Character Table for Point Group D43h

Character table for the D_43h point group

D43h E 2 C43 2 C43^2 2 C43^3 2 C43^4 2 C43^5 2 C43^6 2 C43^7 2 C43^8 2 C43^9 2 C43^10 2 C43^11 2 C43^12 2 C43^13 2 C43^14 2 C43^15 2 C43^16 2 C43^17 2 C43^18 2 C43^19 2 C43^20 2 C43^21 43 C2' sh 2 S43 2 S43^3 2 S43^5 2 S43^7 2 S43^9 2 S43^11 2 S43^13 2 S43^15 2 S43^17 2 S43^19 2 S43^21 2 S43^23 2 S43^25 2 S43^27 2 S43^29 2 S43^31 2 S43^33 2 S43^35 2 S43^37 2 S43^39 2 S43^41 43 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 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 ... ... ..... ....... ......... ........... ............. 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 ... ..... ....... ......... ........... ............. 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 ..... ......T ......... ..........T ............. E1' 2.00000 1.97869 1.91520 1.81090 1.66800 1.48954 1.27935 1.04188 0.78221 0.50587 0.21874 -0.07304 -0.36327 -0.64576 -0.91448 -1.16372 -1.38815 -1.58299 -1.74410 -1.86803 -1.95215 -1.99466 0.00000 2.00000 1.97869 1.81090 1.48954 1.04188 0.50587 -0.07304 -0.64576 -1.16372 -1.58299 -1.86803 -1.99466 -1.95215 -1.74410 -1.38815 -0.91448 -0.36327 0.21874 0.78221 1.27935 1.66800 1.91520 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E1" 2.00000 1.97869 1.91520 1.81090 1.66800 1.48954 1.27935 1.04188 0.78221 0.50587 0.21874 -0.07304 -0.36327 -0.64576 -0.91448 -1.16372 -1.38815 -1.58299 -1.74410 -1.86803 -1.95215 -1.99466 0.00000 -2.00000 -1.97869 -1.81090 -1.48954 -1.04188 -0.50587 0.07304 0.64576 1.16372 1.58299 1.86803 1.99466 1.95215 1.74410 1.38815 0.91448 0.36327 -0.21874 -0.78221 -1.27935 -1.66800 -1.91520 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. E2' 2.00000 1.91520 1.66800 1.27935 0.78221 0.21874 -0.36327 -0.91448 -1.38815 -1.74410 -1.95215 -1.99466 -1.86803 -1.58299 -1.16372 -0.64576 -0.07304 0.50587 1.04188 1.48954 1.81090 1.97869 0.00000 2.00000 1.91520 1.27935 0.21874 -0.91448 -1.74410 -1.99466 -1.58299 -0.64576 0.50587 1.48954 1.97869 1.81090 1.04188 -0.07304 -1.16372 -1.86803 -1.95215 -1.38815 -0.36327 0.78221 1.66800 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E2" 2.00000 1.91520 1.66800 1.27935 0.78221 0.21874 -0.36327 -0.91448 -1.38815 -1.74410 -1.95215 -1.99466 -1.86803 -1.58299 -1.16372 -0.64576 -0.07304 0.50587 1.04188 1.48954 1.81090 1.97869 0.00000 -2.00000 -1.91520 -1.27935 -0.21874 0.91448 1.74410 1.99466 1.58299 0.64576 -0.50587 -1.48954 -1.97869 -1.81090 -1.04188 0.07304 1.16372 1.86803 1.95215 1.38815 0.36327 -0.78221 -1.66800 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E3' 2.00000 1.81090 1.27935 0.50587 -0.36327 -1.16372 -1.74410 -1.99466 -1.86803 -1.38815 -0.64576 0.21874 1.04188 1.66800 1.97869 1.91520 1.48954 0.78221 -0.07304 -0.91448 -1.58299 -1.95215 0.00000 2.00000 1.81090 0.50587 -1.16372 -1.99466 -1.38815 0.21874 1.66800 1.91520 0.78221 -0.91448 -1.95215 -1.58299 -0.07304 1.48954 1.97869 1.04188 -0.64576 -1.86803 -1.74410 -0.36327 1.27935 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E3" 2.00000 1.81090 1.27935 0.50587 -0.36327 -1.16372 -1.74410 -1.99466 -1.86803 -1.38815 -0.64576 0.21874 1.04188 1.66800 1.97869 1.91520 1.48954 0.78221 -0.07304 -0.91448 -1.58299 -1.95215 0.00000 -2.00000 -1.81090 -0.50587 1.16372 1.99466 1.38815 -0.21874 -1.66800 -1.91520 -0.78221 0.91448 1.95215 1.58299 0.07304 -1.48954 -1.97869 -1.04188 0.64576 1.86803 1.74410 0.36327 -1.27935 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E4' 2.00000 1.66800 0.78221 -0.36327 -1.38815 -1.95215 -1.86803 -1.16372 -0.07304 1.04188 1.81090 1.97869 1.48954 0.50587 -0.64576 -1.58299 -1.99466 -1.74410 -0.91448 0.21874 1.27935 1.91520 0.00000 2.00000 1.66800 -0.36327 -1.95215 -1.16372 1.04188 1.97869 0.50587 -1.58299 -1.74410 0.21874 1.91520 1.27935 -0.91448 -1.99466 -0.64576 1.48954 1.81090 -0.07304 -1.86803 -1.38815 0.78221 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E4" 2.00000 1.66800 0.78221 -0.36327 -1.38815 -1.95215 -1.86803 -1.16372 -0.07304 1.04188 1.81090 1.97869 1.48954 0.50587 -0.64576 -1.58299 -1.99466 -1.74410 -0.91448 0.21874 1.27935 1.91520 0.00000 -2.00000 -1.66800 0.36327 1.95215 1.16372 -1.04188 -1.97869 -0.50587 1.58299 1.74410 -0.21874 -1.91520 -1.27935 0.91448 1.99466 0.64576 -1.48954 -1.81090 0.07304 1.86803 1.38815 -0.78221 0.00000 ... ... ..... ....... ......... ..TT....... ............. E5' 2.00000 1.48954 0.21874 -1.16372 -1.95215 -1.74410 -0.64576 0.78221 1.81090 1.91520 1.04188 -0.36327 -1.58299 -1.99466 -1.38815 -0.07304 1.27935 1.97869 1.66800 0.50587 -0.91448 -1.86803 0.00000 2.00000 1.48954 -1.16372 -1.74410 0.78221 1.91520 -0.36327 -1.99466 -0.07304 1.97869 0.50587 -1.86803 -0.91448 1.66800 1.27935 -1.38815 -1.58299 1.04188 1.81090 -0.64576 -1.95215 0.21874 0.00000 ... ... ..... ....... ......... TT......... ............. E5" 2.00000 1.48954 0.21874 -1.16372 -1.95215 -1.74410 -0.64576 0.78221 1.81090 1.91520 1.04188 -0.36327 -1.58299 -1.99466 -1.38815 -0.07304 1.27935 1.97869 1.66800 0.50587 -0.91448 -1.86803 0.00000 -2.00000 -1.48954 1.16372 1.74410 -0.78221 -1.91520 0.36327 1.99466 0.07304 -1.97869 -0.50587 1.86803 0.91448 -1.66800 -1.27935 1.38815 1.58299 -1.04188 -1.81090 0.64576 1.95215 -0.21874 0.00000 ... ... ..... ....... ......... ........... ..TT......... E6' 2.00000 1.27935 -0.36327 -1.74410 -1.86803 -0.64576 1.04188 1.97869 1.48954 -0.07304 -1.58299 -1.95215 -0.91448 0.78221 1.91520 1.66800 0.21874 -1.38815 -1.99466 -1.16372 0.50587 1.81090 0.00000 2.00000 1.27935 -1.74410 -0.64576 1.97869 -0.07304 -1.95215 0.78221 1.66800 -1.38815 -1.16372 1.81090 0.50587 -1.99466 0.21874 1.91520 -0.91448 -1.58299 1.48954 1.04188 -1.86803 -0.36327 0.00000 ... ... ..... ....... ......... ........... TT........... E6" 2.00000 1.27935 -0.36327 -1.74410 -1.86803 -0.64576 1.04188 1.97869 1.48954 -0.07304 -1.58299 -1.95215 -0.91448 0.78221 1.91520 1.66800 0.21874 -1.38815 -1.99466 -1.16372 0.50587 1.81090 0.00000 -2.00000 -1.27935 1.74410 0.64576 -1.97869 0.07304 1.95215 -0.78221 -1.66800 1.38815 1.16372 -1.81090 -0.50587 1.99466 -0.21874 -1.91520 0.91448 1.58299 -1.48954 -1.04188 1.86803 0.36327 0.00000 ... ... ..... ....... ......... ........... ............. E7' 2.00000 1.04188 -0.91448 -1.99466 -1.16372 0.78221 1.97869 1.27935 -0.64576 -1.95215 -1.38815 0.50587 1.91520 1.48954 -0.36327 -1.86803 -1.58299 0.21874 1.81090 1.66800 -0.07304 -1.74410 0.00000 2.00000 1.04188 -1.99466 0.78221 1.27935 -1.95215 0.50587 1.48954 -1.86803 0.21874 1.66800 -1.74410 -0.07304 1.81090 -1.58299 -0.36327 1.91520 -1.38815 -0.64576 1.97869 -1.16372 -0.91448 0.00000 ... ... ..... ....... ......... ........... ............. E7" 2.00000 1.04188 -0.91448 -1.99466 -1.16372 0.78221 1.97869 1.27935 -0.64576 -1.95215 -1.38815 0.50587 1.91520 1.48954 -0.36327 -1.86803 -1.58299 0.21874 1.81090 1.66800 -0.07304 -1.74410 0.00000 -2.00000 -1.04188 1.99466 -0.78221 -1.27935 1.95215 -0.50587 -1.48954 1.86803 -0.21874 -1.66800 1.74410 0.07304 -1.81090 1.58299 0.36327 -1.91520 1.38815 0.64576 -1.97869 1.16372 0.91448 0.00000 ... ... ..... ....... ......... ........... ............. E8' 2.00000 0.78221 -1.38815 -1.86803 -0.07304 1.81090 1.48954 -0.64576 -1.99466 -0.91448 1.27935 1.91520 0.21874 -1.74410 -1.58299 0.50587 1.97869 1.04188 -1.16372 -1.95215 -0.36327 1.66800 0.00000 2.00000 0.78221 -1.86803 1.81090 -0.64576 -0.91448 1.91520 -1.74410 0.50587 1.04188 -1.95215 1.66800 -0.36327 -1.16372 1.97869 -1.58299 0.21874 1.27935 -1.99466 1.48954 -0.07304 -1.38815 0.00000 ... ... ..... ....... ......... ........... ............. E8" 2.00000 0.78221 -1.38815 -1.86803 -0.07304 1.81090 1.48954 -0.64576 -1.99466 -0.91448 1.27935 1.91520 0.21874 -1.74410 -1.58299 0.50587 1.97869 1.04188 -1.16372 -1.95215 -0.36327 1.66800 0.00000 -2.00000 -0.78221 1.86803 -1.81090 0.64576 0.91448 -1.91520 1.74410 -0.50587 -1.04188 1.95215 -1.66800 0.36327 1.16372 -1.97869 1.58299 -0.21874 -1.27935 1.99466 -1.48954 0.07304 1.38815 0.00000 ... ... ..... ....... ......... ........... ............. E9' 2.00000 0.50587 -1.74410 -1.38815 1.04188 1.91520 -0.07304 -1.95215 -0.91448 1.48954 1.66800 -0.64576 -1.99466 -0.36327 1.81090 1.27935 -1.16372 -1.86803 0.21874 1.97869 0.78221 -1.58299 0.00000 2.00000 0.50587 -1.38815 1.91520 -1.95215 1.48954 -0.64576 -0.36327 1.27935 -1.86803 1.97869 -1.58299 0.78221 0.21874 -1.16372 1.81090 -1.99466 1.66800 -0.91448 -0.07304 1.04188 -1.74410 0.00000 ... ... ..... ....... ......... ........... ............. E9" 2.00000 0.50587 -1.74410 -1.38815 1.04188 1.91520 -0.07304 -1.95215 -0.91448 1.48954 1.66800 -0.64576 -1.99466 -0.36327 1.81090 1.27935 -1.16372 -1.86803 0.21874 1.97869 0.78221 -1.58299 0.00000 -2.00000 -0.50587 1.38815 -1.91520 1.95215 -1.48954 0.64576 0.36327 -1.27935 1.86803 -1.97869 1.58299 -0.78221 -0.21874 1.16372 -1.81090 1.99466 -1.66800 0.91448 0.07304 -1.04188 1.74410 0.00000 ... ... ..... ....... ......... ........... ............. E10' 2.00000 0.21874 -1.95215 -0.64576 1.81090 1.04188 -1.58299 -1.38815 1.27935 1.66800 -0.91448 -1.86803 0.50587 1.97869 -0.07304 -1.99466 -0.36327 1.91520 0.78221 -1.74410 -1.16372 1.48954 0.00000 2.00000 0.21874 -0.64576 1.04188 -1.38815 1.66800 -1.86803 1.97869 -1.99466 1.91520 -1.74410 1.48954 -1.16372 0.78221 -0.36327 -0.07304 0.50587 -0.91448 1.27935 -1.58299 1.81090 -1.95215 0.00000 ... ... ..... ....... ......... ........... ............. E10" 2.00000 0.21874 -1.95215 -0.64576 1.81090 1.04188 -1.58299 -1.38815 1.27935 1.66800 -0.91448 -1.86803 0.50587 1.97869 -0.07304 -1.99466 -0.36327 1.91520 0.78221 -1.74410 -1.16372 1.48954 0.00000 -2.00000 -0.21874 0.64576 -1.04188 1.38815 -1.66800 1.86803 -1.97869 1.99466 -1.91520 1.74410 -1.48954 1.16372 -0.78221 0.36327 0.07304 -0.50587 0.91448 -1.27935 1.58299 -1.81090 1.95215 0.00000 ... ... ..... ....... ......... ........... ............. E11' 2.00000 -0.07304 -1.99466 0.21874 1.97869 -0.36327 -1.95215 0.50587 1.91520 -0.64576 -1.86803 0.78221 1.81090 -0.91448 -1.74410 1.04188 1.66800 -1.16372 -1.58299 1.27935 1.48954 -1.38815 0.00000 2.00000 -0.07304 0.21874 -0.36327 0.50587 -0.64576 0.78221 -0.91448 1.04188 -1.16372 1.27935 -1.38815 1.48954 -1.58299 1.66800 -1.74410 1.81090 -1.86803 1.91520 -1.95215 1.97869 -1.99466 0.00000 ... ... ..... ....... ......... ........... ............. E11" 2.00000 -0.07304 -1.99466 0.21874 1.97869 -0.36327 -1.95215 0.50587 1.91520 -0.64576 -1.86803 0.78221 1.81090 -0.91448 -1.74410 1.04188 1.66800 -1.16372 -1.58299 1.27935 1.48954 -1.38815 0.00000 -2.00000 0.07304 -0.21874 0.36327 -0.50587 0.64576 -0.78221 0.91448 -1.04188 1.16372 -1.27935 1.38815 -1.48954 1.58299 -1.66800 1.74410 -1.81090 1.86803 -1.91520 1.95215 -1.97869 1.99466 0.00000 ... ... ..... ....... ......... ........... ............. E12' 2.00000 -0.36327 -1.86803 1.04188 1.48954 -1.58299 -0.91448 1.91520 0.21874 -1.99466 0.50587 1.81090 -1.16372 -1.38815 1.66800 0.78221 -1.95215 -0.07304 1.97869 -0.64576 -1.74410 1.27935 0.00000 2.00000 -0.36327 1.04188 -1.58299 1.91520 -1.99466 1.81090 -1.38815 0.78221 -0.07304 -0.64576 1.27935 -1.74410 1.97869 -1.95215 1.66800 -1.16372 0.50587 0.21874 -0.91448 1.48954 -1.86803 0.00000 ... ... ..... ....... ......... ........... ............. E12" 2.00000 -0.36327 -1.86803 1.04188 1.48954 -1.58299 -0.91448 1.91520 0.21874 -1.99466 0.50587 1.81090 -1.16372 -1.38815 1.66800 0.78221 -1.95215 -0.07304 1.97869 -0.64576 -1.74410 1.27935 0.00000 -2.00000 0.36327 -1.04188 1.58299 -1.91520 1.99466 -1.81090 1.38815 -0.78221 0.07304 0.64576 -1.27935 1.74410 -1.97869 1.95215 -1.66800 1.16372 -0.50587 -0.21874 0.91448 -1.48954 1.86803 0.00000 ... ... ..... ....... ......... ........... ............. E13' 2.00000 -0.64576 -1.58299 1.66800 0.50587 -1.99466 0.78221 1.48954 -1.74410 -0.36327 1.97869 -0.91448 -1.38815 1.81090 0.21874 -1.95215 1.04188 1.27935 -1.86803 -0.07304 1.91520 -1.16372 0.00000 2.00000 -0.64576 1.66800 -1.99466 1.48954 -0.36327 -0.91448 1.81090 -1.95215 1.27935 -0.07304 -1.16372 1.91520 -1.86803 1.04188 0.21874 -1.38815 1.97869 -1.74410 0.78221 0.50587 -1.58299 0.00000 ... ... ..... ....... ......... ........... ............. E13" 2.00000 -0.64576 -1.58299 1.66800 0.50587 -1.99466 0.78221 1.48954 -1.74410 -0.36327 1.97869 -0.91448 -1.38815 1.81090 0.21874 -1.95215 1.04188 1.27935 -1.86803 -0.07304 1.91520 -1.16372 0.00000 -2.00000 0.64576 -1.66800 1.99466 -1.48954 0.36327 0.91448 -1.81090 1.95215 -1.27935 0.07304 1.16372 -1.91520 1.86803 -1.04188 -0.21874 1.38815 -1.97869 1.74410 -0.78221 -0.50587 1.58299 0.00000 ... ... ..... ....... ......... ........... ............. E14' 2.00000 -0.91448 -1.16372 1.97869 -0.64576 -1.38815 1.91520 -0.36327 -1.58299 1.81090 -0.07304 -1.74410 1.66800 0.21874 -1.86803 1.48954 0.50587 -1.95215 1.27935 0.78221 -1.99466 1.04188 0.00000 2.00000 -0.91448 1.97869 -1.38815 -0.36327 1.81090 -1.74410 0.21874 1.48954 -1.95215 0.78221 1.04188 -1.99466 1.27935 0.50587 -1.86803 1.66800 -0.07304 -1.58299 1.91520 -0.64576 -1.16372 0.00000 ... ... ..... ....... ......... ........... ............. E14" 2.00000 -0.91448 -1.16372 1.97869 -0.64576 -1.38815 1.91520 -0.36327 -1.58299 1.81090 -0.07304 -1.74410 1.66800 0.21874 -1.86803 1.48954 0.50587 -1.95215 1.27935 0.78221 -1.99466 1.04188 0.00000 -2.00000 0.91448 -1.97869 1.38815 0.36327 -1.81090 1.74410 -0.21874 -1.48954 1.95215 -0.78221 -1.04188 1.99466 -1.27935 -0.50587 1.86803 -1.66800 0.07304 1.58299 -1.91520 0.64576 1.16372 0.00000 ... ... ..... ....... ......... ........... ............. E15' 2.00000 -1.16372 -0.64576 1.91520 -1.58299 -0.07304 1.66800 -1.86803 0.50587 1.27935 -1.99466 1.04188 0.78221 -1.95215 1.48954 0.21874 -1.74410 1.81090 -0.36327 -1.38815 1.97869 -0.91448 0.00000 2.00000 -1.16372 1.91520 -0.07304 -1.86803 1.27935 1.04188 -1.95215 0.21874 1.81090 -1.38815 -0.91448 1.97869 -0.36327 -1.74410 1.48954 0.78221 -1.99466 0.50587 1.66800 -1.58299 -0.64576 0.00000 ... ... ..... ....... ......... ........... ............. E15" 2.00000 -1.16372 -0.64576 1.91520 -1.58299 -0.07304 1.66800 -1.86803 0.50587 1.27935 -1.99466 1.04188 0.78221 -1.95215 1.48954 0.21874 -1.74410 1.81090 -0.36327 -1.38815 1.97869 -0.91448 0.00000 -2.00000 1.16372 -1.91520 0.07304 1.86803 -1.27935 -1.04188 1.95215 -0.21874 -1.81090 1.38815 0.91448 -1.97869 0.36327 1.74410 -1.48954 -0.78221 1.99466 -0.50587 -1.66800 1.58299 0.64576 0.00000 ... ... ..... ....... ......... ........... ............. E16' 2.00000 -1.38815 -0.07304 1.48954 -1.99466 1.27935 0.21874 -1.58299 1.97869 -1.16372 -0.36327 1.66800 -1.95215 1.04188 0.50587 -1.74410 1.91520 -0.91448 -0.64576 1.81090 -1.86803 0.78221 0.00000 2.00000 -1.38815 1.48954 1.27935 -1.58299 -1.16372 1.66800 1.04188 -1.74410 -0.91448 1.81090 0.78221 -1.86803 -0.64576 1.91520 0.50587 -1.95215 -0.36327 1.97869 0.21874 -1.99466 -0.07304 0.00000 ... ... ..... ....... ......... ........... ............. E16" 2.00000 -1.38815 -0.07304 1.48954 -1.99466 1.27935 0.21874 -1.58299 1.97869 -1.16372 -0.36327 1.66800 -1.95215 1.04188 0.50587 -1.74410 1.91520 -0.91448 -0.64576 1.81090 -1.86803 0.78221 0.00000 -2.00000 1.38815 -1.48954 -1.27935 1.58299 1.16372 -1.66800 -1.04188 1.74410 0.91448 -1.81090 -0.78221 1.86803 0.64576 -1.91520 -0.50587 1.95215 0.36327 -1.97869 -0.21874 1.99466 0.07304 0.00000 ... ... ..... ....... ......... ........... ............. E17' 2.00000 -1.58299 0.50587 0.78221 -1.74410 1.97869 -1.38815 0.21874 1.04188 -1.86803 1.91520 -1.16372 -0.07304 1.27935 -1.95215 1.81090 -0.91448 -0.36327 1.48954 -1.99466 1.66800 -0.64576 0.00000 2.00000 -1.58299 0.78221 1.97869 0.21874 -1.86803 -1.16372 1.27935 1.81090 -0.36327 -1.99466 -0.64576 1.66800 1.48954 -0.91448 -1.95215 -0.07304 1.91520 1.04188 -1.38815 -1.74410 0.50587 0.00000 ... ... ..... ....... ......... ........... ............. E17" 2.00000 -1.58299 0.50587 0.78221 -1.74410 1.97869 -1.38815 0.21874 1.04188 -1.86803 1.91520 -1.16372 -0.07304 1.27935 -1.95215 1.81090 -0.91448 -0.36327 1.48954 -1.99466 1.66800 -0.64576 0.00000 -2.00000 1.58299 -0.78221 -1.97869 -0.21874 1.86803 1.16372 -1.27935 -1.81090 0.36327 1.99466 0.64576 -1.66800 -1.48954 0.91448 1.95215 0.07304 -1.91520 -1.04188 1.38815 1.74410 -0.50587 0.00000 ... ... ..... ....... ......... ........... ............. E18' 2.00000 -1.74410 1.04188 -0.07304 -0.91448 1.66800 -1.99466 1.81090 -1.16372 0.21874 0.78221 -1.58299 1.97869 -1.86803 1.27935 -0.36327 -0.64576 1.48954 -1.95215 1.91520 -1.38815 0.50587 0.00000 2.00000 -1.74410 -0.07304 1.66800 1.81090 0.21874 -1.58299 -1.86803 -0.36327 1.48954 1.91520 0.50587 -1.38815 -1.95215 -0.64576 1.27935 1.97869 0.78221 -1.16372 -1.99466 -0.91448 1.04188 0.00000 ... ... ..... ....... ......... ........... ............. E18" 2.00000 -1.74410 1.04188 -0.07304 -0.91448 1.66800 -1.99466 1.81090 -1.16372 0.21874 0.78221 -1.58299 1.97869 -1.86803 1.27935 -0.36327 -0.64576 1.48954 -1.95215 1.91520 -1.38815 0.50587 0.00000 -2.00000 1.74410 0.07304 -1.66800 -1.81090 -0.21874 1.58299 1.86803 0.36327 -1.48954 -1.91520 -0.50587 1.38815 1.95215 0.64576 -1.27935 -1.97869 -0.78221 1.16372 1.99466 0.91448 -1.04188 0.00000 ... ... ..... ....... ......... ........... ............. E19' 2.00000 -1.86803 1.48954 -0.91448 0.21874 0.50587 -1.16372 1.66800 -1.95215 1.97869 -1.74410 1.27935 -0.64576 -0.07304 0.78221 -1.38815 1.81090 -1.99466 1.91520 -1.58299 1.04188 -0.36327 0.00000 2.00000 -1.86803 -0.91448 0.50587 1.66800 1.97869 1.27935 -0.07304 -1.38815 -1.99466 -1.58299 -0.36327 1.04188 1.91520 1.81090 0.78221 -0.64576 -1.74410 -1.95215 -1.16372 0.21874 1.48954 0.00000 ... ... ..... ....... ......... ........... ............. E19" 2.00000 -1.86803 1.48954 -0.91448 0.21874 0.50587 -1.16372 1.66800 -1.95215 1.97869 -1.74410 1.27935 -0.64576 -0.07304 0.78221 -1.38815 1.81090 -1.99466 1.91520 -1.58299 1.04188 -0.36327 0.00000 -2.00000 1.86803 0.91448 -0.50587 -1.66800 -1.97869 -1.27935 0.07304 1.38815 1.99466 1.58299 0.36327 -1.04188 -1.91520 -1.81090 -0.78221 0.64576 1.74410 1.95215 1.16372 -0.21874 -1.48954 0.00000 ... ... ..... ....... ......... ........... ............. E20' 2.00000 -1.95215 1.81090 -1.58299 1.27935 -0.91448 0.50587 -0.07304 -0.36327 0.78221 -1.16372 1.48954 -1.74410 1.91520 -1.99466 1.97869 -1.86803 1.66800 -1.38815 1.04188 -0.64576 0.21874 0.00000 2.00000 -1.95215 -1.58299 -0.91448 -0.07304 0.78221 1.48954 1.91520 1.97869 1.66800 1.04188 0.21874 -0.64576 -1.38815 -1.86803 -1.99466 -1.74410 -1.16372 -0.36327 0.50587 1.27935 1.81090 0.00000 ... ... ..... ....... ......... ........... ............. E20" 2.00000 -1.95215 1.81090 -1.58299 1.27935 -0.91448 0.50587 -0.07304 -0.36327 0.78221 -1.16372 1.48954 -1.74410 1.91520 -1.99466 1.97869 -1.86803 1.66800 -1.38815 1.04188 -0.64576 0.21874 0.00000 -2.00000 1.95215 1.58299 0.91448 0.07304 -0.78221 -1.48954 -1.91520 -1.97869 -1.66800 -1.04188 -0.21874 0.64576 1.38815 1.86803 1.99466 1.74410 1.16372 0.36327 -0.50587 -1.27935 -1.81090 0.00000 ... ... ..... ....... ......... ........... ............. E21' 2.00000 -1.99466 1.97869 -1.95215 1.91520 -1.86803 1.81090 -1.74410 1.66800 -1.58299 1.48954 -1.38815 1.27935 -1.16372 1.04188 -0.91448 0.78221 -0.64576 0.50587 -0.36327 0.21874 -0.07304 0.00000 2.00000 -1.99466 -1.95215 -1.86803 -1.74410 -1.58299 -1.38815 -1.16372 -0.91448 -0.64576 -0.36327 -0.07304 0.21874 0.50587 0.78221 1.04188 1.27935 1.48954 1.66800 1.81090 1.91520 1.97869 0.00000 ... ... ..... ....... ......... ........... ............. E21" 2.00000 -1.99466 1.97869 -1.95215 1.91520 -1.86803 1.81090 -1.74410 1.66800 -1.58299 1.48954 -1.38815 1.27935 -1.16372 1.04188 -0.91448 0.78221 -0.64576 0.50587 -0.36327 0.21874 -0.07304 0.00000 -2.00000 1.99466 1.95215 1.86803 1.74410 1.58299 1.38815 1.16372 0.91448 0.64576 0.36327 0.07304 -0.21874 -0.50587 -0.78221 -1.04188 -1.27935 -1.48954 -1.66800 -1.81090 -1.91520 -1.97869 0.00000 ... ... ..... ....... ......... ........... ............. Irrational character values: 1.994664567327 = 2*cos(2*π/86) = 2*cos(π/43) 1.978686736150 = 2*cos(4*π/86) = 2*cos(2*π/43) 1.952151755112 = 2*cos(6*π/86) = 2*cos(3*π/43) 1.915201199817 = 2*cos(8*π/86) = 2*cos(4*π/43) 1.868032217465 = 2*cos(10*π/86) = 2*cos(5*π/43) 1.810896474986 = 2*cos(12*π/86) = 2*cos(6*π/43) 1.744098816288 = 2*cos(14*π/86) = 2*cos(7*π/43) 1.667995635780 = 2*cos(16*π/86) = 2*cos(8*π/43) 1.582992976859 = 2*cos(18*π/86) = 2*cos(9*π/43) 1.489544365488 = 2*cos(20*π/86) = 2*cos(10*π/43) 1.388148390441 = 2*cos(22*π/86) = 2*cos(11*π/43) 1.279346043118 = 2*cos(24*π/86) = 2*cos(12*π/43) 1.163717831116 = 2*cos(26*π/86) = 2*cos(13*π/43) 1.041880680976 = 2*cos(28*π/86) = 2*cos(14*π/43) 0.914484646609 = 2*cos(30*π/86) = 2*cos(15*π/43) 0.782209440980 = 2*cos(32*π/86) = 2*cos(16*π/43) 0.645760809543 = 2*cos(34*π/86) = 2*cos(17*π/43) 0.505866764783 = 2*cos(36*π/86) = 2*cos(18*π/43) 0.363273701959 = 2*cos(38*π/86) = 2*cos(19*π/43) 0.218742416756 = 2*cos(40*π/86) = 2*cos(20*π/43) 0.073044046115 = 2*cos(42*π/86) = 2*cos(21*π/43) Symmetry of Rotations and Cartesian products A1' d+g+i+k+m z², z⁴, z⁶ A2' R R_z A2" p+f+h+j+l z, z³, z⁵ E1' p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E1" R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} E2' d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E2" f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E3' f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E3" g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E4' g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(x²−y²)} E4" h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E5' h+j+l {x(x²−(5+2√5)y²)(x²−(5−2√5)y²), y((5+2√5)x²−y²)((5−2√5)x²−y²)} E5" i+k+m {xz(x²−(5+2√5)y²)(x²−(5−2√5)y²), yz((5+2√5)x²−y²)((5−2√5)x²−y²)} E6' i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E6" j+l E7' j+l E7" k+m E8' k+m E8" l E9' l E9" m E10' m Notes: α The order of the D_43h point group is 172, and the order of the principal axis (S₄₃) is 86. The group has 46 irreducible representations. β The D_43h point group is isomorphic to D_43d, C_86v and D₈₆. γ The D_43h point group is generated by two symmetry elements, S₄₃ and either a perpendicular C₂^′ or a vertical σ_v. Also, the group may be generated from any two σ_v planes, or any σ_v and a non-coplanar C₂^′. The canonical choice, however, is to use redundant generators: C₄₃, C₂^′ and σ_h. δ The group contains one set of C₂^′ symmetry axes perpendicular to the principal (z) axis. The x axis (but not the y axis) is a member of that set. Similarly, the single set of symmetry planes denoted σ_d contains the xz plane but not the yz plane. ε The lowest nonvanishing multipole moment in D_43h 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 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 D_43h point group was created by Gernot Katzer.

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

	D_41h
	D_42h
C₄₃ C_43v C_43h D₄₃	D_43h	D_43d
	D_44h
	D_45h

Character table for the D43h point group

Character table for the D_43h point group