Character Table for Point Group D118d

Character table for the D_118d point group

D118d E 2 S236 2 C118 2 S236^3 2 C59 2 S236^5 2 C118^3 2 S236^7 2 C59^2 2 S236^9 2 C118^5 2 S236^11 2 C59^3 2 S236^13 2 C118^7 2 S236^15 2 C59^4 2 S236^17 2 C118^9 2 S236^19 2 C59^5 2 S236^21 2 C118^11 2 S236^23 2 C59^6 2 S236^25 2 C118^13 2 S236^27 2 C59^7 2 S236^29 2 C118^15 2 S236^31 2 C59^8 2 S236^33 2 C118^17 2 S236^35 2 C59^9 2 S236^37 2 C118^19 2 S236^39 2 C59^10 2 S236^41 2 C118^21 2 S236^43 2 C59^11 2 S236^45 2 C118^23 2 S236^47 2 C59^12 2 S236^49 2 C118^25 2 S236^51 2 C59^13 2 S236^53 2 C118^27 2 S236^55 2 C59^14 2 S236^57 2 C118^29 2 S4 2 C59^15 2 S236^61 2 C118^31 2 S236^63 2 C59^16 2 S236^65 2 C118^33 2 S236^67 2 C59^17 2 S236^69 2 C118^35 2 S236^71 2 C59^18 2 S236^73 2 C118^37 2 S236^75 2 C59^19 2 S236^77 2 C118^39 2 S236^79 2 C59^20 2 S236^81 2 C118^41 2 S236^83 2 C59^21 2 S236^85 2 C118^43 2 S236^87 2 C59^22 2 S236^89 2 C118^45 2 S236^91 2 C59^23 2 S236^93 2 C118^47 2 S236^95 2 C59^24 2 S236^97 2 C118^49 2 S236^99 2 C59^25 2 S236^101 2 C118^51 2 S236^103 2 C59^26 2 S236^105 2 C118^53 2 S236^107 2 C59^27 2 S236^109 2 C118^55 2 S236^111 2 C59^28 2 S236^113 2 C118^57 2 S236^115 2 C59^29 2 S236^117 C2 118 C2' 118 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 ... ... ....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 ..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 ... ... ..... ....... ......... ........... ............. 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 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99929 1.99717 1.99362 1.98867 1.98231 1.97454 1.96537 1.95481 1.94286 1.92954 1.91484 1.89880 1.88140 1.86267 1.84262 1.82127 1.79862 1.77470 1.74953 1.72311 1.69547 1.66663 1.63661 1.60542 1.57310 1.53967 1.50514 1.46955 1.43291 1.39526 1.35662 1.31702 1.27649 1.23505 1.19273 1.14957 1.10560 1.06084 1.01533 0.96910 0.92219 0.87461 0.82642 0.77765 0.72832 0.67848 0.62815 0.57738 0.52621 0.47465 0.42277 0.37058 0.31813 0.26545 0.21259 0.15957 0.10644 0.05324 0.00000 -0.05324 -0.10644 -0.15957 -0.21259 -0.26545 -0.31813 -0.37058 -0.42277 -0.47465 -0.52621 -0.57738 -0.62815 -0.67848 -0.72832 -0.77765 -0.82642 -0.87461 -0.92219 -0.96910 -1.01533 -1.06084 -1.10560 -1.14957 -1.19273 -1.23505 -1.27649 -1.31702 -1.35662 -1.39526 -1.43291 -1.46955 -1.50514 -1.53967 -1.57310 -1.60542 -1.63661 -1.66663 -1.69547 -1.72311 -1.74953 -1.77470 -1.79862 -1.82127 -1.84262 -1.86267 -1.88140 -1.89880 -1.91484 -1.92954 -1.94286 -1.95481 -1.96537 -1.97454 -1.98231 -1.98867 -1.99362 -1.99717 -1.99929 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99717 1.98867 1.97454 1.95481 1.92954 1.89880 1.86267 1.82127 1.77470 1.72311 1.66663 1.60542 1.53967 1.46955 1.39526 1.31702 1.23505 1.14957 1.06084 0.96910 0.87461 0.77765 0.67848 0.57738 0.47465 0.37058 0.26545 0.15957 0.05324 -0.05324 -0.15957 -0.26545 -0.37058 -0.47465 -0.57738 -0.67848 -0.77765 -0.87461 -0.96910 -1.06084 -1.14957 -1.23505 -1.31702 -1.39526 -1.46955 -1.53967 -1.60542 -1.66663 -1.72311 -1.77470 -1.82127 -1.86267 -1.89880 -1.92954 -1.95481 -1.97454 -1.98867 -1.99717 -2.00000 -1.99717 -1.98867 -1.97454 -1.95481 -1.92954 -1.89880 -1.86267 -1.82127 -1.77470 -1.72311 -1.66663 -1.60542 -1.53967 -1.46955 -1.39526 -1.31702 -1.23505 -1.14957 -1.06084 -0.96910 -0.87461 -0.77765 -0.67848 -0.57738 -0.47465 -0.37058 -0.26545 -0.15957 -0.05324 0.05324 0.15957 0.26545 0.37058 0.47465 0.57738 0.67848 0.77765 0.87461 0.96910 1.06084 1.14957 1.23505 1.31702 1.39526 1.46955 1.53967 1.60542 1.66663 1.72311 1.77470 1.82127 1.86267 1.89880 1.92954 1.95481 1.97454 1.98867 1.99717 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99362 1.97454 1.94286 1.89880 1.84262 1.77470 1.69547 1.60542 1.50514 1.39526 1.27649 1.14957 1.01533 0.87461 0.72832 0.57738 0.42277 0.26545 0.10644 -0.05324 -0.21259 -0.37058 -0.52621 -0.67848 -0.82642 -0.96910 -1.10560 -1.23505 -1.35662 -1.46955 -1.57310 -1.66663 -1.74953 -1.82127 -1.88140 -1.92954 -1.96537 -1.98867 -1.99929 -1.99717 -1.98231 -1.95481 -1.91484 -1.86267 -1.79862 -1.72311 -1.63661 -1.53967 -1.43291 -1.31702 -1.19273 -1.06084 -0.92219 -0.77765 -0.62815 -0.47465 -0.31813 -0.15957 0.00000 0.15957 0.31813 0.47465 0.62815 0.77765 0.92219 1.06084 1.19273 1.31702 1.43291 1.53967 1.63661 1.72311 1.79862 1.86267 1.91484 1.95481 1.98231 1.99717 1.99929 1.98867 1.96537 1.92954 1.88140 1.82127 1.74953 1.66663 1.57310 1.46955 1.35662 1.23505 1.10560 0.96910 0.82642 0.67848 0.52621 0.37058 0.21259 0.05324 -0.10644 -0.26545 -0.42277 -0.57738 -0.72832 -0.87461 -1.01533 -1.14957 -1.27649 -1.39526 -1.50514 -1.60542 -1.69547 -1.77470 -1.84262 -1.89880 -1.94286 -1.97454 -1.99362 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 2.00000 1.98867 1.95481 1.89880 1.82127 1.72311 1.60542 1.46955 1.31702 1.14957 0.96910 0.77765 0.57738 0.37058 0.15957 -0.05324 -0.26545 -0.47465 -0.67848 -0.87461 -1.06084 -1.23505 -1.39526 -1.53967 -1.66663 -1.77470 -1.86267 -1.92954 -1.97454 -1.99717 -1.99717 -1.97454 -1.92954 -1.86267 -1.77470 -1.66663 -1.53967 -1.39526 -1.23505 -1.06084 -0.87461 -0.67848 -0.47465 -0.26545 -0.05324 0.15957 0.37058 0.57738 0.77765 0.96910 1.14957 1.31702 1.46955 1.60542 1.72311 1.82127 1.89880 1.95481 1.98867 2.00000 1.98867 1.95481 1.89880 1.82127 1.72311 1.60542 1.46955 1.31702 1.14957 0.96910 0.77765 0.57738 0.37058 0.15957 -0.05324 -0.26545 -0.47465 -0.67848 -0.87461 -1.06084 -1.23505 -1.39526 -1.53967 -1.66663 -1.77470 -1.86267 -1.92954 -1.97454 -1.99717 -1.99717 -1.97454 -1.92954 -1.86267 -1.77470 -1.66663 -1.53967 -1.39526 -1.23505 -1.06084 -0.87461 -0.67848 -0.47465 -0.26545 -0.05324 0.15957 0.37058 0.57738 0.77765 0.96910 1.14957 1.31702 1.46955 1.60542 1.72311 1.82127 1.89880 1.95481 1.98867 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.98231 1.92954 1.84262 1.72311 1.57310 1.39526 1.19273 0.96910 0.72832 0.47465 0.21259 -0.05324 -0.31813 -0.57738 -0.82642 -1.06084 -1.27649 -1.46955 -1.63661 -1.77470 -1.88140 -1.95481 -1.99362 -1.99717 -1.96537 -1.89880 -1.79862 -1.66663 -1.50514 -1.31702 -1.10560 -0.87461 -0.62815 -0.37058 -0.10644 0.15957 0.42277 0.67848 0.92219 1.14957 1.35662 1.53967 1.69547 1.82127 1.91484 1.97454 1.99929 1.98867 1.94286 1.86267 1.74953 1.60542 1.43291 1.23505 1.01533 0.77765 0.52621 0.26545 0.00000 -0.26545 -0.52621 -0.77765 -1.01533 -1.23505 -1.43291 -1.60542 -1.74953 -1.86267 -1.94286 -1.98867 -1.99929 -1.97454 -1.91484 -1.82127 -1.69547 -1.53967 -1.35662 -1.14957 -0.92219 -0.67848 -0.42277 -0.15957 0.10644 0.37058 0.62815 0.87461 1.10560 1.31702 1.50514 1.66663 1.79862 1.89880 1.96537 1.99717 1.99362 1.95481 1.88140 1.77470 1.63661 1.46955 1.27649 1.06084 0.82642 0.57738 0.31813 0.05324 -0.21259 -0.47465 -0.72832 -0.96910 -1.19273 -1.39526 -1.57310 -1.72311 -1.84262 -1.92954 -1.98231 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.97454 1.89880 1.77470 1.60542 1.39526 1.14957 0.87461 0.57738 0.26545 -0.05324 -0.37058 -0.67848 -0.96910 -1.23505 -1.46955 -1.66663 -1.82127 -1.92954 -1.98867 -1.99717 -1.95481 -1.86267 -1.72311 -1.53967 -1.31702 -1.06084 -0.77765 -0.47465 -0.15957 0.15957 0.47465 0.77765 1.06084 1.31702 1.53967 1.72311 1.86267 1.95481 1.99717 1.98867 1.92954 1.82127 1.66663 1.46955 1.23505 0.96910 0.67848 0.37058 0.05324 -0.26545 -0.57738 -0.87461 -1.14957 -1.39526 -1.60542 -1.77470 -1.89880 -1.97454 -2.00000 -1.97454 -1.89880 -1.77470 -1.60542 -1.39526 -1.14957 -0.87461 -0.57738 -0.26545 0.05324 0.37058 0.67848 0.96910 1.23505 1.46955 1.66663 1.82127 1.92954 1.98867 1.99717 1.95481 1.86267 1.72311 1.53967 1.31702 1.06084 0.77765 0.47465 0.15957 -0.15957 -0.47465 -0.77765 -1.06084 -1.31702 -1.53967 -1.72311 -1.86267 -1.95481 -1.99717 -1.98867 -1.92954 -1.82127 -1.66663 -1.46955 -1.23505 -0.96910 -0.67848 -0.37058 -0.05324 0.26545 0.57738 0.87461 1.14957 1.39526 1.60542 1.77470 1.89880 1.97454 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.96537 1.86267 1.69547 1.46955 1.19273 0.87461 0.52621 0.15957 -0.21259 -0.57738 -0.92219 -1.23505 -1.50514 -1.72311 -1.88140 -1.97454 -1.99929 -1.95481 -1.84262 -1.66663 -1.43291 -1.14957 -0.82642 -0.47465 -0.10644 0.26545 0.62815 0.96910 1.27649 1.53967 1.74953 1.89880 1.98231 1.99717 1.94286 1.82127 1.63661 1.39526 1.10560 0.77765 0.42277 0.05324 -0.31813 -0.67848 -1.01533 -1.31702 -1.57310 -1.77470 -1.91484 -1.98867 -1.99362 -1.92954 -1.79862 -1.60542 -1.35662 -1.06084 -0.72832 -0.37058 0.00000 0.37058 0.72832 1.06084 1.35662 1.60542 1.79862 1.92954 1.99362 1.98867 1.91484 1.77470 1.57310 1.31702 1.01533 0.67848 0.31813 -0.05324 -0.42277 -0.77765 -1.10560 -1.39526 -1.63661 -1.82127 -1.94286 -1.99717 -1.98231 -1.89880 -1.74953 -1.53967 -1.27649 -0.96910 -0.62815 -0.26545 0.10644 0.47465 0.82642 1.14957 1.43291 1.66663 1.84262 1.95481 1.99929 1.97454 1.88140 1.72311 1.50514 1.23505 0.92219 0.57738 0.21259 -0.15957 -0.52621 -0.87461 -1.19273 -1.46955 -1.69547 -1.86267 -1.96537 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. E8 2.00000 1.95481 1.82127 1.60542 1.31702 0.96910 0.57738 0.15957 -0.26545 -0.67848 -1.06084 -1.39526 -1.66663 -1.86267 -1.97454 -1.99717 -1.92954 -1.77470 -1.53967 -1.23505 -0.87461 -0.47465 -0.05324 0.37058 0.77765 1.14957 1.46955 1.72311 1.89880 1.98867 1.98867 1.89880 1.72311 1.46955 1.14957 0.77765 0.37058 -0.05324 -0.47465 -0.87461 -1.23505 -1.53967 -1.77470 -1.92954 -1.99717 -1.97454 -1.86267 -1.66663 -1.39526 -1.06084 -0.67848 -0.26545 0.15957 0.57738 0.96910 1.31702 1.60542 1.82127 1.95481 2.00000 1.95481 1.82127 1.60542 1.31702 0.96910 0.57738 0.15957 -0.26545 -0.67848 -1.06084 -1.39526 -1.66663 -1.86267 -1.97454 -1.99717 -1.92954 -1.77470 -1.53967 -1.23505 -0.87461 -0.47465 -0.05324 0.37058 0.77765 1.14957 1.46955 1.72311 1.89880 1.98867 1.98867 1.89880 1.72311 1.46955 1.14957 0.77765 0.37058 -0.05324 -0.47465 -0.87461 -1.23505 -1.53967 -1.77470 -1.92954 -1.99717 -1.97454 -1.86267 -1.66663 -1.39526 -1.06084 -0.67848 -0.26545 0.15957 0.57738 0.96910 1.31702 1.60542 1.82127 1.95481 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E116 2.00000 -1.99717 1.98867 -1.97454 1.95481 -1.92954 1.89880 -1.86267 1.82127 -1.77470 1.72311 -1.66663 1.60542 -1.53967 1.46955 -1.39526 1.31702 -1.23505 1.14957 -1.06084 0.96910 -0.87461 0.77765 -0.67848 0.57738 -0.47465 0.37058 -0.26545 0.15957 -0.05324 -0.05324 0.15957 -0.26545 0.37058 -0.47465 0.57738 -0.67848 0.77765 -0.87461 0.96910 -1.06084 1.14957 -1.23505 1.31702 -1.39526 1.46955 -1.53967 1.60542 -1.66663 1.72311 -1.77470 1.82127 -1.86267 1.89880 -1.92954 1.95481 -1.97454 1.98867 -1.99717 2.00000 -1.99717 1.98867 -1.97454 1.95481 -1.92954 1.89880 -1.86267 1.82127 -1.77470 1.72311 -1.66663 1.60542 -1.53967 1.46955 -1.39526 1.31702 -1.23505 1.14957 -1.06084 0.96910 -0.87461 0.77765 -0.67848 0.57738 -0.47465 0.37058 -0.26545 0.15957 -0.05324 -0.05324 0.15957 -0.26545 0.37058 -0.47465 0.57738 -0.67848 0.77765 -0.87461 0.96910 -1.06084 1.14957 -1.23505 1.31702 -1.39526 1.46955 -1.53967 1.60542 -1.66663 1.72311 -1.77470 1.82127 -1.86267 1.89880 -1.92954 1.95481 -1.97454 1.98867 -1.99717 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E117 2.00000 -1.99929 1.99717 -1.99362 1.98867 -1.98231 1.97454 -1.96537 1.95481 -1.94286 1.92954 -1.91484 1.89880 -1.88140 1.86267 -1.84262 1.82127 -1.79862 1.77470 -1.74953 1.72311 -1.69547 1.66663 -1.63661 1.60542 -1.57310 1.53967 -1.50514 1.46955 -1.43291 1.39526 -1.35662 1.31702 -1.27649 1.23505 -1.19273 1.14957 -1.10560 1.06084 -1.01533 0.96910 -0.92219 0.87461 -0.82642 0.77765 -0.72832 0.67848 -0.62815 0.57738 -0.52621 0.47465 -0.42277 0.37058 -0.31813 0.26545 -0.21259 0.15957 -0.10644 0.05324 0.00000 -0.05324 0.10644 -0.15957 0.21259 -0.26545 0.31813 -0.37058 0.42277 -0.47465 0.52621 -0.57738 0.62815 -0.67848 0.72832 -0.77765 0.82642 -0.87461 0.92219 -0.96910 1.01533 -1.06084 1.10560 -1.14957 1.19273 -1.23505 1.27649 -1.31702 1.35662 -1.39526 1.43291 -1.46955 1.50514 -1.53967 1.57310 -1.60542 1.63661 -1.66663 1.69547 -1.72311 1.74953 -1.77470 1.79862 -1.82127 1.84262 -1.86267 1.88140 -1.89880 1.91484 -1.92954 1.94286 -1.95481 1.96537 -1.97454 1.98231 -1.98867 1.99362 -1.99717 1.99929 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999291222247 = 2*cos(2*π/236) = 2*cos(π/118) 1.997165391354 = 2*cos(4*π/236) = 2*cos(π/59) 1.993624014062 = 2*cos(6*π/236) = 2*cos(3*π/118) 1.988669600420 = 2*cos(8*π/236) = 2*cos(2*π/59) 1.982305662008 = 2*cos(10*π/236) = 2*cos(5*π/118) 1.974536709443 = 2*cos(12*π/236) = 2*cos(3*π/59) 1.965368249185 = 2*cos(14*π/236) = 2*cos(7*π/118) 1.954806779636 = 2*cos(16*π/236) = 2*cos(4*π/59) 1.942859786529 = 2*cos(18*π/236) = 2*cos(9*π/118) 1.929535737629 = 2*cos(20*π/236) = 2*cos(5*π/59) 1.914844076724 = 2*cos(22*π/236) = 2*cos(11*π/118) 1.898795216937 = 2*cos(24*π/236) = 2*cos(6*π/59) 1.881400533342 = 2*cos(26*π/236) = 2*cos(13*π/118) 1.862672354905 = 2*cos(28*π/236) = 2*cos(7*π/59) 1.842623955741 = 2*cos(30*π/236) = 2*cos(15*π/118) 1.821269545710 = 2*cos(32*π/236) = 2*cos(8*π/59) 1.798624260342 = 2*cos(34*π/236) = 2*cos(17*π/118) 1.774704150113 = 2*cos(36*π/236) = 2*cos(9*π/59) 1.749526169064 = 2*cos(38*π/236) = 2*cos(19*π/118) 1.723108162788 = 2*cos(40*π/236) = 2*cos(10*π/59) 1.695468855779 = 2*cos(42*π/236) = 2*cos(21*π/118) 1.666627838165 = 2*cos(44*π/236) = 2*cos(11*π/59) 1.636605551816 = 2*cos(46*π/236) = 2*cos(23*π/118) 1.605423275862 = 2*cos(48*π/236) = 2*cos(12*π/59) 1.573103111605 = 2*cos(50*π/236) = 2*cos(25*π/118) 1.539667966860 = 2*cos(52*π/236) = 2*cos(13*π/59) 1.505141539712 = 2*cos(54*π/236) = 2*cos(27*π/118) 1.469548301726 = 2*cos(56*π/236) = 2*cos(14*π/59) 1.432913480597 = 2*cos(58*π/236) = 2*cos(29*π/118) 1.395263042270 = 2*cos(60*π/236) = 2*cos(15*π/59) 1.356623672539 = 2*cos(62*π/236) = 2*cos(31*π/118) 1.317022758130 = 2*cos(64*π/236) = 2*cos(16*π/59) 1.276488367290 = 2*cos(66*π/236) = 2*cos(33*π/118) 1.235049229892 = 2*cos(68*π/236) = 2*cos(17*π/59) 1.192734717077 = 2*cos(70*π/236) = 2*cos(35*π/118) 1.149574820429 = 2*cos(72*π/236) = 2*cos(18*π/59) 1.105600130722 = 2*cos(74*π/236) = 2*cos(37*π/118) 1.060841816239 = 2*cos(76*π/236) = 2*cos(19*π/59) 1.015331600678 = 2*cos(78*π/236) = 2*cos(39*π/118) 0.969101740665 = 2*cos(80*π/236) = 2*cos(20*π/59) 0.922185002899 = 2*cos(82*π/236) = 2*cos(41*π/118) 0.874614640918 = 2*cos(84*π/236) = 2*cos(21*π/59) 0.826424371537 = 2*cos(86*π/236) = 2*cos(43*π/118) 0.777648350947 = 2*cos(88*π/236) = 2*cos(22*π/59) 0.728321150506 = 2*cos(90*π/236) = 2*cos(45*π/118) 0.678477732236 = 2*cos(92*π/236) = 2*cos(23*π/59) 0.628153424044 = 2*cos(94*π/236) = 2*cos(47*π/118) 0.577383894679 = 2*cos(96*π/236) = 2*cos(24*π/59) 0.526205128455 = 2*cos(98*π/236) = 2*cos(49*π/118) 0.474653399742 = 2*cos(100*π/236) = 2*cos(25*π/59) 0.422765247259 = 2*cos(102*π/236) = 2*cos(51*π/118) 0.370577448174 = 2*cos(104*π/236) = 2*cos(26*π/59) 0.318126992038 = 2*cos(106*π/236) = 2*cos(53*π/118) 0.265451054567 = 2*cos(108*π/236) = 2*cos(27*π/59) 0.212586971295 = 2*cos(110*π/236) = 2*cos(55*π/118) 0.159572211106 = 2*cos(112*π/236) = 2*cos(28*π/59) 0.106444349684 = 2*cos(114*π/236) = 2*cos(57*π/118) 0.053241042876 = 2*cos(116*π/236) = 2*cos(29*π/59) 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 E109 m E110 l E111 k+m E112 j+l E113 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)} E114 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E115 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E116 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E117 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_118d point group is 472, and the order of the principal axis (S₂₃₆) is 236. The group has 121 irreducible representations. β The D_118d point group is isomorphic to C_236v and D₂₃₆. γ The D_118d point group is generated by two symmetry elements, S₂₃₆ 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_118d 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_118d point group was created by Gernot Katzer.

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

	D_116d
	D_117d
C₁₁₈ C_118v C_118h D₁₁₈ D_118h	D_118d	S₁₁₈
	D_119d
	D_120d

Character table for the D118d point group

Character table for the D_118d point group