Character Table for Point Group C119v

Character table for the C_119v point group

C119v E 2 C119 2 C119^2 2 C119^3 2 C119^4 2 C119^5 2 C119^6 2 C17 2 C119^8 2 C119^9 2 C119^10 2 C119^11 2 C119^12 2 C119^13 2 C17^2 2 C119^15 2 C119^16 2 C7 2 C119^18 2 C119^19 2 C119^20 2 C17^3 2 C119^22 2 C119^23 2 C119^24 2 C119^25 2 C119^26 2 C119^27 2 C17^4 2 C119^29 2 C119^30 2 C119^31 2 C119^32 2 C119^33 2 C7^2 2 C17^5 2 C119^36 2 C119^37 2 C119^38 2 C119^39 2 C119^40 2 C119^41 2 C17^6 2 C119^43 2 C119^44 2 C119^45 2 C119^46 2 C119^47 2 C119^48 2 C17^7 2 C119^50 2 C7^3 2 C119^52 2 C119^53 2 C119^54 2 C119^55 2 C17^8 2 C119^57 2 C119^58 2 C119^59 119 sv <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 ... ..T ....T ......T ........T ..........T ............T A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 ..T ... ..... ....... ......... ........... ............. E1 2.00000 1.99721 1.98886 1.97496 1.95556 1.93071 1.90047 1.86494 1.82422 1.77840 1.72763 1.67205 1.61180 1.54707 1.47802 1.40485 1.32776 1.24698 1.16272 1.07522 0.98472 0.89148 0.79575 0.69780 0.59791 0.49636 0.39342 0.28938 0.18454 0.07918 -0.02640 -0.13190 -0.23704 -0.34152 -0.44504 -0.54733 -0.64808 -0.74704 -0.84391 -0.93843 -1.03033 -1.11936 -1.20527 -1.28782 -1.36678 -1.44194 -1.51307 -1.57999 -1.64250 -1.70043 -1.75363 -1.80194 -1.84522 -1.88337 -1.91626 -1.94381 -1.96595 -1.98260 -1.99373 -1.99930 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.98886 1.95556 1.90047 1.82422 1.72763 1.61180 1.47802 1.32776 1.16272 0.98472 0.79575 0.59791 0.39342 0.18454 -0.02640 -0.23704 -0.44504 -0.64808 -0.84391 -1.03033 -1.20527 -1.36678 -1.51307 -1.64250 -1.75363 -1.84522 -1.91626 -1.96595 -1.99373 -1.99930 -1.98260 -1.94381 -1.88337 -1.80194 -1.70043 -1.57999 -1.44194 -1.28782 -1.11936 -0.93843 -0.74704 -0.54733 -0.34152 -0.13190 0.07918 0.28938 0.49636 0.69780 0.89148 1.07522 1.24698 1.40485 1.54707 1.67205 1.77840 1.86494 1.93071 1.97496 1.99721 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.97496 1.90047 1.77840 1.61180 1.40485 1.16272 0.89148 0.59791 0.28938 -0.02640 -0.34152 -0.64808 -0.93843 -1.20527 -1.44194 -1.64250 -1.80194 -1.91626 -1.98260 -1.99930 -1.96595 -1.88337 -1.75363 -1.57999 -1.36678 -1.11936 -0.84391 -0.54733 -0.23704 0.07918 0.39342 0.69780 0.98472 1.24698 1.47802 1.67205 1.82422 1.93071 1.98886 1.99721 1.95556 1.86494 1.72763 1.54707 1.32776 1.07522 0.79575 0.49636 0.18454 -0.13190 -0.44504 -0.74704 -1.03033 -1.28782 -1.51307 -1.70043 -1.84522 -1.94381 -1.99373 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.95556 1.82422 1.61180 1.32776 0.98472 0.59791 0.18454 -0.23704 -0.64808 -1.03033 -1.36678 -1.64250 -1.84522 -1.96595 -1.99930 -1.94381 -1.80194 -1.57999 -1.28782 -0.93843 -0.54733 -0.13190 0.28938 0.69780 1.07522 1.40485 1.67205 1.86494 1.97496 1.99721 1.93071 1.77840 1.54707 1.24698 0.89148 0.49636 0.07918 -0.34152 -0.74704 -1.11936 -1.44194 -1.70043 -1.88337 -1.98260 -1.99373 -1.91626 -1.75363 -1.51307 -1.20527 -0.84391 -0.44504 -0.02640 0.39342 0.79575 1.16272 1.47802 1.72763 1.90047 1.98886 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.93071 1.72763 1.40485 0.98472 0.49636 -0.02640 -0.54733 -1.03033 -1.44194 -1.75363 -1.94381 -1.99930 -1.91626 -1.70043 -1.36678 -0.93843 -0.44504 0.07918 0.59791 1.07522 1.47802 1.77840 1.95556 1.99721 1.90047 1.67205 1.32776 0.89148 0.39342 -0.13190 -0.64808 -1.11936 -1.51307 -1.80194 -1.96595 -1.99373 -1.88337 -1.64250 -1.28782 -0.84391 -0.34152 0.18454 0.69780 1.16272 1.54707 1.82422 1.97496 1.98886 1.86494 1.61180 1.24698 0.79575 0.28938 -0.23704 -0.74704 -1.20527 -1.57999 -1.84522 -1.98260 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.90047 1.61180 1.16272 0.59791 -0.02640 -0.64808 -1.20527 -1.64250 -1.91626 -1.99930 -1.88337 -1.57999 -1.11936 -0.54733 0.07918 0.69780 1.24698 1.67205 1.93071 1.99721 1.86494 1.54707 1.07522 0.49636 -0.13190 -0.74704 -1.28782 -1.70043 -1.94381 -1.99373 -1.84522 -1.51307 -1.03033 -0.44504 0.18454 0.79575 1.32776 1.72763 1.95556 1.98886 1.82422 1.47802 0.98472 0.39342 -0.23704 -0.84391 -1.36678 -1.75363 -1.96595 -1.98260 -1.80194 -1.44194 -0.93843 -0.34152 0.28938 0.89148 1.40485 1.77840 1.97496 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 -1.96595 -1.70043 -1.20527 -0.54733 0.18454 0.89148 1.47802 1.86494 2.00000 1.86494 1.47802 0.89148 0.18454 -0.54733 -1.20527 -1.70043 -1.96595 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.82422 1.32776 0.59791 -0.23704 -1.03033 -1.64250 -1.96595 -1.94381 -1.57999 -0.93843 -0.13190 0.69780 1.40485 1.86494 1.99721 1.77840 1.24698 0.49636 -0.34152 -1.11936 -1.70043 -1.98260 -1.91626 -1.51307 -0.84391 -0.02640 0.79575 1.47802 1.90047 1.98886 1.72763 1.16272 0.39342 -0.44504 -1.20527 -1.75363 -1.99373 -1.88337 -1.44194 -0.74704 0.07918 0.89148 1.54707 1.93071 1.97496 1.67205 1.07522 0.28938 -0.54733 -1.28782 -1.80194 -1.99930 -1.84522 -1.36678 -0.64808 0.18454 0.98472 1.61180 1.95556 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.77840 1.16272 0.28938 -0.64808 -1.44194 -1.91626 -1.96595 -1.57999 -0.84391 0.07918 0.98472 1.67205 1.98886 1.86494 1.32776 0.49636 -0.44504 -1.28782 -1.84522 -1.99373 -1.70043 -1.03033 -0.13190 0.79575 1.54707 1.95556 1.93071 1.47802 0.69780 -0.23704 -1.11936 -1.75363 -1.99930 -1.80194 -1.20527 -0.34152 0.59791 1.40485 1.90047 1.97496 1.61180 0.89148 -0.02640 -0.93843 -1.64250 -1.98260 -1.88337 -1.36678 -0.54733 0.39342 1.24698 1.82422 1.99721 1.72763 1.07522 0.18454 -0.74704 -1.51307 -1.94381 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.72763 0.98472 -0.02640 -1.03033 -1.75363 -1.99930 -1.70043 -0.93843 0.07918 1.07522 1.77840 1.99721 1.67205 0.89148 -0.13190 -1.11936 -1.80194 -1.99373 -1.64250 -0.84391 0.18454 1.16272 1.82422 1.98886 1.61180 0.79575 -0.23704 -1.20527 -1.84522 -1.98260 -1.57999 -0.74704 0.28938 1.24698 1.86494 1.97496 1.54707 0.69780 -0.34152 -1.28782 -1.88337 -1.96595 -1.51307 -0.64808 0.39342 1.32776 1.90047 1.95556 1.47802 0.59791 -0.44504 -1.36678 -1.91626 -1.94381 -1.44194 -0.54733 0.49636 1.40485 1.93071 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.67205 0.79575 -0.34152 -1.36678 -1.94381 -1.88337 -1.20527 -0.13190 0.98472 1.77840 1.98886 1.54707 0.59791 -0.54733 -1.51307 -1.98260 -1.80194 -1.03033 0.07918 1.16272 1.86494 1.95556 1.40485 0.39342 -0.74704 -1.64250 -1.99930 -1.70043 -0.84391 0.28938 1.32776 1.93071 1.90047 1.24698 0.18454 -0.93843 -1.75363 -1.99373 -1.57999 -0.64808 0.49636 1.47802 1.97496 1.82422 1.07522 -0.02640 -1.11936 -1.84522 -1.96595 -1.44194 -0.44504 0.69780 1.61180 1.99721 1.72763 0.89148 -0.23704 -1.28782 -1.91626 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.61180 0.59791 -0.64808 -1.64250 -1.99930 -1.57999 -0.54733 0.69780 1.67205 1.99721 1.54707 0.49636 -0.74704 -1.70043 -1.99373 -1.51307 -0.44504 0.79575 1.72763 1.98886 1.47802 0.39342 -0.84391 -1.75363 -1.98260 -1.44194 -0.34152 0.89148 1.77840 1.97496 1.40485 0.28938 -0.93843 -1.80194 -1.96595 -1.36678 -0.23704 0.98472 1.82422 1.95556 1.32776 0.18454 -1.03033 -1.84522 -1.94381 -1.28782 -0.13190 1.07522 1.86494 1.93071 1.24698 0.07918 -1.11936 -1.88337 -1.91626 -1.20527 -0.02640 1.16272 1.90047 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.54707 0.39342 -0.93843 -1.84522 -1.91626 -1.11936 0.18454 1.40485 1.98886 1.67205 0.59791 -0.74704 -1.75363 -1.96595 -1.28782 -0.02640 1.24698 1.95556 1.77840 0.79575 -0.54733 -1.64250 -1.99373 -1.44194 -0.23704 1.07522 1.90047 1.86494 0.98472 -0.34152 -1.51307 -1.99930 -1.57999 -0.44504 0.89148 1.82422 1.93071 1.16272 -0.13190 -1.36678 -1.98260 -1.70043 -0.64808 0.69780 1.72763 1.97496 1.32776 0.07918 -1.20527 -1.94381 -1.80194 -0.84391 0.49636 1.61180 1.99721 1.47802 0.28938 -1.03033 -1.88337 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 1.86494 0.89148 -0.54733 -1.70043 -1.96595 -1.20527 0.18454 1.47802 2.00000 1.47802 0.18454 -1.20527 -1.96595 -1.70043 -0.54733 0.89148 1.86494 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 1.40485 -0.02640 -1.44194 -1.99930 -1.36678 0.07918 1.47802 1.99721 1.32776 -0.13190 -1.51307 -1.99373 -1.28782 0.18454 1.54707 1.98886 1.24698 -0.23704 -1.57999 -1.98260 -1.20527 0.28938 1.61180 1.97496 1.16272 -0.34152 -1.64250 -1.96595 -1.11936 0.39342 1.67205 1.95556 1.07522 -0.44504 -1.70043 -1.94381 -1.03033 0.49636 1.72763 1.93071 0.98472 -0.54733 -1.75363 -1.91626 -0.93843 0.59791 1.77840 1.90047 0.89148 -0.64808 -1.80194 -1.88337 -0.84391 0.69780 1.82422 1.86494 0.79575 -0.74704 -1.84522 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 1.32776 -0.23704 -1.64250 -1.94381 -0.93843 0.69780 1.86494 1.77840 0.49636 -1.11936 -1.98260 -1.51307 -0.02640 1.47802 1.98886 1.16272 -0.44504 -1.75363 -1.88337 -0.74704 0.89148 1.93071 1.67205 0.28938 -1.28782 -1.99930 -1.36678 0.18454 1.61180 1.95556 0.98472 -0.64808 -1.84522 -1.80194 -0.54733 1.07522 1.97496 1.54707 0.07918 -1.44194 -1.99373 -1.20527 0.39342 1.72763 1.90047 0.79575 -0.84391 -1.91626 -1.70043 -0.34152 1.24698 1.99721 1.40485 -0.13190 -1.57999 -1.96595 -1.03033 0.59791 1.82422 0.00000 ... ... ..... ....... ......... ........... ............. E17 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 -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 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 1.16272 -0.64808 -1.91626 -1.57999 0.07918 1.67205 1.86494 0.49636 -1.28782 -1.99373 -1.03033 0.79575 1.95556 1.47802 -0.23704 -1.75363 -1.80194 -0.34152 1.40485 1.97496 0.89148 -0.93843 -1.98260 -1.36678 0.39342 1.82422 1.72763 0.18454 -1.51307 -1.94381 -0.74704 1.07522 1.99721 1.24698 -0.54733 -1.88337 -1.64250 -0.02640 1.61180 1.90047 0.59791 -1.20527 -1.99930 -1.11936 0.69780 1.93071 1.54707 -0.13190 -1.70043 -1.84522 -0.44504 1.32776 1.98886 0.98472 -0.84391 -1.96595 -1.44194 0.28938 1.77840 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 1.07522 -0.84391 -1.98260 -1.28782 0.59791 1.93071 1.47802 -0.34152 -1.84522 -1.64250 0.07918 1.72763 1.77840 0.18454 -1.57999 -1.88337 -0.44504 1.40485 1.95556 0.69780 -1.20527 -1.99373 -0.93843 0.98472 1.99721 1.16272 -0.74704 -1.96595 -1.36678 0.49636 1.90047 1.54707 -0.23704 -1.80194 -1.70043 -0.02640 1.67205 1.82422 0.28938 -1.51307 -1.91626 -0.54733 1.32776 1.97496 0.79575 -1.11936 -1.99930 -1.03033 0.89148 1.98886 1.24698 -0.64808 -1.94381 -1.44194 0.39342 1.86494 1.61180 -0.13190 -1.75363 0.00000 ... ... ..... ....... ......... ........... ............. E20 2.00000 0.98472 -1.03033 -1.99930 -0.93843 1.07522 1.99721 0.89148 -1.11936 -1.99373 -0.84391 1.16272 1.98886 0.79575 -1.20527 -1.98260 -0.74704 1.24698 1.97496 0.69780 -1.28782 -1.96595 -0.64808 1.32776 1.95556 0.59791 -1.36678 -1.94381 -0.54733 1.40485 1.93071 0.49636 -1.44194 -1.91626 -0.44504 1.47802 1.90047 0.39342 -1.51307 -1.88337 -0.34152 1.54707 1.86494 0.28938 -1.57999 -1.84522 -0.23704 1.61180 1.82422 0.18454 -1.64250 -1.80194 -0.13190 1.67205 1.77840 0.07918 -1.70043 -1.75363 -0.02640 1.72763 0.00000 ... ... ..... ....... ......... ........... ............. E21 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 -1.70043 0.18454 1.86494 1.47802 -0.54733 -1.96595 -1.20527 0.89148 2.00000 0.89148 -1.20527 -1.96595 -0.54733 1.47802 1.86494 0.18454 -1.70043 0.00000 ... ... ..... ....... ......... ........... ............. E22 2.00000 0.79575 -1.36678 -1.88337 -0.13190 1.77840 1.54707 -0.54733 -1.98260 -1.03033 1.16272 1.95556 0.39342 -1.64250 -1.70043 0.28938 1.93071 1.24698 -0.93843 -1.99373 -0.64808 1.47802 1.82422 -0.02640 -1.84522 -1.44194 0.69780 1.99721 0.89148 -1.28782 -1.91626 -0.23704 1.72763 1.61180 -0.44504 -1.96595 -1.11936 1.07522 1.97496 0.49636 -1.57999 -1.75363 0.18454 1.90047 1.32776 -0.84391 -1.99930 -0.74704 1.40485 1.86494 0.07918 -1.80194 -1.51307 0.59791 1.98886 0.98472 -1.20527 -1.94381 -0.34152 1.67205 0.00000 ... ... ..... ....... ......... ........... ............. E23 2.00000 0.69780 -1.51307 -1.75363 0.28938 1.95556 1.07522 -1.20527 -1.91626 -0.13190 1.82422 1.40485 -0.84391 -1.99373 -0.54733 1.61180 1.67205 -0.44504 -1.98260 -0.93843 1.32776 1.86494 -0.02640 -1.88337 -1.28782 0.98472 1.97496 0.39342 -1.70043 -1.57999 0.59791 1.99721 0.79575 -1.44194 -1.80194 0.18454 1.93071 1.16272 -1.11936 -1.94381 -0.23704 1.77840 1.47802 -0.74704 -1.99930 -0.64808 1.54707 1.72763 -0.34152 -1.96595 -1.03033 1.24698 1.90047 0.07918 -1.84522 -1.36678 0.89148 1.98886 0.49636 -1.64250 0.00000 ... ... ..... ....... ......... ........... ............. 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E51 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 -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 0.00000 ... ... ..... ....... ......... ........... ............. E52 2.00000 -1.84522 1.40485 -0.74704 -0.02640 0.79575 -1.44194 1.86494 -1.99930 1.82422 -1.36678 0.69780 0.07918 -0.84391 1.47802 -1.88337 1.99721 -1.80194 1.32776 -0.64808 -0.13190 0.89148 -1.51307 1.90047 -1.99373 1.77840 -1.28782 0.59791 0.18454 -0.93843 1.54707 -1.91626 1.98886 -1.75363 1.24698 -0.54733 -0.23704 0.98472 -1.57999 1.93071 -1.98260 1.72763 -1.20527 0.49636 0.28938 -1.03033 1.61180 -1.94381 1.97496 -1.70043 1.16272 -0.44504 -0.34152 1.07522 -1.64250 1.95556 -1.96595 1.67205 -1.11936 0.39342 0.00000 ... ... ..... ....... ......... ........... ............. E53 2.00000 -1.88337 1.54707 -1.03033 0.39342 0.28938 -0.93843 1.47802 -1.84522 1.99721 -1.91626 1.61180 -1.11936 0.49636 0.18454 -0.84391 1.40485 -1.80194 1.98886 -1.94381 1.67205 -1.20527 0.59791 0.07918 -0.74704 1.32776 -1.75363 1.97496 -1.96595 1.72763 -1.28782 0.69780 -0.02640 -0.64808 1.24698 -1.70043 1.95556 -1.98260 1.77840 -1.36678 0.79575 -0.13190 -0.54733 1.16272 -1.64250 1.93071 -1.99373 1.82422 -1.44194 0.89148 -0.23704 -0.44504 1.07522 -1.57999 1.90047 -1.99930 1.86494 -1.51307 0.98472 -0.34152 0.00000 ... ... ..... ....... ......... ........... ............. E54 2.00000 -1.91626 1.67205 -1.28782 0.79575 -0.23704 -0.34152 0.89148 -1.36678 1.72763 -1.94381 1.99721 -1.88337 1.61180 -1.20527 0.69780 -0.13190 -0.44504 0.98472 -1.44194 1.77840 -1.96595 1.98886 -1.84522 1.54707 -1.11936 0.59791 -0.02640 -0.54733 1.07522 -1.51307 1.82422 -1.98260 1.97496 -1.80194 1.47802 -1.03033 0.49636 0.07918 -0.64808 1.16272 -1.57999 1.86494 -1.99373 1.95556 -1.75363 1.40485 -0.93843 0.39342 0.18454 -0.74704 1.24698 -1.64250 1.90047 -1.99930 1.93071 -1.70043 1.32776 -0.84391 0.28938 0.00000 ... ... ..... ....... ......... ........... ............. E55 2.00000 -1.94381 1.77840 -1.51307 1.16272 -0.74704 0.28938 0.18454 -0.64808 1.07522 -1.44194 1.72763 -1.91626 1.99721 -1.96595 1.82422 -1.57999 1.24698 -0.84391 0.39342 0.07918 -0.54733 0.98472 -1.36678 1.67205 -1.88337 1.98886 -1.98260 1.86494 -1.64250 1.32776 -0.93843 0.49636 -0.02640 -0.44504 0.89148 -1.28782 1.61180 -1.84522 1.97496 -1.99373 1.90047 -1.70043 1.40485 -1.03033 0.59791 -0.13190 -0.34152 0.79575 -1.20527 1.54707 -1.80194 1.95556 -1.99930 1.93071 -1.75363 1.47802 -1.11936 0.69780 -0.23704 0.00000 ... ... ..... ....... ......... ........... ............. E56 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.18454 -0.54733 0.89148 -1.20527 1.47802 -1.70043 1.86494 -1.96595 2.00000 -1.96595 1.86494 -1.70043 1.47802 -1.20527 0.89148 -0.54733 0.18454 0.00000 ... ... ..... ....... ......... ........... ............. E57 2.00000 -1.98260 1.93071 -1.84522 1.72763 -1.57999 1.40485 -1.20527 0.98472 -0.74704 0.49636 -0.23704 -0.02640 0.28938 -0.54733 0.79575 -1.03033 1.24698 -1.44194 1.61180 -1.75363 1.86494 -1.94381 1.98886 -1.99930 1.97496 -1.91626 1.82422 -1.70043 1.54707 -1.36678 1.16272 -0.93843 0.69780 -0.44504 0.18454 0.07918 -0.34152 0.59791 -0.84391 1.07522 -1.28782 1.47802 -1.64250 1.77840 -1.88337 1.95556 -1.99373 1.99721 -1.96595 1.90047 -1.80194 1.67205 -1.51307 1.32776 -1.11936 0.89148 -0.64808 0.39342 -0.13190 0.00000 ... ... ..... ....... ......... ........... ............. E58 2.00000 -1.99373 1.97496 -1.94381 1.90047 -1.84522 1.77840 -1.70043 1.61180 -1.51307 1.40485 -1.28782 1.16272 -1.03033 0.89148 -0.74704 0.59791 -0.44504 0.28938 -0.13190 -0.02640 0.18454 -0.34152 0.49636 -0.64808 0.79575 -0.93843 1.07522 -1.20527 1.32776 -1.44194 1.54707 -1.64250 1.72763 -1.80194 1.86494 -1.91626 1.95556 -1.98260 1.99721 -1.99930 1.98886 -1.96595 1.93071 -1.88337 1.82422 -1.75363 1.67205 -1.57999 1.47802 -1.36678 1.24698 -1.11936 0.98472 -0.84391 0.69780 -0.54733 0.39342 -0.23704 0.07918 0.00000 ... ... ..... ....... ......... ........... ............. E59 2.00000 -1.99930 1.99721 -1.99373 1.98886 -1.98260 1.97496 -1.96595 1.95556 -1.94381 1.93071 -1.91626 1.90047 -1.88337 1.86494 -1.84522 1.82422 -1.80194 1.77840 -1.75363 1.72763 -1.70043 1.67205 -1.64250 1.61180 -1.57999 1.54707 -1.51307 1.47802 -1.44194 1.40485 -1.36678 1.32776 -1.28782 1.24698 -1.20527 1.16272 -1.11936 1.07522 -1.03033 0.98472 -0.93843 0.89148 -0.84391 0.79575 -0.74704 0.69780 -0.64808 0.59791 -0.54733 0.49636 -0.44504 0.39342 -0.34152 0.28938 -0.23704 0.18454 -0.13190 0.07918 -0.02640 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.997212820643 = 2*cos(2*π/119) 1.988859050941 = 2*cos(4*π/119) 1.974961974348 = 2*cos(6*π/119) 1.955560324510 = 2*cos(8*π/119) 1.930708177304 = 2*cos(10*π/119) 1.900474800122 = 2*cos(12*π/119) 1.864944458809 = 2*cos(14*π/119) = 2*cos(2*π/17) = (−1+√17+√34−2*√17+2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 1.824216182798 = 2*cos(16*π/119) 1.778403489100 = 2*cos(18*π/119) 1.727634065909 = 2*cos(20*π/119) 1.672049416713 = 2*cos(22*π/119) 1.611804465899 = 2*cos(24*π/119) 1.547067126950 = 2*cos(26*π/119) 1.478017834441 = 2*cos(28*π/119) = 2*cos(4*π/17) = (−1+√17−√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 1.404849041135 = 2*cos(30*π/119) 1.327764681582 = 2*cos(32*π/119) 1.246979603717 = 2*cos(34*π/119) = 2*cos(2*π/7) 1.162718970043 = 2*cos(36*π/119) 1.075217630057 = 2*cos(38*π/119) 0.984719465689 = 2*cos(40*π/119) 0.891476711553 = 2*cos(42*π/119) = 2*cos(6*π/17) = (−1−√17+√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 0.795749251930 = 2*cos(44*π/119) 0.697803896418 = 2*cos(46*π/119) 0.597913636292 = 2*cos(48*π/119) 0.496356883620 = 2*cos(50*π/119) 0.393416695290 = 2*cos(52*π/119) 0.289379984067 = 2*cos(54*π/119) 0.184536718927 = 2*cos(56*π/119) = 2*cos(8*π/17) = (−1+√17+√34−2*√17−2*√17+3*√17−√34−2*√17−2*√34+2*√17)/8 0.079179116853 = 2*cos(58*π/119) -0.026399171622 = 2*cos(60*π/119) -0.131903880869 = 2*cos(62*π/119) -0.237040950343 = 2*cos(64*π/119) -0.341517344174 = 2*cos(66*π/119) -0.445041867913 = 2*cos(68*π/119) = 2*cos(4*π/7) -0.547325980144 = 2*cos(70*π/119) = 2*cos(10*π/17) = −(1+√17−√34+2*√17+2*√17−3*√17−√34+2*√17+2*√34−2*√17)/8 -0.648084596702 = 2*cos(72*π/119) -0.747036885251 = 2*cos(74*π/119) -0.843907048014 = 2*cos(76*π/119) -0.938425090474 = 2*cos(78*π/119) -1.030327573894 = 2*cos(80*π/119) -1.119358349569 = 2*cos(82*π/119) -1.205269272759 = 2*cos(84*π/119) = 2*cos(12*π/17) = −(1+√17+√34+2*√17−2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 -1.287820894312 = 2*cos(86*π/119) -1.366783128053 = 2*cos(88*π/119) -1.441935892074 = 2*cos(90*π/119) -1.513069722143 = 2*cos(92*π/119) -1.579986355517 = 2*cos(94*π/119) -1.642499283537 = 2*cos(96*π/119) -1.700434271459 = 2*cos(98*π/119) = 2*cos(14*π/17) = −(1+√17+√34+2*√17+2*√17−3*√17+√34+2*√17−2*√34−2*√17)/8 -1.753629844083 = 2*cos(100*π/119) -1.801937735805 = 2*cos(102*π/119) = 2*cos(6*π/7) -1.845223303867 = 2*cos(104*π/119) -1.883365903628 = 2*cos(106*π/119) -1.916259224821 = 2*cos(108*π/119) -1.943811587860 = 2*cos(110*π/119) -1.965946199368 = 2*cos(112*π/119) = 2*cos(16*π/17) = −(1−√17+√34−2*√17+2*√17+3*√17+√34−2*√17+2*√34+2*√17)/8 -1.982601366212 = 2*cos(114*π/119) -1.993730667454 = 2*cos(116*π/119) -1.999303083738 = 2*cos(118*π/119) 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 R_z E1 R+p+d+f+g+h+i+j+k+l+m {R_x, R_y}, {x, y}, {xz, yz}, {xz², yz²}, {xz³, yz³}, {xz⁴, yz⁴}, {xz⁵, yz⁵} E2 d+f+g+h+i+j+k+l+m {x²−y², xy}, {z(x²−y²), xyz}, {z²(x²−y²), xyz²}, {z³(x²−y²), xyz³}, {z⁴(x²−y²), xyz⁴} E3 f+g+h+i+j+k+l+m {x(x²−3y²), y(3x²−y²)}, {xz(x²−3y²), yz(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4 g+h+i+j+k+l+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z((x²−y²)²−4x²y²), xyz(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E5 h+i+j+k+l+m {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)}, {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6 i+j+k+l+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+k+l+m E8 k+l+m E9 l+m E10 m Notes: α The order of the C_119v point group is 238, and the order of the principal axis (C₁₁₉) is 119. The group has 61 irreducible representations. β The C_119v point group is isomorphic to D₁₁₉. γ The C_119v point group is generated by two symmetry elements, C₁₁₉ and any σ_v. Also, the group may be generated from two σ_v planes (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The lowest nonvanishing multipole moment in C_119v is 2 (dipole moment). ε This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. 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 much less than half the order of the principal axis. η 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. θ That a regular 17-gon can be constructed with compass and ruler was unknown to mathematicians until Gauss proved it in 1796. The first actual construction was performed thirty years later by Johannes Erchinger in 1825.

This Character Table for the C_119v point group was created by Gernot Katzer.

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

	C_117v
	C_118v
C₁₁₉	C_119v	C_119h D₁₁₉ D_119h D_119d
	C_120v
	C_121v

Character table for the C119v point group

Character table for the C_119v point group