Character Table for Point Group D122d

Character table for the D_122d point group

D122d E 2 S244 2 C122 2 S244^3 2 C61 2 S244^5 2 C122^3 2 S244^7 2 C61^2 2 S244^9 2 C122^5 2 S244^11 2 C61^3 2 S244^13 2 C122^7 2 S244^15 2 C61^4 2 S244^17 2 C122^9 2 S244^19 2 C61^5 2 S244^21 2 C122^11 2 S244^23 2 C61^6 2 S244^25 2 C122^13 2 S244^27 2 C61^7 2 S244^29 2 C122^15 2 S244^31 2 C61^8 2 S244^33 2 C122^17 2 S244^35 2 C61^9 2 S244^37 2 C122^19 2 S244^39 2 C61^10 2 S244^41 2 C122^21 2 S244^43 2 C61^11 2 S244^45 2 C122^23 2 S244^47 2 C61^12 2 S244^49 2 C122^25 2 S244^51 2 C61^13 2 S244^53 2 C122^27 2 S244^55 2 C61^14 2 S244^57 2 C122^29 2 S244^59 2 C61^15 2 S4 2 C122^31 2 S244^63 2 C61^16 2 S244^65 2 C122^33 2 S244^67 2 C61^17 2 S244^69 2 C122^35 2 S244^71 2 C61^18 2 S244^73 2 C122^37 2 S244^75 2 C61^19 2 S244^77 2 C122^39 2 S244^79 2 C61^20 2 S244^81 2 C122^41 2 S244^83 2 C61^21 2 S244^85 2 C122^43 2 S244^87 2 C61^22 2 S244^89 2 C122^45 2 S244^91 2 C61^23 2 S244^93 2 C122^47 2 S244^95 2 C61^24 2 S244^97 2 C122^49 2 S244^99 2 C61^25 2 S244^101 2 C122^51 2 S244^103 2 C61^26 2 S244^105 2 C122^53 2 S244^107 2 C61^27 2 S244^109 2 C122^55 2 S244^111 2 C61^28 2 S244^113 2 C122^57 2 S244^115 2 C61^29 2 S244^117 2 C122^59 2 S244^119 2 C61^30 2 S244^121 C2 122 C2' 122 sd <R> <p> <—d—> <——f——> <———g———> <————h————> <—————i—————> A1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 A2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 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 ... ..... ....... ......... ........... ............. B1 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 1.00000 -1.00000 ... ... ..... ....... ......... ........... ............. B2 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -1.00000 1.00000 -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 1.99934 1.99735 1.99404 1.98940 1.98345 1.97618 1.96760 1.95771 1.94653 1.93406 1.92030 1.90527 1.88898 1.87143 1.85265 1.83263 1.81140 1.78897 1.76536 1.74057 1.71463 1.68755 1.65935 1.63006 1.59968 1.56824 1.53576 1.50226 1.46777 1.43230 1.39589 1.35855 1.32030 1.28119 1.24122 1.20043 1.15884 1.11649 1.07339 1.02959 0.98510 0.93995 0.89419 0.84783 0.80091 0.75346 0.70550 0.65708 0.60823 0.55897 0.50934 0.45938 0.40910 0.35856 0.30778 0.25680 0.20564 0.15435 0.10296 0.05150 0.00000 -0.05150 -0.10296 -0.15435 -0.20564 -0.25680 -0.30778 -0.35856 -0.40910 -0.45938 -0.50934 -0.55897 -0.60823 -0.65708 -0.70550 -0.75346 -0.80091 -0.84783 -0.89419 -0.93995 -0.98510 -1.02959 -1.07339 -1.11649 -1.15884 -1.20043 -1.24122 -1.28119 -1.32030 -1.35855 -1.39589 -1.43230 -1.46777 -1.50226 -1.53576 -1.56824 -1.59968 -1.63006 -1.65935 -1.68755 -1.71463 -1.74057 -1.76536 -1.78897 -1.81140 -1.83263 -1.85265 -1.87143 -1.88898 -1.90527 -1.92030 -1.93406 -1.94653 -1.95771 -1.96760 -1.97618 -1.98345 -1.98940 -1.99404 -1.99735 -1.99934 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99735 1.98940 1.97618 1.95771 1.93406 1.90527 1.87143 1.83263 1.78897 1.74057 1.68755 1.63006 1.56824 1.50226 1.43230 1.35855 1.28119 1.20043 1.11649 1.02959 0.93995 0.84783 0.75346 0.65708 0.55897 0.45938 0.35856 0.25680 0.15435 0.05150 -0.05150 -0.15435 -0.25680 -0.35856 -0.45938 -0.55897 -0.65708 -0.75346 -0.84783 -0.93995 -1.02959 -1.11649 -1.20043 -1.28119 -1.35855 -1.43230 -1.50226 -1.56824 -1.63006 -1.68755 -1.74057 -1.78897 -1.83263 -1.87143 -1.90527 -1.93406 -1.95771 -1.97618 -1.98940 -1.99735 -2.00000 -1.99735 -1.98940 -1.97618 -1.95771 -1.93406 -1.90527 -1.87143 -1.83263 -1.78897 -1.74057 -1.68755 -1.63006 -1.56824 -1.50226 -1.43230 -1.35855 -1.28119 -1.20043 -1.11649 -1.02959 -0.93995 -0.84783 -0.75346 -0.65708 -0.55897 -0.45938 -0.35856 -0.25680 -0.15435 -0.05150 0.05150 0.15435 0.25680 0.35856 0.45938 0.55897 0.65708 0.75346 0.84783 0.93995 1.02959 1.11649 1.20043 1.28119 1.35855 1.43230 1.50226 1.56824 1.63006 1.68755 1.74057 1.78897 1.83263 1.87143 1.90527 1.93406 1.95771 1.97618 1.98940 1.99735 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99404 1.97618 1.94653 1.90527 1.85265 1.78897 1.71463 1.63006 1.53576 1.43230 1.32030 1.20043 1.07339 0.93995 0.80091 0.65708 0.50934 0.35856 0.20564 0.05150 -0.10296 -0.25680 -0.40910 -0.55897 -0.70550 -0.84783 -0.98510 -1.11649 -1.24122 -1.35855 -1.46777 -1.56824 -1.65935 -1.74057 -1.81140 -1.87143 -1.92030 -1.95771 -1.98345 -1.99735 -1.99934 -1.98940 -1.96760 -1.93406 -1.88898 -1.83263 -1.76536 -1.68755 -1.59968 -1.50226 -1.39589 -1.28119 -1.15884 -1.02959 -0.89419 -0.75346 -0.60823 -0.45938 -0.30778 -0.15435 0.00000 0.15435 0.30778 0.45938 0.60823 0.75346 0.89419 1.02959 1.15884 1.28119 1.39589 1.50226 1.59968 1.68755 1.76536 1.83263 1.88898 1.93406 1.96760 1.98940 1.99934 1.99735 1.98345 1.95771 1.92030 1.87143 1.81140 1.74057 1.65935 1.56824 1.46777 1.35855 1.24122 1.11649 0.98510 0.84783 0.70550 0.55897 0.40910 0.25680 0.10296 -0.05150 -0.20564 -0.35856 -0.50934 -0.65708 -0.80091 -0.93995 -1.07339 -1.20043 -1.32030 -1.43230 -1.53576 -1.63006 -1.71463 -1.78897 -1.85265 -1.90527 -1.94653 -1.97618 -1.99404 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 2.00000 1.98940 1.95771 1.90527 1.83263 1.74057 1.63006 1.50226 1.35855 1.20043 1.02959 0.84783 0.65708 0.45938 0.25680 0.05150 -0.15435 -0.35856 -0.55897 -0.75346 -0.93995 -1.11649 -1.28119 -1.43230 -1.56824 -1.68755 -1.78897 -1.87143 -1.93406 -1.97618 -1.99735 -1.99735 -1.97618 -1.93406 -1.87143 -1.78897 -1.68755 -1.56824 -1.43230 -1.28119 -1.11649 -0.93995 -0.75346 -0.55897 -0.35856 -0.15435 0.05150 0.25680 0.45938 0.65708 0.84783 1.02959 1.20043 1.35855 1.50226 1.63006 1.74057 1.83263 1.90527 1.95771 1.98940 2.00000 1.98940 1.95771 1.90527 1.83263 1.74057 1.63006 1.50226 1.35855 1.20043 1.02959 0.84783 0.65708 0.45938 0.25680 0.05150 -0.15435 -0.35856 -0.55897 -0.75346 -0.93995 -1.11649 -1.28119 -1.43230 -1.56824 -1.68755 -1.78897 -1.87143 -1.93406 -1.97618 -1.99735 -1.99735 -1.97618 -1.93406 -1.87143 -1.78897 -1.68755 -1.56824 -1.43230 -1.28119 -1.11649 -0.93995 -0.75346 -0.55897 -0.35856 -0.15435 0.05150 0.25680 0.45938 0.65708 0.84783 1.02959 1.20043 1.35855 1.50226 1.63006 1.74057 1.83263 1.90527 1.95771 1.98940 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.98345 1.93406 1.85265 1.74057 1.59968 1.43230 1.24122 1.02959 0.80091 0.55897 0.30778 0.05150 -0.20564 -0.45938 -0.70550 -0.93995 -1.15884 -1.35855 -1.53576 -1.68755 -1.81140 -1.90527 -1.96760 -1.99735 -1.99404 -1.95771 -1.88898 -1.78897 -1.65935 -1.50226 -1.32030 -1.11649 -0.89419 -0.65708 -0.40910 -0.15435 0.10296 0.35856 0.60823 0.84783 1.07339 1.28119 1.46777 1.63006 1.76536 1.87143 1.94653 1.98940 1.99934 1.97618 1.92030 1.83263 1.71463 1.56824 1.39589 1.20043 0.98510 0.75346 0.50934 0.25680 0.00000 -0.25680 -0.50934 -0.75346 -0.98510 -1.20043 -1.39589 -1.56824 -1.71463 -1.83263 -1.92030 -1.97618 -1.99934 -1.98940 -1.94653 -1.87143 -1.76536 -1.63006 -1.46777 -1.28119 -1.07339 -0.84783 -0.60823 -0.35856 -0.10296 0.15435 0.40910 0.65708 0.89419 1.11649 1.32030 1.50226 1.65935 1.78897 1.88898 1.95771 1.99404 1.99735 1.96760 1.90527 1.81140 1.68755 1.53576 1.35855 1.15884 0.93995 0.70550 0.45938 0.20564 -0.05150 -0.30778 -0.55897 -0.80091 -1.02959 -1.24122 -1.43230 -1.59968 -1.74057 -1.85265 -1.93406 -1.98345 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.97618 1.90527 1.78897 1.63006 1.43230 1.20043 0.93995 0.65708 0.35856 0.05150 -0.25680 -0.55897 -0.84783 -1.11649 -1.35855 -1.56824 -1.74057 -1.87143 -1.95771 -1.99735 -1.98940 -1.93406 -1.83263 -1.68755 -1.50226 -1.28119 -1.02959 -0.75346 -0.45938 -0.15435 0.15435 0.45938 0.75346 1.02959 1.28119 1.50226 1.68755 1.83263 1.93406 1.98940 1.99735 1.95771 1.87143 1.74057 1.56824 1.35855 1.11649 0.84783 0.55897 0.25680 -0.05150 -0.35856 -0.65708 -0.93995 -1.20043 -1.43230 -1.63006 -1.78897 -1.90527 -1.97618 -2.00000 -1.97618 -1.90527 -1.78897 -1.63006 -1.43230 -1.20043 -0.93995 -0.65708 -0.35856 -0.05150 0.25680 0.55897 0.84783 1.11649 1.35855 1.56824 1.74057 1.87143 1.95771 1.99735 1.98940 1.93406 1.83263 1.68755 1.50226 1.28119 1.02959 0.75346 0.45938 0.15435 -0.15435 -0.45938 -0.75346 -1.02959 -1.28119 -1.50226 -1.68755 -1.83263 -1.93406 -1.98940 -1.99735 -1.95771 -1.87143 -1.74057 -1.56824 -1.35855 -1.11649 -0.84783 -0.55897 -0.25680 0.05150 0.35856 0.65708 0.93995 1.20043 1.43230 1.63006 1.78897 1.90527 1.97618 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.96760 1.87143 1.71463 1.50226 1.24122 0.93995 0.60823 0.25680 -0.10296 -0.45938 -0.80091 -1.11649 -1.39589 -1.63006 -1.81140 -1.93406 -1.99404 -1.98940 -1.92030 -1.78897 -1.59968 -1.35855 -1.07339 -0.75346 -0.40910 -0.05150 0.30778 0.65708 0.98510 1.28119 1.53576 1.74057 1.88898 1.97618 1.99934 1.95771 1.85265 1.68755 1.46777 1.20043 0.89419 0.55897 0.20564 -0.15435 -0.50934 -0.84783 -1.15884 -1.43230 -1.65935 -1.83263 -1.94653 -1.99735 -1.98345 -1.90527 -1.76536 -1.56824 -1.32030 -1.02959 -0.70550 -0.35856 0.00000 0.35856 0.70550 1.02959 1.32030 1.56824 1.76536 1.90527 1.98345 1.99735 1.94653 1.83263 1.65935 1.43230 1.15884 0.84783 0.50934 0.15435 -0.20564 -0.55897 -0.89419 -1.20043 -1.46777 -1.68755 -1.85265 -1.95771 -1.99934 -1.97618 -1.88898 -1.74057 -1.53576 -1.28119 -0.98510 -0.65708 -0.30778 0.05150 0.40910 0.75346 1.07339 1.35855 1.59968 1.78897 1.92030 1.98940 1.99404 1.93406 1.81140 1.63006 1.39589 1.11649 0.80091 0.45938 0.10296 -0.25680 -0.60823 -0.93995 -1.24122 -1.50226 -1.71463 -1.87143 -1.96760 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E118 2.00000 -1.98940 1.95771 -1.90527 1.83263 -1.74057 1.63006 -1.50226 1.35855 -1.20043 1.02959 -0.84783 0.65708 -0.45938 0.25680 -0.05150 -0.15435 0.35856 -0.55897 0.75346 -0.93995 1.11649 -1.28119 1.43230 -1.56824 1.68755 -1.78897 1.87143 -1.93406 1.97618 -1.99735 1.99735 -1.97618 1.93406 -1.87143 1.78897 -1.68755 1.56824 -1.43230 1.28119 -1.11649 0.93995 -0.75346 0.55897 -0.35856 0.15435 0.05150 -0.25680 0.45938 -0.65708 0.84783 -1.02959 1.20043 -1.35855 1.50226 -1.63006 1.74057 -1.83263 1.90527 -1.95771 1.98940 -2.00000 1.98940 -1.95771 1.90527 -1.83263 1.74057 -1.63006 1.50226 -1.35855 1.20043 -1.02959 0.84783 -0.65708 0.45938 -0.25680 0.05150 0.15435 -0.35856 0.55897 -0.75346 0.93995 -1.11649 1.28119 -1.43230 1.56824 -1.68755 1.78897 -1.87143 1.93406 -1.97618 1.99735 -1.99735 1.97618 -1.93406 1.87143 -1.78897 1.68755 -1.56824 1.43230 -1.28119 1.11649 -0.93995 0.75346 -0.55897 0.35856 -0.15435 -0.05150 0.25680 -0.45938 0.65708 -0.84783 1.02959 -1.20043 1.35855 -1.50226 1.63006 -1.74057 1.83263 -1.90527 1.95771 -1.98940 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E119 2.00000 -1.99404 1.97618 -1.94653 1.90527 -1.85265 1.78897 -1.71463 1.63006 -1.53576 1.43230 -1.32030 1.20043 -1.07339 0.93995 -0.80091 0.65708 -0.50934 0.35856 -0.20564 0.05150 0.10296 -0.25680 0.40910 -0.55897 0.70550 -0.84783 0.98510 -1.11649 1.24122 -1.35855 1.46777 -1.56824 1.65935 -1.74057 1.81140 -1.87143 1.92030 -1.95771 1.98345 -1.99735 1.99934 -1.98940 1.96760 -1.93406 1.88898 -1.83263 1.76536 -1.68755 1.59968 -1.50226 1.39589 -1.28119 1.15884 -1.02959 0.89419 -0.75346 0.60823 -0.45938 0.30778 -0.15435 0.00000 0.15435 -0.30778 0.45938 -0.60823 0.75346 -0.89419 1.02959 -1.15884 1.28119 -1.39589 1.50226 -1.59968 1.68755 -1.76536 1.83263 -1.88898 1.93406 -1.96760 1.98940 -1.99934 1.99735 -1.98345 1.95771 -1.92030 1.87143 -1.81140 1.74057 -1.65935 1.56824 -1.46777 1.35855 -1.24122 1.11649 -0.98510 0.84783 -0.70550 0.55897 -0.40910 0.25680 -0.10296 -0.05150 0.20564 -0.35856 0.50934 -0.65708 0.80091 -0.93995 1.07339 -1.20043 1.32030 -1.43230 1.53576 -1.63006 1.71463 -1.78897 1.85265 -1.90527 1.94653 -1.97618 1.99404 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E120 2.00000 -1.99735 1.98940 -1.97618 1.95771 -1.93406 1.90527 -1.87143 1.83263 -1.78897 1.74057 -1.68755 1.63006 -1.56824 1.50226 -1.43230 1.35855 -1.28119 1.20043 -1.11649 1.02959 -0.93995 0.84783 -0.75346 0.65708 -0.55897 0.45938 -0.35856 0.25680 -0.15435 0.05150 0.05150 -0.15435 0.25680 -0.35856 0.45938 -0.55897 0.65708 -0.75346 0.84783 -0.93995 1.02959 -1.11649 1.20043 -1.28119 1.35855 -1.43230 1.50226 -1.56824 1.63006 -1.68755 1.74057 -1.78897 1.83263 -1.87143 1.90527 -1.93406 1.95771 -1.97618 1.98940 -1.99735 2.00000 -1.99735 1.98940 -1.97618 1.95771 -1.93406 1.90527 -1.87143 1.83263 -1.78897 1.74057 -1.68755 1.63006 -1.56824 1.50226 -1.43230 1.35855 -1.28119 1.20043 -1.11649 1.02959 -0.93995 0.84783 -0.75346 0.65708 -0.55897 0.45938 -0.35856 0.25680 -0.15435 0.05150 0.05150 -0.15435 0.25680 -0.35856 0.45938 -0.55897 0.65708 -0.75346 0.84783 -0.93995 1.02959 -1.11649 1.20043 -1.28119 1.35855 -1.43230 1.50226 -1.56824 1.63006 -1.68755 1.74057 -1.78897 1.83263 -1.87143 1.90527 -1.93406 1.95771 -1.97618 1.98940 -1.99735 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E121 2.00000 -1.99934 1.99735 -1.99404 1.98940 -1.98345 1.97618 -1.96760 1.95771 -1.94653 1.93406 -1.92030 1.90527 -1.88898 1.87143 -1.85265 1.83263 -1.81140 1.78897 -1.76536 1.74057 -1.71463 1.68755 -1.65935 1.63006 -1.59968 1.56824 -1.53576 1.50226 -1.46777 1.43230 -1.39589 1.35855 -1.32030 1.28119 -1.24122 1.20043 -1.15884 1.11649 -1.07339 1.02959 -0.98510 0.93995 -0.89419 0.84783 -0.80091 0.75346 -0.70550 0.65708 -0.60823 0.55897 -0.50934 0.45938 -0.40910 0.35856 -0.30778 0.25680 -0.20564 0.15435 -0.10296 0.05150 0.00000 -0.05150 0.10296 -0.15435 0.20564 -0.25680 0.30778 -0.35856 0.40910 -0.45938 0.50934 -0.55897 0.60823 -0.65708 0.70550 -0.75346 0.80091 -0.84783 0.89419 -0.93995 0.98510 -1.02959 1.07339 -1.11649 1.15884 -1.20043 1.24122 -1.28119 1.32030 -1.35855 1.39589 -1.43230 1.46777 -1.50226 1.53576 -1.56824 1.59968 -1.63006 1.65935 -1.68755 1.71463 -1.74057 1.76536 -1.78897 1.81140 -1.83263 1.85265 -1.87143 1.88898 -1.90527 1.92030 -1.93406 1.94653 -1.95771 1.96760 -1.97618 1.98345 -1.98940 1.99404 -1.99735 1.99934 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999336935029 = 2*cos(2*π/244) = 2*cos(π/122) 1.997348179770 = 2*cos(4*π/244) = 2*cos(π/61) 1.994035052897 = 2*cos(6*π/244) = 2*cos(3*π/122) 1.989399751229 = 2*cos(8*π/244) = 2*cos(2*π/61) 1.983445348272 = 2*cos(10*π/244) = 2*cos(5*π/122) 1.976175792182 = 2*cos(12*π/244) = 2*cos(3*π/61) 1.967595903147 = 2*cos(14*π/244) = 2*cos(7*π/122) 1.957711370191 = 2*cos(16*π/244) = 2*cos(4*π/61) 1.946528747401 = 2*cos(18*π/244) = 2*cos(9*π/122) 1.934055449583 = 2*cos(20*π/244) = 2*cos(5*π/61) 1.920299747343 = 2*cos(22*π/244) = 2*cos(11*π/122) 1.905270761607 = 2*cos(24*π/244) = 2*cos(6*π/61) 1.888978457567 = 2*cos(26*π/244) = 2*cos(13*π/122) 1.871433638081 = 2*cos(28*π/244) = 2*cos(7*π/61) 1.852647936503 = 2*cos(30*π/244) = 2*cos(15*π/122) 1.832633808974 = 2*cos(32*π/244) = 2*cos(8*π/61) 1.811404526161 = 2*cos(34*π/244) = 2*cos(17*π/122) 1.788974164458 = 2*cos(36*π/244) = 2*cos(9*π/61) 1.765357596651 = 2*cos(38*π/244) = 2*cos(19*π/122) 1.740570482060 = 2*cos(40*π/244) = 2*cos(10*π/61) 1.714629256153 = 2*cos(42*π/244) = 2*cos(21*π/122) 1.687551119646 = 2*cos(44*π/244) = 2*cos(11*π/61) 1.659354027105 = 2*cos(46*π/244) = 2*cos(23*π/122) 1.630056675034 = 2*cos(48*π/244) = 2*cos(12*π/61) 1.599678489479 = 2*cos(50*π/244) = 2*cos(25*π/122) 1.568239613153 = 2*cos(52*π/244) = 2*cos(13*π/61) 1.535760892073 = 2*cos(54*π/244) = 2*cos(27*π/122) 1.502263861741 = 2*cos(56*π/244) = 2*cos(14*π/61) 1.467770732864 = 2*cos(58*π/244) = 2*cos(29*π/122) 1.432304376629 = 2*cos(60*π/244) = 2*cos(15*π/61) 1.395888309533 = 2*cos(62*π/244) = 2*cos(31*π/122) 1.358546677795 = 2*cos(64*π/244) = 2*cos(16*π/61) 1.320304241342 = 2*cos(66*π/244) = 2*cos(33*π/122) 1.281186357396 = 2*cos(68*π/244) = 2*cos(17*π/61) 1.241218963655 = 2*cos(70*π/244) = 2*cos(35*π/122) 1.200428561097 = 2*cos(72*π/244) = 2*cos(18*π/61) 1.158842196409 = 2*cos(74*π/244) = 2*cos(37*π/122) 1.116487444054 = 2*cos(76*π/244) = 2*cos(19*π/61) 1.073392387983 = 2*cos(78*π/244) = 2*cos(39*π/122) 1.029585603020 = 2*cos(80*π/244) = 2*cos(20*π/61) 0.985096135908 = 2*cos(82*π/244) = 2*cos(41*π/122) 0.939953486055 = 2*cos(84*π/244) = 2*cos(21*π/61) 0.894187585970 = 2*cos(86*π/244) = 2*cos(43*π/122) 0.847828781420 = 2*cos(88*π/244) = 2*cos(22*π/61) 0.800907811303 = 2*cos(90*π/244) = 2*cos(45*π/122) 0.753455787270 = 2*cos(92*π/244) = 2*cos(23*π/61) 0.705504173098 = 2*cos(94*π/244) = 2*cos(47*π/122) 0.657084763822 = 2*cos(96*π/244) = 2*cos(24*π/61) 0.608229664655 = 2*cos(98*π/244) = 2*cos(49*π/122) 0.558971269703 = 2*cos(100*π/244) = 2*cos(25*π/61) 0.509342240482 = 2*cos(102*π/244) = 2*cos(51*π/122) 0.459375484264 = 2*cos(104*π/244) = 2*cos(26*π/61) 0.409104132252 = 2*cos(106*π/244) = 2*cos(53*π/122) 0.358561517621 = 2*cos(108*π/244) = 2*cos(27*π/61) 0.307781153408 = 2*cos(110*π/244) = 2*cos(55*π/122) 0.256796710293 = 2*cos(112*π/244) = 2*cos(28*π/61) 0.205641994275 = 2*cos(114*π/244) = 2*cos(57*π/122) 0.154350924253 = 2*cos(116*π/244) = 2*cos(29*π/61) 0.102957509541 = 2*cos(118*π/244) = 2*cos(59*π/122) 0.051495827310 = 2*cos(120*π/244) = 2*cos(30*π/61) Symmetry of Rotations and Cartesian products A1 d+g+i+k+m z², z⁴, z⁶ A2 R R_z B2 p+f+h+j+l z, z³, z⁵ E1 p+f+h+j+l {x, y}, {xz², yz²}, {xz⁴, yz⁴} E2 d+g+i+k+m {x²−y², xy}, {z²(x²−y²), xyz²}, {z⁴(x²−y²), xyz⁴} E3 f+h+j+l {x(x²−3y²), y(3x²−y²)}, {xz²(x²−3y²), yz²(3x²−y²)} E4 g+i+k+m {(x²−y²)²−4x²y², xy(x²−y²)}, {z²((x²−y²)²−4x²y²), xyz²(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)} E6 i+k+m {x²(x²−3y²)²−y²(3x²−y²)², xy(x²−3y²)(3x²−y²)} E7 j+l E8 k+m E9 l E10 m E113 m E114 l E115 k+m E116 j+l E117 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)} E118 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E119 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E120 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E121 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_122d point group is 488, and the order of the principal axis (S₂₄₄) is 244. The group has 125 irreducible representations. β The D_122d point group is isomorphic to C_244v and D₂₄₄. γ The D_122d point group is generated by two symmetry elements, S₂₄₄ and either a perpendicular C₂^′ or a vertical σ_d. Also, the group may be generated from a C₂^′ plus a σ_d (some pairs will yield smaller groups, though; choosing a minimum angle is safe). δ The lowest nonvanishing multipole moment in D_122d is 4 (quadrupole moment). ε This point group is non-Abelian (some symmetry operations are not commutative). Therefore, the character table contains multi-membered classes and degenerate irreducible representations. ζ Some of the characters in the table are irrational because the order of the principal axis is neither 1,2,3,4 nor 6. These irrational values can be expressed as cosine values, or as solutions of algebraic equations with a leading coefficient of 1. All characters are algebraic integers of a degree much less than half the order of the principal axis. 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_122d point group was created by Gernot Katzer.

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

	D_120d
	D_121d
C₁₂₂ C_122v C_122h D₁₂₂ D_122h	D_122d	S₁₂₂
	D_123d
	D_124d

Character table for the D122d point group

Character table for the D_122d point group