Group D27d n 30 Irred Operation 1 A1g E 2 A2g C27 3 E1g C27^2 4 E2g C9 5 E3g C27^4 6 E4g C27^5 7 E5g C9^2 8 E6g C27^7 9 E7g C27^8 10 E8g C3 11 E9g C27^10 12 E10g C27^11 13 E11g C9^4 14 E12g C27^13 15 E13g C2' 16 A1u i 17 A2u S54 18 E1u S18 19 E2u S54^5 20 E3u S54^7 21 E4u S6 22 E5u S54^11 23 E6u S54^13 24 E7u S18^5 25 E8u S54^17 26 E9u S54^19 27 E10u S18^7 28 E11u S54^23 29 E12u S54^25 30 E13u sd Table 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 2 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 3 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648 0.00000 2.00000 -1.98648 -1.87939 -1.67098 -1.37248 -1.00000 -0.57361 -0.11629 0.34730 0.79216 1.19432 1.53209 1.78727 1.94609 0.00000 4 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609 0.00000 2.00000 1.94609 1.53209 0.79216 -0.11629 -1.00000 -1.67098 -1.98648 -1.87939 -1.37248 -0.57361 0.34730 1.19432 1.78727 0.00000 5 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000 2.00000 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 0.00000 6 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727 0.00000 2.00000 1.78727 0.34730 -1.37248 -1.98648 -1.00000 0.79216 1.94609 1.53209 -0.11629 -1.67098 -1.87939 -0.57361 1.19432 0.00000 7 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098 0.00000 2.00000 -1.67098 0.34730 1.94609 1.19432 -1.00000 -1.98648 -0.57361 1.53209 1.78727 -0.11629 -1.87939 -1.37248 0.79216 0.00000 8 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 0.00000 2.00000 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 0.00000 9 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248 0.00000 2.00000 -1.37248 1.53209 1.19432 -1.67098 -1.00000 1.78727 0.79216 -1.87939 -0.57361 1.94609 0.34730 -1.98648 -0.11629 0.00000 10 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432 0.00000 2.00000 1.19432 -1.87939 -0.11629 1.94609 -1.00000 -1.37248 1.78727 0.34730 -1.98648 0.79216 1.53209 -1.67098 -0.57361 0.00000 11 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 2.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 0.00000 12 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216 0.00000 2.00000 0.79216 -1.87939 1.78727 -0.57361 -1.00000 1.94609 -1.67098 0.34730 1.19432 -1.98648 1.53209 -0.11629 -1.37248 0.00000 13 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361 0.00000 2.00000 -0.57361 1.53209 -1.98648 1.78727 -1.00000 -0.11629 1.19432 -1.87939 1.94609 -1.37248 0.34730 0.79216 -1.67098 0.00000 14 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000 2.00000 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 0.00000 15 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629 0.00000 2.00000 -0.11629 0.34730 -0.57361 0.79216 -1.00000 1.19432 -1.37248 1.53209 -1.67098 1.78727 -1.87939 1.94609 -1.98648 0.00000 16 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 17 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000 1.00000 18 2.00000 1.94609 1.78727 1.53209 1.19432 0.79216 0.34730 -0.11629 -0.57361 -1.00000 -1.37248 -1.67098 -1.87939 -1.98648 0.00000 -2.00000 1.98648 1.87939 1.67098 1.37248 1.00000 0.57361 0.11629 -0.34730 -0.79216 -1.19432 -1.53209 -1.78727 -1.94609 0.00000 19 2.00000 1.78727 1.19432 0.34730 -0.57361 -1.37248 -1.87939 -1.98648 -1.67098 -1.00000 -0.11629 0.79216 1.53209 1.94609 0.00000 -2.00000 -1.94609 -1.53209 -0.79216 0.11629 1.00000 1.67098 1.98648 1.87939 1.37248 0.57361 -0.34730 -1.19432 -1.78727 0.00000 20 2.00000 1.53209 0.34730 -1.00000 -1.87939 -1.87939 -1.00000 0.34730 1.53209 2.00000 1.53209 0.34730 -1.00000 -1.87939 0.00000 -2.00000 1.87939 1.00000 -0.34730 -1.53209 -2.00000 -1.53209 -0.34730 1.00000 1.87939 1.87939 1.00000 -0.34730 -1.53209 0.00000 21 2.00000 1.19432 -0.57361 -1.87939 -1.67098 -0.11629 1.53209 1.94609 0.79216 -1.00000 -1.98648 -1.37248 0.34730 1.78727 0.00000 -2.00000 -1.78727 -0.34730 1.37248 1.98648 1.00000 -0.79216 -1.94609 -1.53209 0.11629 1.67098 1.87939 0.57361 -1.19432 0.00000 22 2.00000 0.79216 -1.37248 -1.87939 -0.11629 1.78727 1.53209 -0.57361 -1.98648 -1.00000 1.19432 1.94609 0.34730 -1.67098 0.00000 -2.00000 1.67098 -0.34730 -1.94609 -1.19432 1.00000 1.98648 0.57361 -1.53209 -1.78727 0.11629 1.87939 1.37248 -0.79216 0.00000 23 2.00000 0.34730 -1.87939 -1.00000 1.53209 1.53209 -1.00000 -1.87939 0.34730 2.00000 0.34730 -1.87939 -1.00000 1.53209 0.00000 -2.00000 -1.53209 1.00000 1.87939 -0.34730 -2.00000 -0.34730 1.87939 1.00000 -1.53209 -1.53209 1.00000 1.87939 -0.34730 0.00000 24 2.00000 -0.11629 -1.98648 0.34730 1.94609 -0.57361 -1.87939 0.79216 1.78727 -1.00000 -1.67098 1.19432 1.53209 -1.37248 0.00000 -2.00000 1.37248 -1.53209 -1.19432 1.67098 1.00000 -1.78727 -0.79216 1.87939 0.57361 -1.94609 -0.34730 1.98648 0.11629 0.00000 25 2.00000 -0.57361 -1.67098 1.53209 0.79216 -1.98648 0.34730 1.78727 -1.37248 -1.00000 1.94609 -0.11629 -1.87939 1.19432 0.00000 -2.00000 -1.19432 1.87939 0.11629 -1.94609 1.00000 1.37248 -1.78727 -0.34730 1.98648 -0.79216 -1.53209 1.67098 0.57361 0.00000 26 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 -1.00000 2.00000 -1.00000 0.00000 -2.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 -2.00000 1.00000 1.00000 0.00000 27 2.00000 -1.37248 -0.11629 1.53209 -1.98648 1.19432 0.34730 -1.67098 1.94609 -1.00000 -0.57361 1.78727 -1.87939 0.79216 0.00000 -2.00000 -0.79216 1.87939 -1.78727 0.57361 1.00000 -1.94609 1.67098 -0.34730 -1.19432 1.98648 -1.53209 0.11629 1.37248 0.00000 28 2.00000 -1.67098 0.79216 0.34730 -1.37248 1.94609 -1.87939 1.19432 -0.11629 -1.00000 1.78727 -1.98648 1.53209 -0.57361 0.00000 -2.00000 0.57361 -1.53209 1.98648 -1.78727 1.00000 0.11629 -1.19432 1.87939 -1.94609 1.37248 -0.34730 -0.79216 1.67098 0.00000 29 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.34730 -1.00000 1.53209 -1.87939 2.00000 -1.87939 1.53209 -1.00000 0.34730 0.00000 -2.00000 -0.34730 1.00000 -1.53209 1.87939 -2.00000 1.87939 -1.53209 1.00000 -0.34730 -0.34730 1.00000 -1.53209 1.87939 0.00000 30 2.00000 -1.98648 1.94609 -1.87939 1.78727 -1.67098 1.53209 -1.37248 1.19432 -1.00000 0.79216 -0.57361 0.34730 -0.11629 0.00000 -2.00000 0.11629 -0.34730 0.57361 -0.79216 1.00000 -1.19432 1.37248 -1.53209 1.67098 -1.78727 1.87939 -1.94609 1.98648 0.00000