Character Table for Point Group C43h

Character table for the C_43h point group

C43h 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 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 <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A' 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A" 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -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 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 ... 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 -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 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 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 ... ... 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 -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 ... ... ..... ..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 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 ... ... ..... 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 -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 ... ... ..... ....... ..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 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 ... ... ..... ....... 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 -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 ... ... ..... ....... ......... ..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 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 ... ... ..... ....... ......... 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 -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 ... ... ..... ....... ......... ........... ..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 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 ... ... ..... ....... ......... ........... 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 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 ... ... ..... ....... ......... ........... ............. 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 -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 ... ... ..... ....... ......... ........... ............. 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 A' R+d+g+i+k+m R_z, z², z⁴, z⁶ A" 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 C_43h point group is 86, and the order of the principal axis (S₄₃) is 86. The group has 44 irreducible representations. β The C_43h point group could also be named S₄₃, as it contains the S₄₃ axis as its only symmetry element. Another rare designation is C_86i because the S₄₃ axis is identical to a roto-inversion axis of order 86. γ The C_43h point group is isomorphic to C₈₆ and S₈₆. δ The C_43h point group is generated by one single symmetry element, S₄₃. Therefore, it is a cyclic group. The canonical choice, however, is to use redundant generators: C₄₃ and σ_h. ε The lowest nonvanishing multipole moment in C_43h is 4 (quadrupole moment). ζ This is an Abelian point group (the commutative law holds between all symmetry operations). The C_43h group is Abelian because it contains only one symmetry element, all the powers of which necessarily commute (sufficient condition). In Abelian groups, all symmetry operations form a class of their own, and all irreducible representations are one-dimensional. η Because the group is Abelian and the maximum order of rotation is >2, some irreducible representations have complex characters. These 84 cases have been combined into 42 two-dimensional representations that are no longer irreducible but have real-valued characters. Accordingly, 42 pairs of left and right rotations have been combined into one two-membered pseudo-class each. θ The 42 reducible “E” representations almost behave like true irreducible representations. Their norm, however, is twice the group order. Therefore, they have been marked with an asterisk in the table. This is essential when trying to decompose a reducible representation into “irreducible” ones using the familiar projection formula. ι 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_43h point group was created by Gernot Katzer.

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

	C_41h
	C_42h
C₄₃ C_43v	C_43h	D₄₃ D_43h D_43d
	C_44h
	C_45h

Character table for the C43h point group

Character table for the C_43h point group