2*cos(74*π/87)
                              -1.844285553852 = 2*cos(76*π/87)
                              -1.895306342366 = 2*cos(78*π/87) = 2*cos(26*π/29)
                              -1.936445881205 = 2*cos(80*π/87)
                              -1.967489687864 = 2*cos(82*π/87)
                              -1.988275914309 = 2*cos(84*π/87) = 2*cos(28*π/29)
                              -1.998696190779 = 2*cos(86*π/87)



 Symmetry of Rotations and Cartesian products

A1   d+g+i+k+m              z2, z4, z6 
A2   R+p+f+h+j+l            Rz, z, z3, z5 
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 D87 point group is 174, and the order of the principal axis (C87) is 87. The group has 45 irreducible representations.

    β  The D87 point group is isomorphic to C87v.

    γ  The D87 point group is generated by two symmetry elements, C87 and a perpendicular C2.
       Also, the group may be generated from two C2 axes (some pairs will yield smaller groups, though; choosing a minimum angle is safe).

    δ  The group contains one set of C2 symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set.

    ε  The lowest nonvanishing multipole moment in D87 is 4 (quadrupole 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  The point group is chiral, as it does not contain any mirroring operation.

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

This Character Table for the D87 point group was created by Gernot Katzer.

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