Character Table for Point Group C89v

Character table for the C_89v point group

C89v E 2 C89 2 C89^2 2 C89^3 2 C89^4 2 C89^5 2 C89^6 2 C89^7 2 C89^8 2 C89^9 2 C89^10 2 C89^11 2 C89^12 2 C89^13 2 C89^14 2 C89^15 2 C89^16 2 C89^17 2 C89^18 2 C89^19 2 C89^20 2 C89^21 2 C89^22 2 C89^23 2 C89^24 2 C89^25 2 C89^26 2 C89^27 2 C89^28 2 C89^29 2 C89^30 2 C89^31 2 C89^32 2 C89^33 2 C89^34 2 C89^35 2 C89^36 2 C89^37 2 C89^38 2 C89^39 2 C89^40 2 C89^41 2 C89^42 2 C89^43 2 C89^44 89 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 ... ..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 ..T ... ..... ....... ......... ........... ............. E1 2.00000 1.99502 1.98010 1.95531 1.92078 1.87669 1.82324 1.76071 1.68941 1.60969 1.52196 1.42664 1.32421 1.21519 1.10011 0.97955 0.85411 0.72442 0.59112 0.45487 0.31635 0.17626 0.03530 -0.10585 -0.24646 -0.38585 -0.52332 -0.65818 -0.78976 -0.91740 -1.04048 -1.15837 -1.27049 -1.37628 -1.47522 -1.56680 -1.65058 -1.72614 -1.79309 -1.85112 -1.89992 -1.93926 -1.96893 -1.98880 -1.99875 0.00000 TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT. E2 2.00000 1.98010 1.92078 1.82324 1.68941 1.52196 1.32421 1.10011 0.85411 0.59112 0.31635 0.03530 -0.24646 -0.52332 -0.78976 -1.04048 -1.27049 -1.47522 -1.65058 -1.79309 -1.89992 -1.96893 -1.99875 -1.98880 -1.93926 -1.85112 -1.72614 -1.56680 -1.37628 -1.15837 -0.91740 -0.65818 -0.38585 -0.10585 0.17626 0.45487 0.72442 0.97955 1.21519 1.42664 1.60969 1.76071 1.87669 1.95531 1.99502 0.00000 ... ... TT... ..TT... ....TT... ......TT... ........TT... E3 2.00000 1.95531 1.82324 1.60969 1.32421 0.97955 0.59112 0.17626 -0.24646 -0.65818 -1.04048 -1.37628 -1.65058 -1.85112 -1.96893 -1.99875 -1.93926 -1.79309 -1.56680 -1.27049 -0.91740 -0.52332 -0.10585 0.31635 0.72442 1.10011 1.42664 1.68941 1.87669 1.98010 1.99502 1.92078 1.76071 1.52196 1.21519 0.85411 0.45487 0.03530 -0.38585 -0.78976 -1.15837 -1.47522 -1.72614 -1.89992 -1.98880 0.00000 ... ... ..... TT..... ..TT..... ....TT..... ......TT..... E4 2.00000 1.92078 1.68941 1.32421 0.85411 0.31635 -0.24646 -0.78976 -1.27049 -1.65058 -1.89992 -1.99875 -1.93926 -1.72614 -1.37628 -0.91740 -0.38585 0.17626 0.72442 1.21519 1.60969 1.87669 1.99502 1.95531 1.76071 1.42664 0.97955 0.45487 -0.10585 -0.65818 -1.15837 -1.56680 -1.85112 -1.98880 -1.96893 -1.79309 -1.47522 -1.04048 -0.52332 0.03530 0.59112 1.10011 1.52196 1.82324 1.98010 0.00000 ... ... ..... ....... TT....... ..TT....... ....TT....... E5 2.00000 1.87669 1.52196 0.97955 0.31635 -0.38585 -1.04048 -1.56680 -1.89992 -1.99875 -1.85112 -1.47522 -0.91740 -0.24646 0.45487 1.10011 1.60969 1.92078 1.99502 1.82324 1.42664 0.85411 0.17626 -0.52332 -1.15837 -1.65058 -1.93926 -1.98880 -1.79309 -1.37628 -0.78976 -0.10585 0.59112 1.21519 1.68941 1.95531 1.98010 1.76071 1.32421 0.72442 0.03530 -0.65818 -1.27049 -1.72614 -1.96893 0.00000 ... ... ..... ....... ......... TT......... ..TT......... E6 2.00000 1.82324 1.32421 0.59112 -0.24646 -1.04048 -1.65058 -1.96893 -1.93926 -1.56680 -0.91740 -0.10585 0.72442 1.42664 1.87669 1.99502 1.76071 1.21519 0.45487 -0.38585 -1.15837 -1.72614 -1.98880 -1.89992 -1.47522 -0.78976 0.03530 0.85411 1.52196 1.92078 1.98010 1.68941 1.10011 0.31635 -0.52332 -1.27049 -1.79309 -1.99875 -1.85112 -1.37628 -0.65818 0.17626 0.97955 1.60969 1.95531 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.76071 1.10011 0.17626 -0.78976 -1.56680 -1.96893 -1.89992 -1.37628 -0.52332 0.45487 1.32421 1.87669 1.98010 1.60969 0.85411 -0.10585 -1.04048 -1.72614 -1.99875 -1.79309 -1.15837 -0.24646 0.72442 1.52196 1.95531 1.92078 1.42664 0.59112 -0.38585 -1.27049 -1.85112 -1.98880 -1.65058 -0.91740 0.03530 0.97955 1.68941 1.99502 1.82324 1.21519 0.31635 -0.65818 -1.47522 -1.93926 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.68941 0.85411 -0.24646 -1.27049 -1.89992 -1.93926 -1.37628 -0.38585 0.72442 1.60969 1.99502 1.76071 0.97955 -0.10585 -1.15837 -1.85112 -1.96893 -1.47522 -0.52332 0.59112 1.52196 1.98010 1.82324 1.10011 0.03530 -1.04048 -1.79309 -1.98880 -1.56680 -0.65818 0.45487 1.42664 1.95531 1.87669 1.21519 0.17626 -0.91740 -1.72614 -1.99875 -1.65058 -0.78976 0.31635 1.32421 1.92078 0.00000 ... ... ..... ....... ......... ........... ............. E9 2.00000 1.60969 0.59112 -0.65818 -1.65058 -1.99875 -1.56680 -0.52332 0.72442 1.68941 1.99502 1.52196 0.45487 -0.78976 -1.72614 -1.98880 -1.47522 -0.38585 0.85411 1.76071 1.98010 1.42664 0.31635 -0.91740 -1.79309 -1.96893 -1.37628 -0.24646 0.97955 1.82324 1.95531 1.32421 0.17626 -1.04048 -1.85112 -1.93926 -1.27049 -0.10585 1.10011 1.87669 1.92078 1.21519 0.03530 -1.15837 -1.89992 0.00000 ... ... ..... ....... ......... ........... ............. E10 2.00000 1.52196 0.31635 -1.04048 -1.89992 -1.85112 -0.91740 0.45487 1.60969 1.99502 1.42664 0.17626 -1.15837 -1.93926 -1.79309 -0.78976 0.59112 1.68941 1.98010 1.32421 0.03530 -1.27049 -1.96893 -1.72614 -0.65818 0.72442 1.76071 1.95531 1.21519 -0.10585 -1.37628 -1.98880 -1.65058 -0.52332 0.85411 1.82324 1.92078 1.10011 -0.24646 -1.47522 -1.99875 -1.56680 -0.38585 0.97955 1.87669 0.00000 ... ... ..... ....... ......... ........... ............. E11 2.00000 1.42664 0.03530 -1.37628 -1.99875 -1.47522 -0.10585 1.32421 1.99502 1.52196 0.17626 -1.27049 -1.98880 -1.56680 -0.24646 1.21519 1.98010 1.60969 0.31635 -1.15837 -1.96893 -1.65058 -0.38585 1.10011 1.95531 1.68941 0.45487 -1.04048 -1.93926 -1.72614 -0.52332 0.97955 1.92078 1.76071 0.59112 -0.91740 -1.89992 -1.79309 -0.65818 0.85411 1.87669 1.82324 0.72442 -0.78976 -1.85112 0.00000 ... ... ..... ....... ......... ........... ............. E12 2.00000 1.32421 -0.24646 -1.65058 -1.93926 -0.91740 0.72442 1.87669 1.76071 0.45487 -1.15837 -1.98880 -1.47522 0.03530 1.52196 1.98010 1.10011 -0.52332 -1.79309 -1.85112 -0.65818 0.97955 1.95531 1.60969 0.17626 -1.37628 -1.99875 -1.27049 0.31635 1.68941 1.92078 0.85411 -0.78976 -1.89992 -1.72614 -0.38585 1.21519 1.99502 1.42664 -0.10585 -1.56680 -1.96893 -1.04048 0.59112 1.82324 0.00000 ... ... ..... ....... ......... ........... ............. E13 2.00000 1.21519 -0.52332 -1.85112 -1.72614 -0.24646 1.42664 1.98010 0.97955 -0.78976 -1.93926 -1.56680 0.03530 1.60969 1.92078 0.72442 -1.04048 -1.98880 -1.37628 0.31635 1.76071 1.82324 0.45487 -1.27049 -1.99875 -1.15837 0.59112 1.87669 1.68941 0.17626 -1.47522 -1.96893 -0.91740 0.85411 1.95531 1.52196 -0.10585 -1.65058 -1.89992 -0.65818 1.10011 1.99502 1.32421 -0.38585 -1.79309 0.00000 ... ... ..... ....... ......... ........... ............. E14 2.00000 1.10011 -0.78976 -1.96893 -1.37628 0.45487 1.87669 1.60969 -0.10585 -1.72614 -1.79309 -0.24646 1.52196 1.92078 0.59112 -1.27049 -1.98880 -0.91740 0.97955 1.99502 1.21519 -0.65818 -1.93926 -1.47522 0.31635 1.82324 1.68941 0.03530 -1.65058 -1.85112 -0.38585 1.42664 1.95531 0.72442 -1.15837 -1.99875 -1.04048 0.85411 1.98010 1.32421 -0.52332 -1.89992 -1.56680 0.17626 1.76071 0.00000 ... ... ..... ....... ......... ........... ............. E15 2.00000 0.97955 -1.04048 -1.99875 -0.91740 1.10011 1.99502 0.85411 -1.15837 -1.98880 -0.78976 1.21519 1.98010 0.72442 -1.27049 -1.96893 -0.65818 1.32421 1.95531 0.59112 -1.37628 -1.93926 -0.52332 1.42664 1.92078 0.45487 -1.47522 -1.89992 -0.38585 1.52196 1.87669 0.31635 -1.56680 -1.85112 -0.24646 1.60969 1.82324 0.17626 -1.65058 -1.79309 -0.10585 1.68941 1.76071 0.03530 -1.72614 0.00000 ... ... ..... ....... ......... ........... ............. E16 2.00000 0.85411 -1.27049 -1.93926 -0.38585 1.60969 1.76071 -0.10585 -1.85112 -1.47522 0.59112 1.98010 1.10011 -1.04048 -1.98880 -0.65818 1.42664 1.87669 0.17626 -1.72614 -1.65058 0.31635 1.92078 1.32421 -0.78976 -1.99875 -0.91740 1.21519 1.95531 0.45487 -1.56680 -1.79309 0.03530 1.82324 1.52196 -0.52332 -1.96893 -1.15837 0.97955 1.99502 0.72442 -1.37628 -1.89992 -0.24646 1.68941 0.00000 ... ... ..... ....... ......... ........... ............. E17 2.00000 0.72442 -1.47522 -1.79309 0.17626 1.92078 1.21519 -1.04048 -1.96893 -0.38585 1.68941 1.60969 -0.52332 -1.98880 -0.91740 1.32421 1.87669 0.03530 -1.85112 -1.37628 0.85411 1.99502 0.59112 -1.56680 -1.72614 0.31635 1.95531 1.10011 -1.15837 -1.93926 -0.24646 1.76071 1.52196 -0.65818 -1.99875 -0.78976 1.42664 1.82324 -0.10585 -1.89992 -1.27049 0.97955 1.98010 0.45487 -1.65058 0.00000 ... ... ..... ....... ......... ........... ............. E18 2.00000 0.59112 -1.65058 -1.56680 0.72442 1.99502 0.45487 -1.72614 -1.47522 0.85411 1.98010 0.31635 -1.79309 -1.37628 0.97955 1.95531 0.17626 -1.85112 -1.27049 1.10011 1.92078 0.03530 -1.89992 -1.15837 1.21519 1.87669 -0.10585 -1.93926 -1.04048 1.32421 1.82324 -0.24646 -1.96893 -0.91740 1.42664 1.76071 -0.38585 -1.98880 -0.78976 1.52196 1.68941 -0.52332 -1.99875 -0.65818 1.60969 0.00000 ... ... ..... ....... ......... ........... ............. E19 2.00000 0.45487 -1.79309 -1.27049 1.21519 1.82324 -0.38585 -1.99875 -0.52332 1.76071 1.32421 -1.15837 -1.85112 0.31635 1.99502 0.59112 -1.72614 -1.37628 1.10011 1.87669 -0.24646 -1.98880 -0.65818 1.68941 1.42664 -1.04048 -1.89992 0.17626 1.98010 0.72442 -1.65058 -1.47522 0.97955 1.92078 -0.10585 -1.96893 -0.78976 1.60969 1.52196 -0.91740 -1.93926 0.03530 1.95531 0.85411 -1.56680 0.00000 ... ... ..... ....... ......... ........... ............. E20 2.00000 0.31635 -1.89992 -0.91740 1.60969 1.42664 -1.15837 -1.79309 0.59112 1.98010 0.03530 -1.96893 -0.65818 1.76071 1.21519 -1.37628 -1.65058 0.85411 1.92078 -0.24646 -1.99875 -0.38585 1.87669 0.97955 -1.56680 -1.47522 1.10011 1.82324 -0.52332 -1.98880 -0.10585 1.95531 0.72442 -1.72614 -1.27049 1.32421 1.68941 -0.78976 -1.93926 0.17626 1.99502 0.45487 -1.85112 -1.04048 1.52196 0.00000 ... ... ..... ....... ......... ........... ............. E21 2.00000 0.17626 -1.96893 -0.52332 1.87669 0.85411 -1.72614 -1.15837 1.52196 1.42664 -1.27049 -1.65058 0.97955 1.82324 -0.65818 -1.93926 0.31635 1.99502 0.03530 -1.98880 -0.38585 1.92078 0.72442 -1.79309 -1.04048 1.60969 1.32421 -1.37628 -1.56680 1.10011 1.76071 -0.78976 -1.89992 0.45487 1.98010 -0.10585 -1.99875 -0.24646 1.95531 0.59112 -1.85112 -0.91740 1.68941 1.21519 -1.47522 0.00000 ... ... ..... ....... ......... ........... ............. E22 2.00000 0.03530 -1.99875 -0.10585 1.99502 0.17626 -1.98880 -0.24646 1.98010 0.31635 -1.96893 -0.38585 1.95531 0.45487 -1.93926 -0.52332 1.92078 0.59112 -1.89992 -0.65818 1.87669 0.72442 -1.85112 -0.78976 1.82324 0.85411 -1.79309 -0.91740 1.76071 0.97955 -1.72614 -1.04048 1.68941 1.10011 -1.65058 -1.15837 1.60969 1.21519 -1.56680 -1.27049 1.52196 1.32421 -1.47522 -1.37628 1.42664 0.00000 ... ... ..... ....... ......... ........... ............. E23 2.00000 -0.10585 -1.98880 0.31635 1.95531 -0.52332 -1.89992 0.72442 1.82324 -0.91740 -1.72614 1.10011 1.60969 -1.27049 -1.47522 1.42664 1.32421 -1.56680 -1.15837 1.68941 0.97955 -1.79309 -0.78976 1.87669 0.59112 -1.93926 -0.38585 1.98010 0.17626 -1.99875 0.03530 1.99502 -0.24646 -1.96893 0.45487 1.92078 -0.65818 -1.85112 0.85411 1.76071 -1.04048 -1.65058 1.21519 1.52196 -1.37628 0.00000 ... ... ..... ....... ......... ........... ............. E24 2.00000 -0.24646 -1.93926 0.72442 1.76071 -1.15837 -1.47522 1.52196 1.10011 -1.79309 -0.65818 1.95531 0.17626 -1.99875 0.31635 1.92078 -0.78976 -1.72614 1.21519 1.42664 -1.56680 -1.04048 1.82324 0.59112 -1.96893 -0.10585 1.99502 -0.38585 -1.89992 0.85411 1.68941 -1.27049 -1.37628 1.60969 0.97955 -1.85112 -0.52332 1.98010 0.03530 -1.98880 0.45487 1.87669 -0.91740 -1.65058 1.32421 0.00000 ... ... ..... ....... ......... ........... ............. E25 2.00000 -0.38585 -1.85112 1.10011 1.42664 -1.65058 -0.78976 1.95531 0.03530 -1.96893 0.72442 1.68941 -1.37628 -1.15837 1.82324 0.45487 -1.99875 0.31635 1.87669 -1.04048 -1.47522 1.60969 0.85411 -1.93926 -0.10585 1.98010 -0.65818 -1.72614 1.32421 1.21519 -1.79309 -0.52332 1.99502 -0.24646 -1.89992 0.97955 1.52196 -1.56680 -0.91740 1.92078 0.17626 -1.98880 0.59112 1.76071 -1.27049 0.00000 ... ... ..... ....... ......... ........... ............. E26 2.00000 -0.52332 -1.72614 1.42664 0.97955 -1.93926 0.03530 1.92078 -1.04048 -1.37628 1.76071 0.45487 -1.99875 0.59112 1.68941 -1.47522 -0.91740 1.95531 -0.10585 -1.89992 1.10011 1.32421 -1.79309 -0.38585 1.99502 -0.65818 -1.65058 1.52196 0.85411 -1.96893 0.17626 1.87669 -1.15837 -1.27049 1.82324 0.31635 -1.98880 0.72442 1.60969 -1.56680 -0.78976 1.98010 -0.24646 -1.85112 1.21519 0.00000 ... ... ..... ....... ......... ........... ............. E27 2.00000 -0.65818 -1.56680 1.68941 0.45487 -1.98880 0.85411 1.42664 -1.79309 -0.24646 1.95531 -1.04048 -1.27049 1.87669 0.03530 -1.89992 1.21519 1.10011 -1.93926 0.17626 1.82324 -1.37628 -0.91740 1.98010 -0.38585 -1.72614 1.52196 0.72442 -1.99875 0.59112 1.60969 -1.65058 -0.52332 1.99502 -0.78976 -1.47522 1.76071 0.31635 -1.96893 0.97955 1.32421 -1.85112 -0.10585 1.92078 -1.15837 0.00000 ... ... ..... ....... ......... ........... ............. E28 2.00000 -0.78976 -1.37628 1.87669 -0.10585 -1.79309 1.52196 0.59112 -1.98880 0.97955 1.21519 -1.93926 0.31635 1.68941 -1.65058 -0.38585 1.95531 -1.15837 -1.04048 1.98010 -0.52332 -1.56680 1.76071 0.17626 -1.89992 1.32421 0.85411 -1.99875 0.72442 1.42664 -1.85112 0.03530 1.82324 -1.47522 -0.65818 1.99502 -0.91740 -1.27049 1.92078 -0.24646 -1.72614 1.60969 0.45487 -1.96893 1.10011 0.00000 ... ... ..... ....... ......... ........... ............. E29 2.00000 -0.91740 -1.15837 1.98010 -0.65818 -1.37628 1.92078 -0.38585 -1.56680 1.82324 -0.10585 -1.72614 1.68941 0.17626 -1.85112 1.52196 0.45487 -1.93926 1.32421 0.72442 -1.98880 1.10011 0.97955 -1.99875 0.85411 1.21519 -1.96893 0.59112 1.42664 -1.89992 0.31635 1.60969 -1.79309 0.03530 1.76071 -1.65058 -0.24646 1.87669 -1.47522 -0.52332 1.95531 -1.27049 -0.78976 1.99502 -1.04048 0.00000 ... ... ..... ....... ......... ........... ............. E30 2.00000 -1.04048 -0.91740 1.99502 -1.15837 -0.78976 1.98010 -1.27049 -0.65818 1.95531 -1.37628 -0.52332 1.92078 -1.47522 -0.38585 1.87669 -1.56680 -0.24646 1.82324 -1.65058 -0.10585 1.76071 -1.72614 0.03530 1.68941 -1.79309 0.17626 1.60969 -1.85112 0.31635 1.52196 -1.89992 0.45487 1.42664 -1.93926 0.59112 1.32421 -1.96893 0.72442 1.21519 -1.98880 0.85411 1.10011 -1.99875 0.97955 0.00000 ... ... ..... ....... ......... ........... ............. E31 2.00000 -1.15837 -0.65818 1.92078 -1.56680 -0.10585 1.68941 -1.85112 0.45487 1.32421 -1.98880 0.97955 0.85411 -1.96893 1.42664 0.31635 -1.79309 1.76071 -0.24646 -1.47522 1.95531 -0.78976 -1.04048 1.99502 -1.27049 -0.52332 1.87669 -1.65058 0.03530 1.60969 -1.89992 0.59112 1.21519 -1.99875 1.10011 0.72442 -1.93926 1.52196 0.17626 -1.72614 1.82324 -0.38585 -1.37628 1.98010 -0.91740 0.00000 ... ... ..... ....... ......... ........... ............. E32 2.00000 -1.27049 -0.38585 1.76071 -1.85112 0.59112 1.10011 -1.98880 1.42664 0.17626 -1.65058 1.92078 -0.78976 -0.91740 1.95531 -1.56680 0.03530 1.52196 -1.96893 0.97955 0.72442 -1.89992 1.68941 -0.24646 -1.37628 1.99502 -1.15837 -0.52332 1.82324 -1.79309 0.45487 1.21519 -1.99875 1.32421 0.31635 -1.72614 1.87669 -0.65818 -1.04048 1.98010 -1.47522 -0.10585 1.60969 -1.93926 0.85411 0.00000 ... ... ..... ....... ......... ........... ............. E33 2.00000 -1.37628 -0.10585 1.52196 -1.98880 1.21519 0.31635 -1.65058 1.95531 -1.04048 -0.52332 1.76071 -1.89992 0.85411 0.72442 -1.85112 1.82324 -0.65818 -0.91740 1.92078 -1.72614 0.45487 1.10011 -1.96893 1.60969 -0.24646 -1.27049 1.99502 -1.47522 0.03530 1.42664 -1.99875 1.32421 0.17626 -1.56680 1.98010 -1.15837 -0.38585 1.68941 -1.93926 0.97955 0.59112 -1.79309 1.87669 -0.78976 0.00000 ... ... ..... ....... ......... ........... ............. E34 2.00000 -1.47522 0.17626 1.21519 -1.96893 1.68941 -0.52332 -0.91740 1.87669 -1.85112 0.85411 0.59112 -1.72614 1.95531 -1.15837 -0.24646 1.52196 -1.99875 1.42664 -0.10585 -1.27049 1.98010 -1.65058 0.45487 0.97955 -1.89992 1.82324 -0.78976 -0.65818 1.76071 -1.93926 1.10011 0.31635 -1.56680 1.99502 -1.37628 0.03530 1.32421 -1.98880 1.60969 -0.38585 -1.04048 1.92078 -1.79309 0.72442 0.00000 ... ... ..... ....... ......... ........... ............. E35 2.00000 -1.56680 0.45487 0.85411 -1.79309 1.95531 -1.27049 0.03530 1.21519 -1.93926 1.82324 -0.91740 -0.38585 1.52196 -1.99875 1.60969 -0.52332 -0.78976 1.76071 -1.96893 1.32421 -0.10585 -1.15837 1.92078 -1.85112 0.97955 0.31635 -1.47522 1.99502 -1.65058 0.59112 0.72442 -1.72614 1.98010 -1.37628 0.17626 1.10011 -1.89992 1.87669 -1.04048 -0.24646 1.42664 -1.98880 1.68941 -0.65818 0.00000 ... ... ..... ....... ......... ........... ............. E36 2.00000 -1.65058 0.72442 0.45487 -1.47522 1.98010 -1.79309 0.97955 0.17626 -1.27049 1.92078 -1.89992 1.21519 -0.10585 -1.04048 1.82324 -1.96893 1.42664 -0.38585 -0.78976 1.68941 -1.99875 1.60969 -0.65818 -0.52332 1.52196 -1.98880 1.76071 -0.91740 -0.24646 1.32421 -1.93926 1.87669 -1.15837 0.03530 1.10011 -1.85112 1.95531 -1.37628 0.31635 0.85411 -1.72614 1.99502 -1.56680 0.59112 0.00000 ... ... ..... ....... ......... ........... ............. E37 2.00000 -1.72614 0.97955 0.03530 -1.04048 1.76071 -1.99875 1.68941 -0.91740 -0.10585 1.10011 -1.79309 1.99502 -1.65058 0.85411 0.17626 -1.15837 1.82324 -1.98880 1.60969 -0.78976 -0.24646 1.21519 -1.85112 1.98010 -1.56680 0.72442 0.31635 -1.27049 1.87669 -1.96893 1.52196 -0.65818 -0.38585 1.32421 -1.89992 1.95531 -1.47522 0.59112 0.45487 -1.37628 1.92078 -1.93926 1.42664 -0.52332 0.00000 ... ... ..... ....... ......... ........... ............. E38 2.00000 -1.79309 1.21519 -0.38585 -0.52332 1.32421 -1.85112 1.99502 -1.72614 1.10011 -0.24646 -0.65818 1.42664 -1.89992 1.98010 -1.65058 0.97955 -0.10585 -0.78976 1.52196 -1.93926 1.95531 -1.56680 0.85411 0.03530 -0.91740 1.60969 -1.96893 1.92078 -1.47522 0.72442 0.17626 -1.04048 1.68941 -1.98880 1.87669 -1.37628 0.59112 0.31635 -1.15837 1.76071 -1.99875 1.82324 -1.27049 0.45487 0.00000 ... ... ..... ....... ......... ........... ............. E39 2.00000 -1.85112 1.42664 -0.78976 0.03530 0.72442 -1.37628 1.82324 -1.99875 1.87669 -1.47522 0.85411 -0.10585 -0.65818 1.32421 -1.79309 1.99502 -1.89992 1.52196 -0.91740 0.17626 0.59112 -1.27049 1.76071 -1.98880 1.92078 -1.56680 0.97955 -0.24646 -0.52332 1.21519 -1.72614 1.98010 -1.93926 1.60969 -1.04048 0.31635 0.45487 -1.15837 1.68941 -1.96893 1.95531 -1.65058 1.10011 -0.38585 0.00000 ... ... ..... ....... ......... ........... ............. E40 2.00000 -1.89992 1.60969 -1.15837 0.59112 0.03530 -0.65818 1.21519 -1.65058 1.92078 -1.99875 1.87669 -1.56680 1.10011 -0.52332 -0.10585 0.72442 -1.27049 1.68941 -1.93926 1.99502 -1.85112 1.52196 -1.04048 0.45487 0.17626 -0.78976 1.32421 -1.72614 1.95531 -1.98880 1.82324 -1.47522 0.97955 -0.38585 -0.24646 0.85411 -1.37628 1.76071 -1.96893 1.98010 -1.79309 1.42664 -0.91740 0.31635 0.00000 ... ... ..... ....... ......... ........... ............. E41 2.00000 -1.93926 1.76071 -1.47522 1.10011 -0.65818 0.17626 0.31635 -0.78976 1.21519 -1.56680 1.82324 -1.96893 1.99502 -1.89992 1.68941 -1.37628 0.97955 -0.52332 0.03530 0.45487 -0.91740 1.32421 -1.65058 1.87669 -1.98880 1.98010 -1.85112 1.60969 -1.27049 0.85411 -0.38585 -0.10585 0.59112 -1.04048 1.42664 -1.72614 1.92078 -1.99875 1.95531 -1.79309 1.52196 -1.15837 0.72442 -0.24646 0.00000 ... ... ..... ....... ......... ........... ............. E42 2.00000 -1.96893 1.87669 -1.72614 1.52196 -1.27049 0.97955 -0.65818 0.31635 0.03530 -0.38585 0.72442 -1.04048 1.32421 -1.56680 1.76071 -1.89992 1.98010 -1.99875 1.95531 -1.85112 1.68941 -1.47522 1.21519 -0.91740 0.59112 -0.24646 -0.10585 0.45487 -0.78976 1.10011 -1.37628 1.60969 -1.79309 1.92078 -1.98880 1.99502 -1.93926 1.82324 -1.65058 1.42664 -1.15837 0.85411 -0.52332 0.17626 0.00000 ... ... ..... ....... ......... ........... ............. E43 2.00000 -1.98880 1.95531 -1.89992 1.82324 -1.72614 1.60969 -1.47522 1.32421 -1.15837 0.97955 -0.78976 0.59112 -0.38585 0.17626 0.03530 -0.24646 0.45487 -0.65818 0.85411 -1.04048 1.21519 -1.37628 1.52196 -1.65058 1.76071 -1.85112 1.92078 -1.96893 1.99502 -1.99875 1.98010 -1.93926 1.87669 -1.79309 1.68941 -1.56680 1.42664 -1.27049 1.10011 -0.91740 0.72442 -0.52332 0.31635 -0.10585 0.00000 ... ... ..... ....... ......... ........... ............. E44 2.00000 -1.99875 1.99502 -1.98880 1.98010 -1.96893 1.95531 -1.93926 1.92078 -1.89992 1.87669 -1.85112 1.82324 -1.79309 1.76071 -1.72614 1.68941 -1.65058 1.60969 -1.56680 1.52196 -1.47522 1.42664 -1.37628 1.32421 -1.27049 1.21519 -1.15837 1.10011 -1.04048 0.97955 -0.91740 0.85411 -0.78976 0.72442 -0.65818 0.59112 -0.52332 0.45487 -0.38585 0.31635 -0.24646 0.17626 -0.10585 0.03530 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.995018050302 = 2*cos(2*π/89) 1.980097021029 = 2*cos(4*π/89) 1.955311247999 = 2*cos(6*π/89) 1.920784212688 = 2*cos(8*π/89) 1.876687927046 = 2*cos(10*π/89) 1.823242076553 = 2*cos(12*π/89) 1.760712925746 = 2*cos(14*π/89) 1.689411991710 = 2*cos(16*π/89) 1.609694492111 = 2*cos(18*π/89) 1.521957575522 = 2*cos(20*π/89) 1.426638342849 = 2*cos(22*π/89) 1.324211669714 = 2*cos(24*π/89) 1.215187840650 = 2*cos(26*π/89) 1.100110006890 = 2*cos(28*π/89) 0.979551480412 = 2*cos(30*π/89) 0.854112877733 = 2*cos(32*π/89) 0.724419127659 = 2*cos(34*π/89) 0.591116357931 = 2*cos(36*π/89) 0.454868676242 = 2*cos(38*π/89) 0.316354861689 = 2*cos(40*π/89) 0.176264983127 = 2*cos(42*π/89) 0.035296961286 = 2*cos(44*π/89) -0.105846908240 = 2*cos(46*π/89) -0.246463453794 = 2*cos(48*π/89) -0.385852130819 = 2*cos(50*π/89) -0.523318511937 = 2*cos(52*π/89) -0.658177746552 = 2*cos(54*π/89) -0.789757972741 = 2*cos(56*π/89) -0.917403664436 = 2*cos(58*π/89) -1.040478897222 = 2*cos(60*π/89) -1.158370516479 = 2*cos(62*π/89) -1.270491192091 = 2*cos(64*π/89) -1.376282344492 = 2*cos(66*π/89) -1.475216927481 = 2*cos(68*π/89) -1.566802053944 = 2*cos(70*π/89) -1.650581451386 = 2*cos(72*π/89) -1.726137735064 = 2*cos(74*π/89) -1.793094487374 = 2*cos(76*π/89) -1.851118133142 = 2*cos(78*π/89) -1.899919601486 = 2*cos(80*π/89) -1.939255765944 = 2*cos(82*π/89) -1.968930655723 = 2*cos(84*π/89) -1.988796432016 = 2*cos(86*π/89) -1.998754124524 = 2*cos(88*π/89) 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_89v point group is 178, and the order of the principal axis (C₈₉) is 89. The group has 46 irreducible representations. β The C_89v point group is isomorphic to D₈₉. γ The C_89v point group is generated by two symmetry elements, C₈₉ and any σ_v. Also, the group may be generated from any two σ_v planes. δ The group contains one set of symmetry planes σ_v intersecting in the principal (z) axis. The xz plane (but not the yz plane) is a member of that set. ε The lowest nonvanishing multipole moment in C_89v 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 just 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 C_89v point group was created by Gernot Katzer.

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

	C_87v
	C_88v
C₈₉	C_89v	C_89h D₈₉ D_89h D_89d
	C_90v
	C_91v

Character table for the C89v point group

Character table for the C_89v point group