Group D28d n 31 Irred Operation 1 A1 E 2 A2 S56 3 B1 C28 4 B2 S56^3 5 E1 C14 6 E2 S56^5 7 E3 C28^3 8 E4 S8 9 E5 C7 10 E6 S56^9 11 E7 C28^5 12 E8 S56^11 13 E9 C14^3 14 E10 S56^13 15 E11 C4 16 E12 S56^15 17 E13 C7^2 18 E14 S56^17 19 E15 C28^9 20 E16 S56^19 21 E17 C14^5 22 E18 S8^3 23 E19 C28^11 24 E20 S56^23 25 E21 C7^3 26 E22 S56^25 27 E23 C28^13 28 E24 S56^27 29 E25 C2 30 E26 C2' 31 E27 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 31 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 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 -1.00000 3 1.00000 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1.56366 1.80194 1.94986 2.00000 0.00000 0.00000 7 2.00000 1.88777 1.56366 1.06406 0.44504 -0.22393 -0.86777 -1.41421 -1.80194 -1.98742 -1.94986 -1.69345 -1.24698 -0.66056 0.00000 0.66056 1.24698 1.69345 1.94986 1.98742 1.80194 1.41421 0.86777 0.22393 -0.44504 -1.06406 -1.56366 -1.88777 -2.00000 0.00000 0.00000 8 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 1.80194 1.24698 0.44504 -0.44504 -1.24698 -1.80194 -2.00000 -1.80194 -1.24698 -0.44504 0.44504 1.24698 1.80194 2.00000 0.00000 0.00000 9 2.00000 1.69345 0.86777 -0.22393 -1.24698 -1.88777 -1.94986 -1.41421 -0.44504 0.66056 1.56366 1.98742 1.80194 1.06406 0.00000 -1.06406 -1.80194 -1.98742 -1.56366 -0.66056 0.44504 1.41421 1.94986 1.88777 1.24698 0.22393 -0.86777 -1.69345 -2.00000 0.00000 0.00000 10 2.00000 1.56366 0.44504 -0.86777 -1.80194 -1.94986 -1.24698 0.00000 1.24698 1.94986 1.80194 0.86777 -0.44504 -1.56366 -2.00000 -1.56366 -0.44504 0.86777 1.80194 1.94986 1.24698 0.00000 -1.24698 -1.94986 -1.80194 -0.86777 0.44504 1.56366 2.00000 0.00000 0.00000 11 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 -1.41421 0.00000 1.41421 2.00000 1.41421 0.00000 -1.41421 -2.00000 0.00000 0.00000 12 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 1.24698 -0.44504 -1.80194 -1.80194 -0.44504 1.24698 2.00000 0.00000 0.00000 13 2.00000 1.06406 -0.86777 -1.98742 -1.24698 0.66056 1.94986 1.41421 -0.44504 -1.88777 -1.56366 0.22393 1.80194 1.69345 0.00000 -1.69345 -1.80194 -0.22393 1.56366 1.88777 0.44504 -1.41421 -1.94986 -0.66056 1.24698 1.98742 0.86777 -1.06406 -2.00000 0.00000 0.00000 14 2.00000 0.86777 -1.24698 -1.94986 -0.44504 1.56366 1.80194 0.00000 -1.80194 -1.56366 0.44504 1.94986 1.24698 -0.86777 -2.00000 -0.86777 1.24698 1.94986 0.44504 -1.56366 -1.80194 0.00000 1.80194 1.56366 -0.44504 -1.94986 -1.24698 0.86777 2.00000 0.00000 0.00000 15 2.00000 0.66056 -1.56366 -1.69345 0.44504 1.98742 0.86777 -1.41421 -1.80194 0.22393 1.94986 1.06406 -1.24698 -1.88777 0.00000 1.88777 1.24698 -1.06406 -1.94986 -0.22393 1.80194 1.41421 -0.86777 -1.98742 -0.44504 1.69345 1.56366 -0.66056 -2.00000 0.00000 0.00000 16 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.44504 -1.80194 -1.24698 1.24698 1.80194 -0.44504 -2.00000 -0.44504 1.80194 1.24698 -1.24698 -1.80194 0.44504 2.00000 0.00000 0.00000 17 2.00000 0.22393 -1.94986 -0.66056 1.80194 1.06406 -1.56366 -1.41421 1.24698 1.69345 -0.86777 -1.88777 0.44504 1.98742 0.00000 -1.98742 -0.44504 1.88777 0.86777 -1.69345 -1.24698 1.41421 1.56366 -1.06406 -1.80194 0.66056 1.94986 -0.22393 -2.00000 0.00000 0.00000 18 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 -2.00000 0.00000 2.00000 0.00000 0.00000 19 2.00000 -0.22393 -1.94986 0.66056 1.80194 -1.06406 -1.56366 1.41421 1.24698 -1.69345 -0.86777 1.88777 0.44504 -1.98742 0.00000 1.98742 -0.44504 -1.88777 0.86777 1.69345 -1.24698 -1.41421 1.56366 1.06406 -1.80194 -0.66056 1.94986 0.22393 -2.00000 0.00000 0.00000 20 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 -0.44504 -1.80194 1.24698 1.24698 -1.80194 -0.44504 2.00000 0.00000 0.00000 21 2.00000 -0.66056 -1.56366 1.69345 0.44504 -1.98742 0.86777 1.41421 -1.80194 -0.22393 1.94986 -1.06406 -1.24698 1.88777 0.00000 -1.88777 1.24698 1.06406 -1.94986 0.22393 1.80194 -1.41421 -0.86777 1.98742 -0.44504 -1.69345 1.56366 0.66056 -2.00000 0.00000 0.00000 22 2.00000 -0.86777 -1.24698 1.94986 -0.44504 -1.56366 1.80194 0.00000 -1.80194 1.56366 0.44504 -1.94986 1.24698 0.86777 -2.00000 0.86777 1.24698 -1.94986 0.44504 1.56366 -1.80194 0.00000 1.80194 -1.56366 -0.44504 1.94986 -1.24698 -0.86777 2.00000 0.00000 0.00000 23 2.00000 -1.06406 -0.86777 1.98742 -1.24698 -0.66056 1.94986 -1.41421 -0.44504 1.88777 -1.56366 -0.22393 1.80194 -1.69345 0.00000 1.69345 -1.80194 0.22393 1.56366 -1.88777 0.44504 1.41421 -1.94986 0.66056 1.24698 -1.98742 0.86777 1.06406 -2.00000 0.00000 0.00000 24 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 -1.24698 -0.44504 1.80194 -1.80194 0.44504 1.24698 -2.00000 1.24698 0.44504 -1.80194 1.80194 -0.44504 -1.24698 2.00000 0.00000 0.00000 25 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 1.41421 0.00000 -1.41421 2.00000 -1.41421 0.00000 1.41421 -2.00000 0.00000 0.00000 26 2.00000 -1.56366 0.44504 0.86777 -1.80194 1.94986 -1.24698 0.00000 1.24698 -1.94986 1.80194 -0.86777 -0.44504 1.56366 -2.00000 1.56366 -0.44504 -0.86777 1.80194 -1.94986 1.24698 0.00000 -1.24698 1.94986 -1.80194 0.86777 0.44504 -1.56366 2.00000 0.00000 0.00000 27 2.00000 -1.69345 0.86777 0.22393 -1.24698 1.88777 -1.94986 1.41421 -0.44504 -0.66056 1.56366 -1.98742 1.80194 -1.06406 0.00000 1.06406 -1.80194 1.98742 -1.56366 0.66056 0.44504 -1.41421 1.94986 -1.88777 1.24698 -0.22393 -0.86777 1.69345 -2.00000 0.00000 0.00000 28 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 -1.80194 1.24698 -0.44504 -0.44504 1.24698 -1.80194 2.00000 0.00000 0.00000 29 2.00000 -1.88777 1.56366 -1.06406 0.44504 0.22393 -0.86777 1.41421 -1.80194 1.98742 -1.94986 1.69345 -1.24698 0.66056 0.00000 -0.66056 1.24698 -1.69345 1.94986 -1.98742 1.80194 -1.41421 0.86777 -0.22393 -0.44504 1.06406 -1.56366 1.88777 -2.00000 0.00000 0.00000 30 2.00000 -1.94986 1.80194 -1.56366 1.24698 -0.86777 0.44504 0.00000 -0.44504 0.86777 -1.24698 1.56366 -1.80194 1.94986 -2.00000 1.94986 -1.80194 1.56366 -1.24698 0.86777 -0.44504 0.00000 0.44504 -0.86777 1.24698 -1.56366 1.80194 -1.94986 2.00000 0.00000 0.00000 31 2.00000 -1.98742 1.94986 -1.88777 1.80194 -1.69345 1.56366 -1.41421 1.24698 -1.06406 0.86777 -0.66056 0.44504 -0.22393 0.00000 0.22393 -0.44504 0.66056 -0.86777 1.06406 -1.24698 1.41421 -1.56366 1.69345 -1.80194 1.88777 -1.94986 1.98742 -2.00000 0.00000 0.00000