Character Table for Point Group D124d

Character table for the D_124d point group

D124d E 2 S248 2 C124 2 S248^3 2 C62 2 S248^5 2 C124^3 2 S248^7 2 C31 2 S248^9 2 C124^5 2 S248^11 2 C62^3 2 S248^13 2 C124^7 2 S248^15 2 C31^2 2 S248^17 2 C124^9 2 S248^19 2 C62^5 2 S248^21 2 C124^11 2 S248^23 2 C31^3 2 S248^25 2 C124^13 2 S248^27 2 C62^7 2 S248^29 2 C124^15 2 S8 2 C31^4 2 S248^33 2 C124^17 2 S248^35 2 C62^9 2 S248^37 2 C124^19 2 S248^39 2 C31^5 2 S248^41 2 C124^21 2 S248^43 2 C62^11 2 S248^45 2 C124^23 2 S248^47 2 C31^6 2 S248^49 2 C124^25 2 S248^51 2 C62^13 2 S248^53 2 C124^27 2 S248^55 2 C31^7 2 S248^57 2 C124^29 2 S248^59 2 C62^15 2 S248^61 2 C4 2 S248^63 2 C31^8 2 S248^65 2 C124^33 2 S248^67 2 C62^17 2 S248^69 2 C124^35 2 S248^71 2 C31^9 2 S248^73 2 C124^37 2 S248^75 2 C62^19 2 S248^77 2 C124^39 2 S248^79 2 C31^10 2 S248^81 2 C124^41 2 S248^83 2 C62^21 2 S248^85 2 C124^43 2 S248^87 2 C31^11 2 S248^89 2 C124^45 2 S248^91 2 C62^23 2 S8^3 2 C124^47 2 S248^95 2 C31^12 2 S248^97 2 C124^49 2 S248^99 2 C62^25 2 S248^101 2 C124^51 2 S248^103 2 C31^13 2 S248^105 2 C124^53 2 S248^107 2 C62^27 2 S248^109 2 C124^55 2 S248^111 2 C31^14 2 S248^113 2 C124^57 2 S248^115 2 C62^29 2 S248^117 2 C124^59 2 S248^119 2 C31^15 2 S248^121 2 C124^61 2 S248^123 C2 124 C2' 124 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 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 -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 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 -1.00000 1.00000 ... ..T ..... ......T ......... ..........T ............. E1 2.00000 1.99936 1.99743 1.99423 1.98974 1.98397 1.97694 1.96863 1.95906 1.94823 1.93615 1.92283 1.90828 1.89250 1.87550 1.85731 1.83792 1.81735 1.79561 1.77272 1.74869 1.72354 1.69729 1.66994 1.64153 1.61206 1.58155 1.55003 1.51752 1.48403 1.44959 1.41421 1.37793 1.34077 1.30274 1.26388 1.22421 1.18375 1.14254 1.10059 1.05793 1.01459 0.97060 0.92599 0.88079 0.83502 0.78871 0.74190 0.69461 0.64688 0.59873 0.55019 0.50131 0.45210 0.40260 0.35284 0.30286 0.25268 0.20234 0.15187 0.10130 0.05067 0.00000 -0.05067 -0.10130 -0.15187 -0.20234 -0.25268 -0.30286 -0.35284 -0.40260 -0.45210 -0.50131 -0.55019 -0.59873 -0.64688 -0.69461 -0.74190 -0.78871 -0.83502 -0.88079 -0.92599 -0.97060 -1.01459 -1.05793 -1.10059 -1.14254 -1.18375 -1.22421 -1.26388 -1.30274 -1.34077 -1.37793 -1.41421 -1.44959 -1.48403 -1.51752 -1.55003 -1.58155 -1.61206 -1.64153 -1.66994 -1.69729 -1.72354 -1.74869 -1.77272 -1.79561 -1.81735 -1.83792 -1.85731 -1.87550 -1.89250 -1.90828 -1.92283 -1.93615 -1.94823 -1.95906 -1.96863 -1.97694 -1.98397 -1.98974 -1.99423 -1.99743 -1.99936 -2.00000 0.00000 0.00000 ... TT. ..... ....TT. ......... ........TT. ............. E2 2.00000 1.99743 1.98974 1.97694 1.95906 1.93615 1.90828 1.87550 1.83792 1.79561 1.74869 1.69729 1.64153 1.58155 1.51752 1.44959 1.37793 1.30274 1.22421 1.14254 1.05793 0.97060 0.88079 0.78871 0.69461 0.59873 0.50131 0.40260 0.30286 0.20234 0.10130 0.00000 -0.10130 -0.20234 -0.30286 -0.40260 -0.50131 -0.59873 -0.69461 -0.78871 -0.88079 -0.97060 -1.05793 -1.14254 -1.22421 -1.30274 -1.37793 -1.44959 -1.51752 -1.58155 -1.64153 -1.69729 -1.74869 -1.79561 -1.83792 -1.87550 -1.90828 -1.93615 -1.95906 -1.97694 -1.98974 -1.99743 -2.00000 -1.99743 -1.98974 -1.97694 -1.95906 -1.93615 -1.90828 -1.87550 -1.83792 -1.79561 -1.74869 -1.69729 -1.64153 -1.58155 -1.51752 -1.44959 -1.37793 -1.30274 -1.22421 -1.14254 -1.05793 -0.97060 -0.88079 -0.78871 -0.69461 -0.59873 -0.50131 -0.40260 -0.30286 -0.20234 -0.10130 0.00000 0.10130 0.20234 0.30286 0.40260 0.50131 0.59873 0.69461 0.78871 0.88079 0.97060 1.05793 1.14254 1.22421 1.30274 1.37793 1.44959 1.51752 1.58155 1.64153 1.69729 1.74869 1.79561 1.83792 1.87550 1.90828 1.93615 1.95906 1.97694 1.98974 1.99743 2.00000 0.00000 0.00000 ... ... TT... ....... ....TT... ........... ........TT... E3 2.00000 1.99423 1.97694 1.94823 1.90828 1.85731 1.79561 1.72354 1.64153 1.55003 1.44959 1.34077 1.22421 1.10059 0.97060 0.83502 0.69461 0.55019 0.40260 0.25268 0.10130 -0.05067 -0.20234 -0.35284 -0.50131 -0.64688 -0.78871 -0.92599 -1.05793 -1.18375 -1.30274 -1.41421 -1.51752 -1.61206 -1.69729 -1.77272 -1.83792 -1.89250 -1.93615 -1.96863 -1.98974 -1.99936 -1.99743 -1.98397 -1.95906 -1.92283 -1.87550 -1.81735 -1.74869 -1.66994 -1.58155 -1.48403 -1.37793 -1.26388 -1.14254 -1.01459 -0.88079 -0.74190 -0.59873 -0.45210 -0.30286 -0.15187 0.00000 0.15187 0.30286 0.45210 0.59873 0.74190 0.88079 1.01459 1.14254 1.26388 1.37793 1.48403 1.58155 1.66994 1.74869 1.81735 1.87550 1.92283 1.95906 1.98397 1.99743 1.99936 1.98974 1.96863 1.93615 1.89250 1.83792 1.77272 1.69729 1.61206 1.51752 1.41421 1.30274 1.18375 1.05793 0.92599 0.78871 0.64688 0.50131 0.35284 0.20234 0.05067 -0.10130 -0.25268 -0.40260 -0.55019 -0.69461 -0.83502 -0.97060 -1.10059 -1.22421 -1.34077 -1.44959 -1.55003 -1.64153 -1.72354 -1.79561 -1.85731 -1.90828 -1.94823 -1.97694 -1.99423 -2.00000 0.00000 0.00000 ... ... ..... TT..... ......... ....TT..... ............. E4 2.00000 1.98974 1.95906 1.90828 1.83792 1.74869 1.64153 1.51752 1.37793 1.22421 1.05793 0.88079 0.69461 0.50131 0.30286 0.10130 -0.10130 -0.30286 -0.50131 -0.69461 -0.88079 -1.05793 -1.22421 -1.37793 -1.51752 -1.64153 -1.74869 -1.83792 -1.90828 -1.95906 -1.98974 -2.00000 -1.98974 -1.95906 -1.90828 -1.83792 -1.74869 -1.64153 -1.51752 -1.37793 -1.22421 -1.05793 -0.88079 -0.69461 -0.50131 -0.30286 -0.10130 0.10130 0.30286 0.50131 0.69461 0.88079 1.05793 1.22421 1.37793 1.51752 1.64153 1.74869 1.83792 1.90828 1.95906 1.98974 2.00000 1.98974 1.95906 1.90828 1.83792 1.74869 1.64153 1.51752 1.37793 1.22421 1.05793 0.88079 0.69461 0.50131 0.30286 0.10130 -0.10130 -0.30286 -0.50131 -0.69461 -0.88079 -1.05793 -1.22421 -1.37793 -1.51752 -1.64153 -1.74869 -1.83792 -1.90828 -1.95906 -1.98974 -2.00000 -1.98974 -1.95906 -1.90828 -1.83792 -1.74869 -1.64153 -1.51752 -1.37793 -1.22421 -1.05793 -0.88079 -0.69461 -0.50131 -0.30286 -0.10130 0.10130 0.30286 0.50131 0.69461 0.88079 1.05793 1.22421 1.37793 1.51752 1.64153 1.74869 1.83792 1.90828 1.95906 1.98974 2.00000 0.00000 0.00000 ... ... ..... ....... TT....... ........... ....TT....... E5 2.00000 1.98397 1.93615 1.85731 1.74869 1.61206 1.44959 1.26388 1.05793 0.83502 0.59873 0.35284 0.10130 -0.15187 -0.40260 -0.64688 -0.88079 -1.10059 -1.30274 -1.48403 -1.64153 -1.77272 -1.87550 -1.94823 -1.98974 -1.99936 -1.97694 -1.92283 -1.83792 -1.72354 -1.58155 -1.41421 -1.22421 -1.01459 -0.78871 -0.55019 -0.30286 -0.05067 0.20234 0.45210 0.69461 0.92599 1.14254 1.34077 1.51752 1.66994 1.79561 1.89250 1.95906 1.99423 1.99743 1.96863 1.90828 1.81735 1.69729 1.55003 1.37793 1.18375 0.97060 0.74190 0.50131 0.25268 0.00000 -0.25268 -0.50131 -0.74190 -0.97060 -1.18375 -1.37793 -1.55003 -1.69729 -1.81735 -1.90828 -1.96863 -1.99743 -1.99423 -1.95906 -1.89250 -1.79561 -1.66994 -1.51752 -1.34077 -1.14254 -0.92599 -0.69461 -0.45210 -0.20234 0.05067 0.30286 0.55019 0.78871 1.01459 1.22421 1.41421 1.58155 1.72354 1.83792 1.92283 1.97694 1.99936 1.98974 1.94823 1.87550 1.77272 1.64153 1.48403 1.30274 1.10059 0.88079 0.64688 0.40260 0.15187 -0.10130 -0.35284 -0.59873 -0.83502 -1.05793 -1.26388 -1.44959 -1.61206 -1.74869 -1.85731 -1.93615 -1.98397 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... TT......... ............. E6 2.00000 1.97694 1.90828 1.79561 1.64153 1.44959 1.22421 0.97060 0.69461 0.40260 0.10130 -0.20234 -0.50131 -0.78871 -1.05793 -1.30274 -1.51752 -1.69729 -1.83792 -1.93615 -1.98974 -1.99743 -1.95906 -1.87550 -1.74869 -1.58155 -1.37793 -1.14254 -0.88079 -0.59873 -0.30286 0.00000 0.30286 0.59873 0.88079 1.14254 1.37793 1.58155 1.74869 1.87550 1.95906 1.99743 1.98974 1.93615 1.83792 1.69729 1.51752 1.30274 1.05793 0.78871 0.50131 0.20234 -0.10130 -0.40260 -0.69461 -0.97060 -1.22421 -1.44959 -1.64153 -1.79561 -1.90828 -1.97694 -2.00000 -1.97694 -1.90828 -1.79561 -1.64153 -1.44959 -1.22421 -0.97060 -0.69461 -0.40260 -0.10130 0.20234 0.50131 0.78871 1.05793 1.30274 1.51752 1.69729 1.83792 1.93615 1.98974 1.99743 1.95906 1.87550 1.74869 1.58155 1.37793 1.14254 0.88079 0.59873 0.30286 0.00000 -0.30286 -0.59873 -0.88079 -1.14254 -1.37793 -1.58155 -1.74869 -1.87550 -1.95906 -1.99743 -1.98974 -1.93615 -1.83792 -1.69729 -1.51752 -1.30274 -1.05793 -0.78871 -0.50131 -0.20234 0.10130 0.40260 0.69461 0.97060 1.22421 1.44959 1.64153 1.79561 1.90828 1.97694 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... TT........... E7 2.00000 1.96863 1.87550 1.72354 1.51752 1.26388 0.97060 0.64688 0.30286 -0.05067 -0.40260 -0.74190 -1.05793 -1.34077 -1.58155 -1.77272 -1.90828 -1.98397 -1.99743 -1.94823 -1.83792 -1.66994 -1.44959 -1.18375 -0.88079 -0.55019 -0.20234 0.15187 0.50131 0.83502 1.14254 1.41421 1.64153 1.81735 1.93615 1.99423 1.98974 1.92283 1.79561 1.61206 1.37793 1.10059 0.78871 0.45210 0.10130 -0.25268 -0.59873 -0.92599 -1.22421 -1.48403 -1.69729 -1.85731 -1.95906 -1.99936 -1.97694 -1.89250 -1.74869 -1.55003 -1.30274 -1.01459 -0.69461 -0.35284 0.00000 0.35284 0.69461 1.01459 1.30274 1.55003 1.74869 1.89250 1.97694 1.99936 1.95906 1.85731 1.69729 1.48403 1.22421 0.92599 0.59873 0.25268 -0.10130 -0.45210 -0.78871 -1.10059 -1.37793 -1.61206 -1.79561 -1.92283 -1.98974 -1.99423 -1.93615 -1.81735 -1.64153 -1.41421 -1.14254 -0.83502 -0.50131 -0.15187 0.20234 0.55019 0.88079 1.18375 1.44959 1.66994 1.83792 1.94823 1.99743 1.98397 1.90828 1.77272 1.58155 1.34077 1.05793 0.74190 0.40260 0.05067 -0.30286 -0.64688 -0.97060 -1.26388 -1.51752 -1.72354 -1.87550 -1.96863 -2.00000 0.00000 0.00000 ... ... ..... ....... ......... ........... ............. 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E120 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 -1.98974 1.95906 -1.90828 1.83792 -1.74869 1.64153 -1.51752 1.37793 -1.22421 1.05793 -0.88079 0.69461 -0.50131 0.30286 -0.10130 -0.10130 0.30286 -0.50131 0.69461 -0.88079 1.05793 -1.22421 1.37793 -1.51752 1.64153 -1.74869 1.83792 -1.90828 1.95906 -1.98974 2.00000 0.00000 0.00000 ... ... ..... ....... ......... ..TT....... ............. E121 2.00000 -1.99423 1.97694 -1.94823 1.90828 -1.85731 1.79561 -1.72354 1.64153 -1.55003 1.44959 -1.34077 1.22421 -1.10059 0.97060 -0.83502 0.69461 -0.55019 0.40260 -0.25268 0.10130 0.05067 -0.20234 0.35284 -0.50131 0.64688 -0.78871 0.92599 -1.05793 1.18375 -1.30274 1.41421 -1.51752 1.61206 -1.69729 1.77272 -1.83792 1.89250 -1.93615 1.96863 -1.98974 1.99936 -1.99743 1.98397 -1.95906 1.92283 -1.87550 1.81735 -1.74869 1.66994 -1.58155 1.48403 -1.37793 1.26388 -1.14254 1.01459 -0.88079 0.74190 -0.59873 0.45210 -0.30286 0.15187 0.00000 -0.15187 0.30286 -0.45210 0.59873 -0.74190 0.88079 -1.01459 1.14254 -1.26388 1.37793 -1.48403 1.58155 -1.66994 1.74869 -1.81735 1.87550 -1.92283 1.95906 -1.98397 1.99743 -1.99936 1.98974 -1.96863 1.93615 -1.89250 1.83792 -1.77272 1.69729 -1.61206 1.51752 -1.41421 1.30274 -1.18375 1.05793 -0.92599 0.78871 -0.64688 0.50131 -0.35284 0.20234 -0.05067 -0.10130 0.25268 -0.40260 0.55019 -0.69461 0.83502 -0.97060 1.10059 -1.22421 1.34077 -1.44959 1.55003 -1.64153 1.72354 -1.79561 1.85731 -1.90828 1.94823 -1.97694 1.99423 -2.00000 0.00000 0.00000 ... ... ..... ....... ..TT..... ........... ......TT..... E122 2.00000 -1.99743 1.98974 -1.97694 1.95906 -1.93615 1.90828 -1.87550 1.83792 -1.79561 1.74869 -1.69729 1.64153 -1.58155 1.51752 -1.44959 1.37793 -1.30274 1.22421 -1.14254 1.05793 -0.97060 0.88079 -0.78871 0.69461 -0.59873 0.50131 -0.40260 0.30286 -0.20234 0.10130 0.00000 -0.10130 0.20234 -0.30286 0.40260 -0.50131 0.59873 -0.69461 0.78871 -0.88079 0.97060 -1.05793 1.14254 -1.22421 1.30274 -1.37793 1.44959 -1.51752 1.58155 -1.64153 1.69729 -1.74869 1.79561 -1.83792 1.87550 -1.90828 1.93615 -1.95906 1.97694 -1.98974 1.99743 -2.00000 1.99743 -1.98974 1.97694 -1.95906 1.93615 -1.90828 1.87550 -1.83792 1.79561 -1.74869 1.69729 -1.64153 1.58155 -1.51752 1.44959 -1.37793 1.30274 -1.22421 1.14254 -1.05793 0.97060 -0.88079 0.78871 -0.69461 0.59873 -0.50131 0.40260 -0.30286 0.20234 -0.10130 0.00000 0.10130 -0.20234 0.30286 -0.40260 0.50131 -0.59873 0.69461 -0.78871 0.88079 -0.97060 1.05793 -1.14254 1.22421 -1.30274 1.37793 -1.44959 1.51752 -1.58155 1.64153 -1.69729 1.74869 -1.79561 1.83792 -1.87550 1.90828 -1.93615 1.95906 -1.97694 1.98974 -1.99743 2.00000 0.00000 0.00000 ... ... ..... ..TT... ......... ......TT... ............. E123 2.00000 -1.99936 1.99743 -1.99423 1.98974 -1.98397 1.97694 -1.96863 1.95906 -1.94823 1.93615 -1.92283 1.90828 -1.89250 1.87550 -1.85731 1.83792 -1.81735 1.79561 -1.77272 1.74869 -1.72354 1.69729 -1.66994 1.64153 -1.61206 1.58155 -1.55003 1.51752 -1.48403 1.44959 -1.41421 1.37793 -1.34077 1.30274 -1.26388 1.22421 -1.18375 1.14254 -1.10059 1.05793 -1.01459 0.97060 -0.92599 0.88079 -0.83502 0.78871 -0.74190 0.69461 -0.64688 0.59873 -0.55019 0.50131 -0.45210 0.40260 -0.35284 0.30286 -0.25268 0.20234 -0.15187 0.10130 -0.05067 0.00000 0.05067 -0.10130 0.15187 -0.20234 0.25268 -0.30286 0.35284 -0.40260 0.45210 -0.50131 0.55019 -0.59873 0.64688 -0.69461 0.74190 -0.78871 0.83502 -0.88079 0.92599 -0.97060 1.01459 -1.05793 1.10059 -1.14254 1.18375 -1.22421 1.26388 -1.30274 1.34077 -1.37793 1.41421 -1.44959 1.48403 -1.51752 1.55003 -1.58155 1.61206 -1.64153 1.66994 -1.69729 1.72354 -1.74869 1.77272 -1.79561 1.81735 -1.83792 1.85731 -1.87550 1.89250 -1.90828 1.92283 -1.93615 1.94823 -1.95906 1.96863 -1.97694 1.98397 -1.98974 1.99423 -1.99743 1.99936 -2.00000 0.00000 0.00000 TT. ... ..TT. ....... ......TT. ........... ..........TT. Irrational character values: 1.999358150593 = 2*cos(2*π/248) = 2*cos(π/124) 1.997433014342 = 2*cos(4*π/248) = 2*cos(π/62) 1.994225826895 = 2*cos(6*π/248) = 2*cos(3*π/124) 1.989738646784 = 2*cos(8*π/248) = 2*cos(π/31) 1.983974354101 = 2*cos(10*π/248) = 2*cos(5*π/124) 1.976936648656 = 2*cos(12*π/248) = 2*cos(3*π/62) 1.968630047595 = 2*cos(14*π/248) = 2*cos(7*π/124) 1.959059882505 = 2*cos(16*π/248) = 2*cos(2*π/31) 1.948232295991 = 2*cos(18*π/248) = 2*cos(9*π/124) 1.936154237732 = 2*cos(20*π/248) = 2*cos(5*π/62) 1.922833460024 = 2*cos(22*π/248) = 2*cos(11*π/124) 1.908278512800 = 2*cos(24*π/248) = 2*cos(3*π/31) 1.892498738144 = 2*cos(26*π/248) = 2*cos(13*π/124) 1.875504264294 = 2*cos(28*π/248) = 2*cos(7*π/62) 1.857305999145 = 2*cos(30*π/248) = 2*cos(15*π/124) 1.837915623240 = 2*cos(32*π/248) = 2*cos(4*π/31) 1.817345582283 = 2*cos(34*π/248) = 2*cos(17*π/124) 1.795609079141 = 2*cos(36*π/248) = 2*cos(9*π/62) 1.772720065377 = 2*cos(38*π/248) = 2*cos(19*π/124) 1.748693232289 = 2*cos(40*π/248) = 2*cos(5*π/31) 1.723544001487 = 2*cos(42*π/248) = 2*cos(21*π/124) 1.697288514990 = 2*cos(44*π/248) = 2*cos(11*π/62) 1.669943624865 = 2*cos(46*π/248) = 2*cos(23*π/124) 1.641526882415 = 2*cos(48*π/248) = 2*cos(6*π/31) 1.612056526908 = 2*cos(50*π/248) = 2*cos(25*π/124) 1.581551473875 = 2*cos(52*π/248) = 2*cos(13*π/62) 1.550031302967 = 2*cos(54*π/248) = 2*cos(27*π/124) 1.517516245386 = 2*cos(56*π/248) = 2*cos(7*π/31) 1.484027170902 = 2*cos(58*π/248) = 2*cos(29*π/124) 1.449585574458 = 2*cos(60*π/248) = 2*cos(15*π/62) 1.414213562373 = 2*cos(62*π/248) = 2*cos(π/4) = √2 1.377933838151 = 2*cos(64*π/248) = 2*cos(8*π/31) 1.340769687913 = 2*cos(66*π/248) = 2*cos(33*π/124) 1.302744965444 = 2*cos(68*π/248) = 2*cos(17*π/62) 1.263884076893 = 2*cos(70*π/248) = 2*cos(35*π/124) 1.224211965095 = 2*cos(72*π/248) = 2*cos(9*π/31) 1.183754093574 = 2*cos(74*π/248) = 2*cos(37*π/124) 1.142536430190 = 2*cos(76*π/248) = 2*cos(19*π/62) 1.100585430475 = 2*cos(78*π/248) = 2*cos(39*π/124) 1.057928020654 = 2*cos(80*π/248) = 2*cos(10*π/31) 1.014591580360 = 2*cos(82*π/248) = 2*cos(41*π/124) 0.970603925062 = 2*cos(84*π/248) = 2*cos(21*π/62) 0.925993288210 = 2*cos(86*π/248) = 2*cos(43*π/124) 0.880788303115 = 2*cos(88*π/248) = 2*cos(11*π/31) 0.835017984570 = 2*cos(90*π/248) = 2*cos(45*π/124) 0.788711710227 = 2*cos(92*π/248) = 2*cos(23*π/62) 0.741899201740 = 2*cos(94*π/248) = 2*cos(47*π/124) 0.694610505690 = 2*cos(96*π/248) = 2*cos(12*π/31) 0.646875974298 = 2*cos(98*π/248) = 2*cos(49*π/124) 0.598726245947 = 2*cos(100*π/248) = 2*cos(25*π/62) 0.550192225509 = 2*cos(102*π/248) = 2*cos(51*π/124) 0.501305064517 = 2*cos(104*π/248) = 2*cos(13*π/31) 0.452096141167 = 2*cos(106*π/248) = 2*cos(53*π/124) 0.402597040177 = 2*cos(108*π/248) = 2*cos(27*π/62) 0.352839532516 = 2*cos(110*π/248) = 2*cos(55*π/124) 0.302855555009 = 2*cos(112*π/248) = 2*cos(14*π/31) 0.252677189844 = 2*cos(114*π/248) = 2*cos(57*π/124) 0.202336643975 = 2*cos(116*π/248) = 2*cos(29*π/62) 0.151866228450 = 2*cos(118*π/248) = 2*cos(59*π/124) 0.101298337677 = 2*cos(120*π/248) = 2*cos(15*π/31) 0.050665428626 = 2*cos(122*π/248) = 2*cos(61*π/124) 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 E115 m E116 l E117 k+m E118 j+l E119 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)} E120 h+j+l {z((x²−y²)²−4x²y²), xyz(x²−y²)} E121 g+i+k+m {xz(x²−3y²), yz(3x²−y²)}, {xz³(x²−3y²), yz³(3x²−y²)} E122 f+h+j+l {z(x²−y²), xyz}, {z³(x²−y²), xyz³} E123 R+d+g+i+k+m {R_x, R_y}, {xz, yz}, {xz³, yz³}, {xz⁵, yz⁵} Notes: α The order of the D_124d point group is 496, and the order of the principal axis (S₂₄₈) is 248. The group has 127 irreducible representations. β The D_124d point group is isomorphic to C_248v and D₂₄₈. γ The D_124d point group is generated by two symmetry elements, S₂₄₈ 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_124d 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, some of the irrational characters cannot be expressed by a closed algebraic form using real numbers only.

This Character Table for the D_124d point group was created by Gernot Katzer.

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

	D_122d
	D_123d
C₁₂₄ C_124v C_124h D₁₂₄ D_124h	D_124d	S₁₂₄
	D_125d
	D_126d

Character table for the D124d point group

Character table for the D_124d point group