Character table for the C70v point group

C70v    E        2 C70    2 C35    2 C70^3  2 C35^2  2 C14    2 C35^3  2 C10    2 C35^4  2 C70^9  2 C7     2 C70^11 2 C35^6  2 C70^13 2 C5     2 C14^3  2 C35^8  2 C70^17 2 C35^9  2 C70^19 2 C7^2   2 C10^3  2 C35^11 2 C70^23 2 C35^12 2 C14^5  2 C35^13 2 C70^27 2 C5^2   2 C70^29 2 C7^3   2 C70^31 2 C35^16 2 C70^33 2 C35^17 C2       35 sv    35 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     ... ..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     ..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     ... ... ..... ....... ......... ........... .............
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     ... ... ..... ....... ......... ........... .............
E1      2.00000  1.99195  1.96786  1.92793  1.87247  1.80194  1.71690  1.61803  1.50614  1.38213  1.24698  1.10179  0.94774  0.78605  0.61803  0.44504  0.26847  0.08973 -0.08973 -0.26847 -0.44504 -0.61803 -0.78605 -0.94774 -1.10179 -1.24698 -1.38213 -1.50614 -1.61803 -1.71690 -1.80194 -1.87247 -1.92793 -1.96786 -1.99195 -2.00000  0.00000  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.96786  1.87247  1.71690  1.50614  1.24698  0.94774  0.61803  0.26847 -0.08973 -0.44504 -0.78605 -1.10179 -1.38213 -1.61803 -1.80194 -1.92793 -1.99195 -1.99195 -1.92793 -1.80194 -1.61803 -1.38213 -1.10179 -0.78605 -0.44504 -0.08973  0.26847  0.61803  0.94774  1.24698  1.50614  1.71690  1.87247  1.96786  2.00000  0.00000  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.92793  1.71690  1.38213  0.94774  0.44504 -0.08973 -0.61803 -1.10179 -1.50614 -1.80194 -1.96786 -1.99195 -1.87247 -1.61803 -1.24698 -0.78605 -0.26847  0.26847  0.78605  1.24698  1.61803  1.87247  1.99195  1.96786  1.80194  1.50614  1.10179  0.61803  0.08973 -0.44504 -0.94774 -1.38213 -1.71690 -1.92793 -2.00000  0.00000  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.87247  1.50614  0.94774  0.26847 -0.44504 -1.10179 -1.61803 -1.92793 -1.99195 -1.80194 -1.38213 -0.78605 -0.08973  0.61803  1.24698  1.71690  1.96786  1.96786  1.71690  1.24698  0.61803 -0.08973 -0.78605 -1.38213 -1.80194 -1.99195 -1.92793 -1.61803 -1.10179 -0.44504  0.26847  0.94774  1.50614  1.87247  2.00000  0.00000  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      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  0.00000  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.71690  0.94774 -0.08973 -1.10179 -1.80194 -1.99195 -1.61803 -0.78605  0.26847  1.24698  1.87247  1.96786  1.50614  0.61803 -0.44504 -1.38213 -1.92793 -1.92793 -1.38213 -0.44504  0.61803  1.50614  1.96786  1.87247  1.24698  0.26847 -0.78605 -1.61803 -1.99195 -1.80194 -1.10179 -0.08973  0.94774  1.71690  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.61803  0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803  0.61803  1.61803  2.00000  1.61803  0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803  0.61803  1.61803  2.00000  1.61803  0.61803 -0.61803 -1.61803 -2.00000 -1.61803 -0.61803  0.61803  1.61803  2.00000  1.61803  0.61803 -0.61803 -1.61803 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.50614  0.26847 -1.10179 -1.92793 -1.80194 -0.78605  0.61803  1.71690  1.96786  1.24698 -0.08973 -1.38213 -1.99195 -1.61803 -0.44504  0.94774  1.87247  1.87247  0.94774 -0.44504 -1.61803 -1.99195 -1.38213 -0.08973  1.24698  1.96786  1.71690  0.61803 -0.78605 -1.80194 -1.92793 -1.10179  0.26847  1.50614  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.38213 -0.08973 -1.50614 -1.99195 -1.24698  0.26847  1.61803  1.96786  1.10179 -0.44504 -1.71690 -1.92793 -0.94774  0.61803  1.80194  1.87247  0.78605 -0.78605 -1.87247 -1.80194 -0.61803  0.94774  1.92793  1.71690  0.44504 -1.10179 -1.96786 -1.61803 -0.26847  1.24698  1.99195  1.50614  0.08973 -1.38213 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10     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  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.10179 -0.78605 -1.96786 -1.38213  0.44504  1.87247  1.61803 -0.08973 -1.71690 -1.80194 -0.26847  1.50614  1.92793  0.61803 -1.24698 -1.99195 -0.94774  0.94774  1.99195  1.24698 -0.61803 -1.92793 -1.50614  0.26847  1.80194  1.71690  0.08973 -1.61803 -1.87247 -0.44504  1.38213  1.96786  0.78605 -1.10179 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  0.94774 -1.10179 -1.99195 -0.78605  1.24698  1.96786  0.61803 -1.38213 -1.92793 -0.44504  1.50614  1.87247  0.26847 -1.61803 -1.80194 -0.08973  1.71690  1.71690 -0.08973 -1.80194 -1.61803  0.26847  1.87247  1.50614 -0.44504 -1.92793 -1.38213  0.61803  1.96786  1.24698 -0.78605 -1.99195 -1.10179  0.94774  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  0.78605 -1.38213 -1.87247 -0.08973  1.80194  1.50614 -0.61803 -1.99195 -0.94774  1.24698  1.92793  0.26847 -1.71690 -1.61803  0.44504  1.96786  1.10179 -1.10179 -1.96786 -0.44504  1.61803  1.71690 -0.26847 -1.92793 -1.24698  0.94774  1.99195  0.61803 -1.50614 -1.80194  0.08973  1.87247  1.38213 -0.78605 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.61803 -1.61803 -1.61803  0.61803  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15     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  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  0.26847 -1.92793 -0.78605  1.71690  1.24698 -1.38213 -1.61803  0.94774  1.87247 -0.44504 -1.99195 -0.08973  1.96786  0.61803 -1.80194 -1.10179  1.50614  1.50614 -1.10179 -1.80194  0.61803  1.96786 -0.08973 -1.99195 -0.44504  1.87247  0.94774 -1.61803 -1.38213  1.24698  1.71690 -0.78605 -1.92793  0.26847  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.08973 -1.99195 -0.26847  1.96786  0.44504 -1.92793 -0.61803  1.87247  0.78605 -1.80194 -0.94774  1.71690  1.10179 -1.61803 -1.24698  1.50614  1.38213 -1.38213 -1.50614  1.24698  1.61803 -1.10179 -1.71690  0.94774  1.80194 -0.78605 -1.87247  0.61803  1.92793 -0.44504 -1.96786  0.26847  1.99195 -0.08973 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000 -0.08973 -1.99195  0.26847  1.96786 -0.44504 -1.92793  0.61803  1.87247 -0.78605 -1.80194  0.94774  1.71690 -1.10179 -1.61803  1.24698  1.50614 -1.38213 -1.38213  1.50614  1.24698 -1.61803 -1.10179  1.71690  0.94774 -1.80194 -0.78605  1.87247  0.61803 -1.92793 -0.44504  1.96786  0.26847 -1.99195 -0.08973  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000 -0.26847 -1.92793  0.78605  1.71690 -1.24698 -1.38213  1.61803  0.94774 -1.87247 -0.44504  1.99195 -0.08973 -1.96786  0.61803  1.80194 -1.10179 -1.50614  1.50614  1.10179 -1.80194 -0.61803  1.96786  0.08973 -1.99195  0.44504  1.87247 -0.94774 -1.61803  1.38213  1.24698 -1.71690 -0.78605  1.92793  0.26847 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E20     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  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000 -0.61803 -1.61803  1.61803  0.61803 -2.00000  0.61803  1.61803 -1.61803 -0.61803  2.00000 -0.61803 -1.61803  1.61803  0.61803 -2.00000  0.61803  1.61803 -1.61803 -0.61803  2.00000 -0.61803 -1.61803  1.61803  0.61803 -2.00000  0.61803  1.61803 -1.61803 -0.61803  2.00000 -0.61803 -1.61803  1.61803  0.61803 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000 -0.78605 -1.38213  1.87247 -0.08973 -1.80194  1.50614  0.61803 -1.99195  0.94774  1.24698 -1.92793  0.26847  1.71690 -1.61803 -0.44504  1.96786 -1.10179 -1.10179  1.96786 -0.44504 -1.61803  1.71690  0.26847 -1.92793  1.24698  0.94774 -1.99195  0.61803  1.50614 -1.80194 -0.08973  1.87247 -1.38213 -0.78605  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000 -0.94774 -1.10179  1.99195 -0.78605 -1.24698  1.96786 -0.61803 -1.38213  1.92793 -0.44504 -1.50614  1.87247 -0.26847 -1.61803  1.80194 -0.08973 -1.71690  1.71690  0.08973 -1.80194  1.61803  0.26847 -1.87247  1.50614  0.44504 -1.92793  1.38213  0.61803 -1.96786  1.24698  0.78605 -1.99195  1.10179  0.94774 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000 -1.10179 -0.78605  1.96786 -1.38213 -0.44504  1.87247 -1.61803 -0.08973  1.71690 -1.80194  0.26847  1.50614 -1.92793  0.61803  1.24698 -1.99195  0.94774  0.94774 -1.99195  1.24698  0.61803 -1.92793  1.50614  0.26847 -1.80194  1.71690 -0.08973 -1.61803  1.87247 -0.44504 -1.38213  1.96786 -0.78605 -1.10179  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E25     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  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -1.38213 -0.08973  1.50614 -1.99195  1.24698  0.26847 -1.61803  1.96786 -1.10179 -0.44504  1.71690 -1.92793  0.94774  0.61803 -1.80194  1.87247 -0.78605 -0.78605  1.87247 -1.80194  0.61803  0.94774 -1.92793  1.71690 -0.44504 -1.10179  1.96786 -1.61803  0.26847  1.24698 -1.99195  1.50614 -0.08973 -1.38213  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -1.50614  0.26847  1.10179 -1.92793  1.80194 -0.78605 -0.61803  1.71690 -1.96786  1.24698  0.08973 -1.38213  1.99195 -1.61803  0.44504  0.94774 -1.87247  1.87247 -0.94774 -0.44504  1.61803 -1.99195  1.38213 -0.08973 -1.24698  1.96786 -1.71690  0.61803  0.78605 -1.80194  1.92793 -1.10179 -0.26847  1.50614 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000 -1.61803  0.61803  0.61803 -1.61803  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -1.71690  0.94774  0.08973 -1.10179  1.80194 -1.99195  1.61803 -0.78605 -0.26847  1.24698 -1.87247  1.96786 -1.50614  0.61803  0.44504 -1.38213  1.92793 -1.92793  1.38213 -0.44504 -0.61803  1.50614 -1.96786  1.87247 -1.24698  0.26847  0.78605 -1.61803  1.99195 -1.80194  1.10179 -0.08973 -0.94774  1.71690 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E30     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  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -1.87247  1.50614 -0.94774  0.26847  0.44504 -1.10179  1.61803 -1.92793  1.99195 -1.80194  1.38213 -0.78605  0.08973  0.61803 -1.24698  1.71690 -1.96786  1.96786 -1.71690  1.24698 -0.61803 -0.08973  0.78605 -1.38213  1.80194 -1.99195  1.92793 -1.61803  1.10179 -0.44504 -0.26847  0.94774 -1.50614  1.87247 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -1.92793  1.71690 -1.38213  0.94774 -0.44504 -0.08973  0.61803 -1.10179  1.50614 -1.80194  1.96786 -1.99195  1.87247 -1.61803  1.24698 -0.78605  0.26847  0.26847 -0.78605  1.24698 -1.61803  1.87247 -1.99195  1.96786 -1.80194  1.50614 -1.10179  0.61803 -0.08973 -0.44504  0.94774 -1.38213  1.71690 -1.92793  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.96786  1.87247 -1.71690  1.50614 -1.24698  0.94774 -0.61803  0.26847  0.08973 -0.44504  0.78605 -1.10179  1.38213 -1.61803  1.80194 -1.92793  1.99195 -1.99195  1.92793 -1.80194  1.61803 -1.38213  1.10179 -0.78605  0.44504 -0.08973 -0.26847  0.61803 -0.94774  1.24698 -1.50614  1.71690 -1.87247  1.96786 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.99195  1.96786 -1.92793  1.87247 -1.80194  1.71690 -1.61803  1.50614 -1.38213  1.24698 -1.10179  0.94774 -0.78605  0.61803 -0.44504  0.26847 -0.08973 -0.08973  0.26847 -0.44504  0.61803 -0.78605  0.94774 -1.10179  1.24698 -1.38213  1.50614 -1.61803  1.71690 -1.80194  1.87247 -1.92793  1.96786 -1.99195  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.991948587990 = 2*cos(2*π/70) = 2*cos(π/35)
                               1.967859177197 = 2*cos(4*π/70) = 2*cos(2*π/35)
                               1.927925721392 = 2*cos(6*π/70) = 2*cos(3*π/35)
                               1.872469741279 = 2*cos(8*π/70) = 2*cos(4*π/35)
                               1.801937735805 = 2*cos(10*π/70) = 2*cos(π/7)
                               1.716897587204 = 2*cos(12*π/70) = 2*cos(6*π/35)
                               1.618033988750 = 2*cos(14*π/70) = 2*cos(π/5) = (√5+1)/2
                               1.506142932007 = 2*cos(16*π/70) = 2*cos(8*π/35)
                               1.382125297974 = 2*cos(18*π/70) = 2*cos(9*π/35)
                               1.246979603717 = 2*cos(20*π/70) = 2*cos(2*π/7)
                               1.101793962904 = 2*cos(22*π/70) = 2*cos(11*π/35)
                               0.947737324946 = 2*cos(24*π/70) = 2*cos(12*π/35)
                               0.786050063308 = 2*cos(26*π/70) = 2*cos(13*π/35)
                               0.618033988750 = 2*cos(28*π/70) = 2*cos(2*π/5) = (√5−1)/2
                               0.445041867913 = 2*cos(30*π/70) = 2*cos(3*π/7)
                               0.268466531635 = 2*cos(32*π/70) = 2*cos(16*π/35)
                               0.089729660701 = 2*cos(34*π/70) = 2*cos(17*π/35)



 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 C70v point group is 140, and the order of the principal axis (C70) is 70. The group has 38 irreducible representations.

    β  The C70v point group is isomorphic to D35d, D35h and D70.

    γ  The C70v point group is generated by two symmetry elements, C70 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 C70v 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.
       While some characters of this group can be expressed using real integers and square roots alone, others need complex numbers and third roots.

This Character Table for the C70v point group was created by Gernot Katzer.

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