Character table for the D38h point group

D38h     E        2 C38    2 C19    2 C38^3  2 C19^2  2 C38^5  2 C19^3  2 C38^7  2 C19^4  2 C38^9  2 C19^5  2 C38^11 2 C19^6  2 C38^13 2 C19^7  2 C38^15 2 C19^8  2 C38^17 2 C19^9  C2       19 C2'   19 C2"   i        2 S38    2 S19    2 S38^3  2 S19^2  2 S38^5  2 S19^3  2 S38^7  2 S19^4  2 S38^9  2 S19^5  2 S38^11 2 S19^6  2 S38^13 2 S19^7  2 S38^15 2 S19^8  2 S38^17 2 S19^9  sh       19 sv    19 sd      <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> 
A1g     1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  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
A2g     1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000 -1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  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 ... ..... ....... ......... ........... .............
B1g     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000 -1.00000  1.00000     ... ... ..... ....... ......... ........... .............
B2g     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000  1.00000  1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000  1.00000 -1.00000     ... ... ..... ....... ......... ........... .............
E1g     2.00000  1.97272  1.89163  1.75895  1.57828  1.35456  1.09390  0.80339  0.49097  0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 -2.00000  0.00000  0.00000  2.00000 -1.97272 -1.89163 -1.75895 -1.57828 -1.35456 -1.09390 -0.80339 -0.49097 -0.16516  0.16516  0.49097  0.80339  1.09390  1.35456  1.57828  1.75895  1.89163  1.97272 -2.00000  0.00000  0.00000     TT. ... ..TT. ....... ......TT. ........... ..........TT.
E2g     2.00000  1.89163  1.57828  1.09390  0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516  0.49097  1.09390  1.57828  1.89163  2.00000  0.00000  0.00000  2.00000  1.89163  1.57828  1.09390  0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516  0.49097  1.09390  1.57828  1.89163  2.00000  0.00000  0.00000     ... ... TT... ....... ....TT... ........... ........TT...
E3g     2.00000  1.75895  1.09390  0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097  0.49097  1.35456  1.89163  1.97272  1.57828  0.80339 -0.16516 -1.09390 -1.75895 -2.00000  0.00000  0.00000  2.00000 -1.75895 -1.09390 -0.16516  0.80339  1.57828  1.97272  1.89163  1.35456  0.49097 -0.49097 -1.35456 -1.89163 -1.97272 -1.57828 -0.80339  0.16516  1.09390  1.75895 -2.00000  0.00000  0.00000     ... ... ..... ....... ..TT..... ........... ......TT.....
E4g     2.00000  1.57828  0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516  1.09390  1.89163  1.89163  1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339  0.49097  1.57828  2.00000  0.00000  0.00000  2.00000  1.57828  0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516  1.09390  1.89163  1.89163  1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339  0.49097  1.57828  2.00000  0.00000  0.00000     ... ... ..... ....... TT....... ........... ....TT.......
E5g     2.00000  1.35456 -0.16516 -1.57828 -1.97272 -1.09390  0.49097  1.75895  1.89163  0.80339 -0.80339 -1.89163 -1.75895 -0.49097  1.09390  1.97272  1.57828  0.16516 -1.35456 -2.00000  0.00000  0.00000  2.00000 -1.35456  0.16516  1.57828  1.97272  1.09390 -0.49097 -1.75895 -1.89163 -0.80339  0.80339  1.89163  1.75895  0.49097 -1.09390 -1.97272 -1.57828 -0.16516  1.35456 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... ..TT.........
E6g     2.00000  1.09390 -0.80339 -1.97272 -1.35456  0.49097  1.89163  1.57828 -0.16516 -1.75895 -1.75895 -0.16516  1.57828  1.89163  0.49097 -1.35456 -1.97272 -0.80339  1.09390  2.00000  0.00000  0.00000  2.00000  1.09390 -0.80339 -1.97272 -1.35456  0.49097  1.89163  1.57828 -0.16516 -1.75895 -1.75895 -0.16516  1.57828  1.89163  0.49097 -1.35456 -1.97272 -0.80339  1.09390  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... TT...........
E7g     2.00000  0.80339 -1.35456 -1.89163 -0.16516  1.75895  1.57828 -0.49097 -1.97272 -1.09390  1.09390  1.97272  0.49097 -1.57828 -1.75895  0.16516  1.89163  1.35456 -0.80339 -2.00000  0.00000  0.00000  2.00000 -0.80339  1.35456  1.89163  0.16516 -1.75895 -1.57828  0.49097  1.97272  1.09390 -1.09390 -1.97272 -0.49097  1.57828  1.75895 -0.16516 -1.89163 -1.35456  0.80339 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8g     2.00000  0.49097 -1.75895 -1.35456  1.09390  1.89163 -0.16516 -1.97272 -0.80339  1.57828  1.57828 -0.80339 -1.97272 -0.16516  1.89163  1.09390 -1.35456 -1.75895  0.49097  2.00000  0.00000  0.00000  2.00000  0.49097 -1.75895 -1.35456  1.09390  1.89163 -0.16516 -1.97272 -0.80339  1.57828  1.57828 -0.80339 -1.97272 -0.16516  1.89163  1.09390 -1.35456 -1.75895  0.49097  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9g     2.00000  0.16516 -1.97272 -0.49097  1.89163  0.80339 -1.75895 -1.09390  1.57828  1.35456 -1.35456 -1.57828  1.09390  1.75895 -0.80339 -1.89163  0.49097  1.97272 -0.16516 -2.00000  0.00000  0.00000  2.00000 -0.16516  1.97272  0.49097 -1.89163 -0.80339  1.75895  1.09390 -1.57828 -1.35456  1.35456  1.57828 -1.09390 -1.75895  0.80339  1.89163 -0.49097 -1.97272  0.16516 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10g    2.00000 -0.16516 -1.97272  0.49097  1.89163 -0.80339 -1.75895  1.09390  1.57828 -1.35456 -1.35456  1.57828  1.09390 -1.75895 -0.80339  1.89163  0.49097 -1.97272 -0.16516  2.00000  0.00000  0.00000  2.00000 -0.16516 -1.97272  0.49097  1.89163 -0.80339 -1.75895  1.09390  1.57828 -1.35456 -1.35456  1.57828  1.09390 -1.75895 -0.80339  1.89163  0.49097 -1.97272 -0.16516  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11g    2.00000 -0.49097 -1.75895  1.35456  1.09390 -1.89163 -0.16516  1.97272 -0.80339 -1.57828  1.57828  0.80339 -1.97272  0.16516  1.89163 -1.09390 -1.35456  1.75895  0.49097 -2.00000  0.00000  0.00000  2.00000  0.49097  1.75895 -1.35456 -1.09390  1.89163  0.16516 -1.97272  0.80339  1.57828 -1.57828 -0.80339  1.97272 -0.16516 -1.89163  1.09390  1.35456 -1.75895 -0.49097 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12g    2.00000 -0.80339 -1.35456  1.89163 -0.16516 -1.75895  1.57828  0.49097 -1.97272  1.09390  1.09390 -1.97272  0.49097  1.57828 -1.75895 -0.16516  1.89163 -1.35456 -0.80339  2.00000  0.00000  0.00000  2.00000 -0.80339 -1.35456  1.89163 -0.16516 -1.75895  1.57828  0.49097 -1.97272  1.09390  1.09390 -1.97272  0.49097  1.57828 -1.75895 -0.16516  1.89163 -1.35456 -0.80339  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13g    2.00000 -1.09390 -0.80339  1.97272 -1.35456 -0.49097  1.89163 -1.57828 -0.16516  1.75895 -1.75895  0.16516  1.57828 -1.89163  0.49097  1.35456 -1.97272  0.80339  1.09390 -2.00000  0.00000  0.00000  2.00000  1.09390  0.80339 -1.97272  1.35456  0.49097 -1.89163  1.57828  0.16516 -1.75895  1.75895 -0.16516 -1.57828  1.89163 -0.49097 -1.35456  1.97272 -0.80339 -1.09390 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14g    2.00000 -1.35456 -0.16516  1.57828 -1.97272  1.09390  0.49097 -1.75895  1.89163 -0.80339 -0.80339  1.89163 -1.75895  0.49097  1.09390 -1.97272  1.57828 -0.16516 -1.35456  2.00000  0.00000  0.00000  2.00000 -1.35456 -0.16516  1.57828 -1.97272  1.09390  0.49097 -1.75895  1.89163 -0.80339 -0.80339  1.89163 -1.75895  0.49097  1.09390 -1.97272  1.57828 -0.16516 -1.35456  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15g    2.00000 -1.57828  0.49097  0.80339 -1.75895  1.97272 -1.35456  0.16516  1.09390 -1.89163  1.89163 -1.09390 -0.16516  1.35456 -1.97272  1.75895 -0.80339 -0.49097  1.57828 -2.00000  0.00000  0.00000  2.00000  1.57828 -0.49097 -0.80339  1.75895 -1.97272  1.35456 -0.16516 -1.09390  1.89163 -1.89163  1.09390  0.16516 -1.35456  1.97272 -1.75895  0.80339  0.49097 -1.57828 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16g    2.00000 -1.75895  1.09390 -0.16516 -0.80339  1.57828 -1.97272  1.89163 -1.35456  0.49097  0.49097 -1.35456  1.89163 -1.97272  1.57828 -0.80339 -0.16516  1.09390 -1.75895  2.00000  0.00000  0.00000  2.00000 -1.75895  1.09390 -0.16516 -0.80339  1.57828 -1.97272  1.89163 -1.35456  0.49097  0.49097 -1.35456  1.89163 -1.97272  1.57828 -0.80339 -0.16516  1.09390 -1.75895  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17g    2.00000 -1.89163  1.57828 -1.09390  0.49097  0.16516 -0.80339  1.35456 -1.75895  1.97272 -1.97272  1.75895 -1.35456  0.80339 -0.16516 -0.49097  1.09390 -1.57828  1.89163 -2.00000  0.00000  0.00000  2.00000  1.89163 -1.57828  1.09390 -0.49097 -0.16516  0.80339 -1.35456  1.75895 -1.97272  1.97272 -1.75895  1.35456 -0.80339  0.16516  0.49097 -1.09390  1.57828 -1.89163 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18g    2.00000 -1.97272  1.89163 -1.75895  1.57828 -1.35456  1.09390 -0.80339  0.49097 -0.16516 -0.16516  0.49097 -0.80339  1.09390 -1.35456  1.57828 -1.75895  1.89163 -1.97272  2.00000  0.00000  0.00000  2.00000 -1.97272  1.89163 -1.75895  1.57828 -1.35456  1.09390 -0.80339  0.49097 -0.16516 -0.16516  0.49097 -0.80339  1.09390 -1.35456  1.57828 -1.75895  1.89163 -1.97272  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
A1u     1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000     ... ... ..... ....... ......... ........... .............
A2u     1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000  1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 .............
B1u     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000  1.00000 -1.00000     ... ... ..... ....... ......... ........... .............
B2u     1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000 -1.00000  1.00000 -1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000 -1.00000  1.00000  1.00000 -1.00000  1.00000     ... ... ..... ....... ......... ........... .............
E1u     2.00000  1.97272  1.89163  1.75895  1.57828  1.35456  1.09390  0.80339  0.49097  0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272 -2.00000  0.00000  0.00000 -2.00000  1.97272  1.89163  1.75895  1.57828  1.35456  1.09390  0.80339  0.49097  0.16516 -0.16516 -0.49097 -0.80339 -1.09390 -1.35456 -1.57828 -1.75895 -1.89163 -1.97272  2.00000  0.00000  0.00000     ... TT. ..... ....TT. ......... ........TT. .............
E2u     2.00000  1.89163  1.57828  1.09390  0.49097 -0.16516 -0.80339 -1.35456 -1.75895 -1.97272 -1.97272 -1.75895 -1.35456 -0.80339 -0.16516  0.49097  1.09390  1.57828  1.89163  2.00000  0.00000  0.00000 -2.00000 -1.89163 -1.57828 -1.09390 -0.49097  0.16516  0.80339  1.35456  1.75895  1.97272  1.97272  1.75895  1.35456  0.80339  0.16516 -0.49097 -1.09390 -1.57828 -1.89163 -2.00000  0.00000  0.00000     ... ... ..... ..TT... ......... ......TT... .............
E3u     2.00000  1.75895  1.09390  0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097  0.49097  1.35456  1.89163  1.97272  1.57828  0.80339 -0.16516 -1.09390 -1.75895 -2.00000  0.00000  0.00000 -2.00000  1.75895  1.09390  0.16516 -0.80339 -1.57828 -1.97272 -1.89163 -1.35456 -0.49097  0.49097  1.35456  1.89163  1.97272  1.57828  0.80339 -0.16516 -1.09390 -1.75895  2.00000  0.00000  0.00000     ... ... ..... TT..... ......... ....TT..... .............
E4u     2.00000  1.57828  0.49097 -0.80339 -1.75895 -1.97272 -1.35456 -0.16516  1.09390  1.89163  1.89163  1.09390 -0.16516 -1.35456 -1.97272 -1.75895 -0.80339  0.49097  1.57828  2.00000  0.00000  0.00000 -2.00000 -1.57828 -0.49097  0.80339  1.75895  1.97272  1.35456  0.16516 -1.09390 -1.89163 -1.89163 -1.09390  0.16516  1.35456  1.97272  1.75895  0.80339 -0.49097 -1.57828 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ..TT....... .............
E5u     2.00000  1.35456 -0.16516 -1.57828 -1.97272 -1.09390  0.49097  1.75895  1.89163  0.80339 -0.80339 -1.89163 -1.75895 -0.49097  1.09390  1.97272  1.57828  0.16516 -1.35456 -2.00000  0.00000  0.00000 -2.00000  1.35456 -0.16516 -1.57828 -1.97272 -1.09390  0.49097  1.75895  1.89163  0.80339 -0.80339 -1.89163 -1.75895 -0.49097  1.09390  1.97272  1.57828  0.16516 -1.35456  2.00000  0.00000  0.00000     ... ... ..... ....... ......... TT......... .............
E6u     2.00000  1.09390 -0.80339 -1.97272 -1.35456  0.49097  1.89163  1.57828 -0.16516 -1.75895 -1.75895 -0.16516  1.57828  1.89163  0.49097 -1.35456 -1.97272 -0.80339  1.09390  2.00000  0.00000  0.00000 -2.00000 -1.09390  0.80339  1.97272  1.35456 -0.49097 -1.89163 -1.57828  0.16516  1.75895  1.75895  0.16516 -1.57828 -1.89163 -0.49097  1.35456  1.97272  0.80339 -1.09390 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E7u     2.00000  0.80339 -1.35456 -1.89163 -0.16516  1.75895  1.57828 -0.49097 -1.97272 -1.09390  1.09390  1.97272  0.49097 -1.57828 -1.75895  0.16516  1.89163  1.35456 -0.80339 -2.00000  0.00000  0.00000 -2.00000  0.80339 -1.35456 -1.89163 -0.16516  1.75895  1.57828 -0.49097 -1.97272 -1.09390  1.09390  1.97272  0.49097 -1.57828 -1.75895  0.16516  1.89163  1.35456 -0.80339  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E8u     2.00000  0.49097 -1.75895 -1.35456  1.09390  1.89163 -0.16516 -1.97272 -0.80339  1.57828  1.57828 -0.80339 -1.97272 -0.16516  1.89163  1.09390 -1.35456 -1.75895  0.49097  2.00000  0.00000  0.00000 -2.00000 -0.49097  1.75895  1.35456 -1.09390 -1.89163  0.16516  1.97272  0.80339 -1.57828 -1.57828  0.80339  1.97272  0.16516 -1.89163 -1.09390  1.35456  1.75895 -0.49097 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E9u     2.00000  0.16516 -1.97272 -0.49097  1.89163  0.80339 -1.75895 -1.09390  1.57828  1.35456 -1.35456 -1.57828  1.09390  1.75895 -0.80339 -1.89163  0.49097  1.97272 -0.16516 -2.00000  0.00000  0.00000 -2.00000  0.16516 -1.97272 -0.49097  1.89163  0.80339 -1.75895 -1.09390  1.57828  1.35456 -1.35456 -1.57828  1.09390  1.75895 -0.80339 -1.89163  0.49097  1.97272 -0.16516  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E10u    2.00000 -0.16516 -1.97272  0.49097  1.89163 -0.80339 -1.75895  1.09390  1.57828 -1.35456 -1.35456  1.57828  1.09390 -1.75895 -0.80339  1.89163  0.49097 -1.97272 -0.16516  2.00000  0.00000  0.00000 -2.00000  0.16516  1.97272 -0.49097 -1.89163  0.80339  1.75895 -1.09390 -1.57828  1.35456  1.35456 -1.57828 -1.09390  1.75895  0.80339 -1.89163 -0.49097  1.97272  0.16516 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E11u    2.00000 -0.49097 -1.75895  1.35456  1.09390 -1.89163 -0.16516  1.97272 -0.80339 -1.57828  1.57828  0.80339 -1.97272  0.16516  1.89163 -1.09390 -1.35456  1.75895  0.49097 -2.00000  0.00000  0.00000 -2.00000 -0.49097 -1.75895  1.35456  1.09390 -1.89163 -0.16516  1.97272 -0.80339 -1.57828  1.57828  0.80339 -1.97272  0.16516  1.89163 -1.09390 -1.35456  1.75895  0.49097  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E12u    2.00000 -0.80339 -1.35456  1.89163 -0.16516 -1.75895  1.57828  0.49097 -1.97272  1.09390  1.09390 -1.97272  0.49097  1.57828 -1.75895 -0.16516  1.89163 -1.35456 -0.80339  2.00000  0.00000  0.00000 -2.00000  0.80339  1.35456 -1.89163  0.16516  1.75895 -1.57828 -0.49097  1.97272 -1.09390 -1.09390  1.97272 -0.49097 -1.57828  1.75895  0.16516 -1.89163  1.35456  0.80339 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E13u    2.00000 -1.09390 -0.80339  1.97272 -1.35456 -0.49097  1.89163 -1.57828 -0.16516  1.75895 -1.75895  0.16516  1.57828 -1.89163  0.49097  1.35456 -1.97272  0.80339  1.09390 -2.00000  0.00000  0.00000 -2.00000 -1.09390 -0.80339  1.97272 -1.35456 -0.49097  1.89163 -1.57828 -0.16516  1.75895 -1.75895  0.16516  1.57828 -1.89163  0.49097  1.35456 -1.97272  0.80339  1.09390  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E14u    2.00000 -1.35456 -0.16516  1.57828 -1.97272  1.09390  0.49097 -1.75895  1.89163 -0.80339 -0.80339  1.89163 -1.75895  0.49097  1.09390 -1.97272  1.57828 -0.16516 -1.35456  2.00000  0.00000  0.00000 -2.00000  1.35456  0.16516 -1.57828  1.97272 -1.09390 -0.49097  1.75895 -1.89163  0.80339  0.80339 -1.89163  1.75895 -0.49097 -1.09390  1.97272 -1.57828  0.16516  1.35456 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E15u    2.00000 -1.57828  0.49097  0.80339 -1.75895  1.97272 -1.35456  0.16516  1.09390 -1.89163  1.89163 -1.09390 -0.16516  1.35456 -1.97272  1.75895 -0.80339 -0.49097  1.57828 -2.00000  0.00000  0.00000 -2.00000 -1.57828  0.49097  0.80339 -1.75895  1.97272 -1.35456  0.16516  1.09390 -1.89163  1.89163 -1.09390 -0.16516  1.35456 -1.97272  1.75895 -0.80339 -0.49097  1.57828  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E16u    2.00000 -1.75895  1.09390 -0.16516 -0.80339  1.57828 -1.97272  1.89163 -1.35456  0.49097  0.49097 -1.35456  1.89163 -1.97272  1.57828 -0.80339 -0.16516  1.09390 -1.75895  2.00000  0.00000  0.00000 -2.00000  1.75895 -1.09390  0.16516  0.80339 -1.57828  1.97272 -1.89163  1.35456 -0.49097 -0.49097  1.35456 -1.89163  1.97272 -1.57828  0.80339  0.16516 -1.09390  1.75895 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E17u    2.00000 -1.89163  1.57828 -1.09390  0.49097  0.16516 -0.80339  1.35456 -1.75895  1.97272 -1.97272  1.75895 -1.35456  0.80339 -0.16516 -0.49097  1.09390 -1.57828  1.89163 -2.00000  0.00000  0.00000 -2.00000 -1.89163  1.57828 -1.09390  0.49097  0.16516 -0.80339  1.35456 -1.75895  1.97272 -1.97272  1.75895 -1.35456  0.80339 -0.16516 -0.49097  1.09390 -1.57828  1.89163  2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............
E18u    2.00000 -1.97272  1.89163 -1.75895  1.57828 -1.35456  1.09390 -0.80339  0.49097 -0.16516 -0.16516  0.49097 -0.80339  1.09390 -1.35456  1.57828 -1.75895  1.89163 -1.97272  2.00000  0.00000  0.00000 -2.00000  1.97272 -1.89163  1.75895 -1.57828  1.35456 -1.09390  0.80339 -0.49097  0.16516  0.16516 -0.49097  0.80339 -1.09390  1.35456 -1.57828  1.75895 -1.89163  1.97272 -2.00000  0.00000  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.972722606805 = 2*cos(2*π/38) = 2*cos(π/19)
                               1.891634483401 = 2*cos(4*π/38) = 2*cos(2*π/19)
                               1.758947502413 = 2*cos(6*π/38) = 2*cos(3*π/19)
                               1.578281018793 = 2*cos(8*π/38) = 2*cos(4*π/19)
                               1.354563143251 = 2*cos(10*π/38) = 2*cos(5*π/19)
                               1.093896316245 = 2*cos(12*π/38) = 2*cos(6*π/19)
                               0.803390849306 = 2*cos(14*π/38) = 2*cos(7*π/19)
                               0.490970974282 = 2*cos(16*π/38) = 2*cos(8*π/19)
                               0.165158690945 = 2*cos(18*π/38) = 2*cos(9*π/19)



 Symmetry of Rotations and Cartesian products

A1g  d+g+i+k+m    z2, z4, z6 
A2g  R            Rz 
E1g  R+d+g+i+k+m  {Rx, Ry}, {xz, yz}, {xz3, yz3}, {xz5, yz5} 
E2g  d+g+i+k+m    {x2y2, xy}, {z2(x2y2), xyz2}, {z4(x2y2), xyz4} 
E3g  g+i+k+m      {xz(x2−3y2), yz(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4g  g+i+k+m      {(x2y2)2−4x2y2, xy(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5g  i+k+m        {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6g  i+k+m        {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7g  k+m 
E8g  k+m 
E9g  m 
E10g m 
A2u  p+f+h+j+l    z, z3, z5 
E1u  p+f+h+j+l    {x, y}, {xz2, yz2}, {xz4, yz4} 
E2u  f+h+j+l      {z(x2y2), xyz}, {z3(x2y2), xyz3} 
E3u  f+h+j+l      {x(x2−3y2), y(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)} 
E4u  h+j+l        {z((x2y2)2−4x2y2), xyz(x2y2)} 
E5u  h+j+l        {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)} 
E6u  j+l 
E7u  j+l 
E8u  l 
E9u  l 

 Notes:

    α  The order of the D38h point group is 152, and the order of the principal axis (C38) is 38. The group has 44 irreducible representations.

    β  The D38h point group is generated by three symmetry elements that are canonically chosen C38, C2 and i.
       Other choices include σh instead of i, or any of C2, σv or σd instead of C2. Also, some ternary combinations of C2, C2, σv and σd act as generators.
       Lastly, the S38 can be chosen, together with σh or C2 and any one of C2, C2, σv or σd.

    γ  There are two different sets of twofold symmetry axes perpendicular to the principal axis (z axis in standard orientation).
       By convention, the set denoted as C2 has the x axis as a member, while the y axis is a member of the C2 set.

    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 D38h 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  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.
       All characters of this group can be expressed using complex numbers, elementary arithmetic operations, square roots and third roots.

This Character Table for the D38h point group was created by Gernot Katzer.

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