Character table for the C71v point group

C71v    E        2 C71    2 C71^2  2 C71^3  2 C71^4  2 C71^5  2 C71^6  2 C71^7  2 C71^8  2 C71^9  2 C71^10 2 C71^11 2 C71^12 2 C71^13 2 C71^14 2 C71^15 2 C71^16 2 C71^17 2 C71^18 2 C71^19 2 C71^20 2 C71^21 2 C71^22 2 C71^23 2 C71^24 2 C71^25 2 C71^26 2 C71^27 2 C71^28 2 C71^29 2 C71^30 2 C71^31 2 C71^32 2 C71^33 2 C71^34 2 C71^35 71 sv       <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     ... ..T ....T ......T ........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     ..T ... ..... ....... ......... ........... .............
E1      2.00000  1.99217  1.96876  1.92993  1.87600  1.80739  1.72463  1.62837  1.51937  1.39848  1.26665  1.12490  0.97435  0.81617  0.65160  0.48194  0.30850  0.13265 -0.04424 -0.22079 -0.39560 -0.56732 -0.73460 -0.89613 -1.05065 -1.19694 -1.33387 -1.46036 -1.57542 -1.67814 -1.76774 -1.84350 -1.90483 -1.95125 -1.98241 -1.99804  0.00000     TT. TT. ..TT. ....TT. ......TT. ........TT. ..........TT.
E2      2.00000  1.96876  1.87600  1.72463  1.51937  1.26665  0.97435  0.65160  0.30850 -0.04424 -0.39560 -0.73460 -1.05065 -1.33387 -1.57542 -1.76774 -1.90483 -1.98241 -1.99804 -1.95125 -1.84350 -1.67814 -1.46036 -1.19694 -0.89613 -0.56732 -0.22079  0.13265  0.48194  0.81617  1.12490  1.39848  1.62837  1.80739  1.92993  1.99217  0.00000     ... ... TT... ..TT... ....TT... ......TT... ........TT...
E3      2.00000  1.92993  1.72463  1.39848  0.97435  0.48194 -0.04424 -0.56732 -1.05065 -1.46036 -1.76774 -1.95125 -1.99804 -1.90483 -1.67814 -1.33387 -0.89613 -0.39560  0.13265  0.65160  1.12490  1.51937  1.80739  1.96876  1.99217  1.87600  1.62837  1.26665  0.81617  0.30850 -0.22079 -0.73460 -1.19694 -1.57542 -1.84350 -1.98241  0.00000     ... ... ..... TT..... ..TT..... ....TT..... ......TT.....
E4      2.00000  1.87600  1.51937  0.97435  0.30850 -0.39560 -1.05065 -1.57542 -1.90483 -1.99804 -1.84350 -1.46036 -0.89613 -0.22079  0.48194  1.12490  1.62837  1.92993  1.99217  1.80739  1.39848  0.81617  0.13265 -0.56732 -1.19694 -1.67814 -1.95125 -1.98241 -1.76774 -1.33387 -0.73460 -0.04424  0.65160  1.26665  1.72463  1.96876  0.00000     ... ... ..... ....... TT....... ..TT....... ....TT.......
E5      2.00000  1.80739  1.26665  0.48194 -0.39560 -1.19694 -1.76774 -1.99804 -1.84350 -1.33387 -0.56732  0.30850  1.12490  1.72463  1.99217  1.87600  1.39848  0.65160 -0.22079 -1.05065 -1.67814 -1.98241 -1.90483 -1.46036 -0.73460  0.13265  0.97435  1.62837  1.96876  1.92993  1.51937  0.81617 -0.04424 -0.89613 -1.57542 -1.95125  0.00000     ... ... ..... ....... ......... TT......... ..TT.........
E6      2.00000  1.72463  0.97435 -0.04424 -1.05065 -1.76774 -1.99804 -1.67814 -0.89613  0.13265  1.12490  1.80739  1.99217  1.62837  0.81617 -0.22079 -1.19694 -1.84350 -1.98241 -1.57542 -0.73460  0.30850  1.26665  1.87600  1.96876  1.51937  0.65160 -0.39560 -1.33387 -1.90483 -1.95125 -1.46036 -0.56732  0.48194  1.39848  1.92993  0.00000     ... ... ..... ....... ......... ........... TT...........
E7      2.00000  1.62837  0.65160 -0.56732 -1.57542 -1.99804 -1.67814 -0.73460  0.48194  1.51937  1.99217  1.72463  0.81617 -0.39560 -1.46036 -1.98241 -1.76774 -0.89613  0.30850  1.39848  1.96876  1.80739  0.97435 -0.22079 -1.33387 -1.95125 -1.84350 -1.05065  0.13265  1.26665  1.92993  1.87600  1.12490 -0.04424 -1.19694 -1.90483  0.00000     ... ... ..... ....... ......... ........... .............
E8      2.00000  1.51937  0.30850 -1.05065 -1.90483 -1.84350 -0.89613  0.48194  1.62837  1.99217  1.39848  0.13265 -1.19694 -1.95125 -1.76774 -0.73460  0.65160  1.72463  1.96876  1.26665 -0.04424 -1.33387 -1.98241 -1.67814 -0.56732  0.81617  1.80739  1.92993  1.12490 -0.22079 -1.46036 -1.99804 -1.57542 -0.39560  0.97435  1.87600  0.00000     ... ... ..... ....... ......... ........... .............
E9      2.00000  1.39848 -0.04424 -1.46036 -1.99804 -1.33387  0.13265  1.51937  1.99217  1.26665 -0.22079 -1.57542 -1.98241 -1.19694  0.30850  1.62837  1.96876  1.12490 -0.39560 -1.67814 -1.95125 -1.05065  0.48194  1.72463  1.92993  0.97435 -0.56732 -1.76774 -1.90483 -0.89613  0.65160  1.80739  1.87600  0.81617 -0.73460 -1.84350  0.00000     ... ... ..... ....... ......... ........... .............
E10     2.00000  1.26665 -0.39560 -1.76774 -1.84350 -0.56732  1.12490  1.99217  1.39848 -0.22079 -1.67814 -1.90483 -0.73460  0.97435  1.96876  1.51937 -0.04424 -1.57542 -1.95125 -0.89613  0.81617  1.92993  1.62837  0.13265 -1.46036 -1.98241 -1.05065  0.65160  1.87600  1.72463  0.30850 -1.33387 -1.99804 -1.19694  0.48194  1.80739  0.00000     ... ... ..... ....... ......... ........... .............
E11     2.00000  1.12490 -0.73460 -1.95125 -1.46036  0.30850  1.80739  1.72463  0.13265 -1.57542 -1.90483 -0.56732  1.26665  1.99217  0.97435 -0.89613 -1.98241 -1.33387  0.48194  1.87600  1.62837 -0.04424 -1.67814 -1.84350 -0.39560  1.39848  1.96876  0.81617 -1.05065 -1.99804 -1.19694  0.65160  1.92993  1.51937 -0.22079 -1.76774  0.00000     ... ... ..... ....... ......... ........... .............
E12     2.00000  0.97435 -1.05065 -1.99804 -0.89613  1.12490  1.99217  0.81617 -1.19694 -1.98241 -0.73460  1.26665  1.96876  0.65160 -1.33387 -1.95125 -0.56732  1.39848  1.92993  0.48194 -1.46036 -1.90483 -0.39560  1.51937  1.87600  0.30850 -1.57542 -1.84350 -0.22079  1.62837  1.80739  0.13265 -1.67814 -1.76774 -0.04424  1.72463  0.00000     ... ... ..... ....... ......... ........... .............
E13     2.00000  0.81617 -1.33387 -1.90483 -0.22079  1.72463  1.62837 -0.39560 -1.95125 -1.19694  0.97435  1.99217  0.65160 -1.46036 -1.84350 -0.04424  1.80739  1.51937 -0.56732 -1.98241 -1.05065  1.12490  1.96876  0.48194 -1.57542 -1.76774  0.13265  1.87600  1.39848 -0.73460 -1.99804 -0.89613  1.26665  1.92993  0.30850 -1.67814  0.00000     ... ... ..... ....... ......... ........... .............
E14     2.00000  0.65160 -1.57542 -1.67814  0.48194  1.99217  0.81617 -1.46036 -1.76774  0.30850  1.96876  0.97435 -1.33387 -1.84350  0.13265  1.92993  1.12490 -1.19694 -1.90483 -0.04424  1.87600  1.26665 -1.05065 -1.95125 -0.22079  1.80739  1.39848 -0.89613 -1.98241 -0.39560  1.72463  1.51937 -0.73460 -1.99804 -0.56732  1.62837  0.00000     ... ... ..... ....... ......... ........... .............
E15     2.00000  0.48194 -1.76774 -1.33387  1.12490  1.87600 -0.22079 -1.98241 -0.73460  1.62837  1.51937 -0.89613 -1.95125 -0.04424  1.92993  0.97435 -1.46036 -1.67814  0.65160  1.99217  0.30850 -1.84350 -1.19694  1.26665  1.80739 -0.39560 -1.99804 -0.56732  1.72463  1.39848 -1.05065 -1.90483  0.13265  1.96876  0.81617 -1.57542  0.00000     ... ... ..... ....... ......... ........... .............
E16     2.00000  0.30850 -1.90483 -0.89613  1.62837  1.39848 -1.19694 -1.76774  0.65160  1.96876 -0.04424 -1.98241 -0.56732  1.80739  1.12490 -1.46036 -1.57542  0.97435  1.87600 -0.39560 -1.99804 -0.22079  1.92993  0.81617 -1.67814 -1.33387  1.26665  1.72463 -0.73460 -1.95125  0.13265  1.99217  0.48194 -1.84350 -1.05065  1.51937  0.00000     ... ... ..... ....... ......... ........... .............
E17     2.00000  0.13265 -1.98241 -0.39560  1.92993  0.65160 -1.84350 -0.89613  1.72463  1.12490 -1.57542 -1.33387  1.39848  1.51937 -1.19694 -1.67814  0.97435  1.80739 -0.73460 -1.90483  0.48194  1.96876 -0.22079 -1.99804 -0.04424  1.99217  0.30850 -1.95125 -0.56732  1.87600  0.81617 -1.76774 -1.05065  1.62837  1.26665 -1.46036  0.00000     ... ... ..... ....... ......... ........... .............
E18     2.00000 -0.04424 -1.99804  0.13265  1.99217 -0.22079 -1.98241  0.30850  1.96876 -0.39560 -1.95125  0.48194  1.92993 -0.56732 -1.90483  0.65160  1.87600 -0.73460 -1.84350  0.81617  1.80739 -0.89613 -1.76774  0.97435  1.72463 -1.05065 -1.67814  1.12490  1.62837 -1.19694 -1.57542  1.26665  1.51937 -1.33387 -1.46036  1.39848  0.00000     ... ... ..... ....... ......... ........... .............
E19     2.00000 -0.22079 -1.95125  0.65160  1.80739 -1.05065 -1.57542  1.39848  1.26665 -1.67814 -0.89613  1.87600  0.48194 -1.98241 -0.04424  1.99217 -0.39560 -1.90483  0.81617  1.72463 -1.19694 -1.46036  1.51937  1.12490 -1.76774 -0.73460  1.92993  0.30850 -1.99804  0.13265  1.96876 -0.56732 -1.84350  0.97435  1.62837 -1.33387  0.00000     ... ... ..... ....... ......... ........... .............
E20     2.00000 -0.39560 -1.84350  1.12490  1.39848 -1.67814 -0.73460  1.96876 -0.04424 -1.95125  0.81617  1.62837 -1.46036 -1.05065  1.87600  0.30850 -1.99804  0.48194  1.80739 -1.19694 -1.33387  1.72463  0.65160 -1.98241  0.13265  1.92993 -0.89613 -1.57542  1.51937  0.97435 -1.90483 -0.22079  1.99217 -0.56732 -1.76774  1.26665  0.00000     ... ... ..... ....... ......... ........... .............
E21     2.00000 -0.56732 -1.67814  1.51937  0.81617 -1.98241  0.30850  1.80739 -1.33387 -1.05065  1.92993 -0.04424 -1.90483  1.12490  1.26665 -1.84350 -0.22079  1.96876 -0.89613 -1.46036  1.72463  0.48194 -1.99804  0.65160  1.62837 -1.57542 -0.73460  1.99217 -0.39560 -1.76774  1.39848  0.97435 -1.95125  0.13265  1.87600 -1.19694  0.00000     ... ... ..... ....... ......... ........... .............
E22     2.00000 -0.73460 -1.46036  1.80739  0.13265 -1.90483  1.26665  0.97435 -1.98241  0.48194  1.62837 -1.67814 -0.39560  1.96876 -1.05065 -1.19694  1.92993 -0.22079 -1.76774  1.51937  0.65160 -1.99804  0.81617  1.39848 -1.84350 -0.04424  1.87600 -1.33387 -0.89613  1.99217 -0.56732 -1.57542  1.72463  0.30850 -1.95125  1.12490  0.00000     ... ... ..... ....... ......... ........... .............
E23     2.00000 -0.89613 -1.19694  1.96876 -0.56732 -1.46036  1.87600 -0.22079 -1.67814  1.72463  0.13265 -1.84350  1.51937  0.48194 -1.95125  1.26665  0.81617 -1.99804  0.97435  1.12490 -1.98241  0.65160  1.39848 -1.90483  0.30850  1.62837 -1.76774 -0.04424  1.80739 -1.57542 -0.39560  1.92993 -1.33387 -0.73460  1.99217 -1.05065  0.00000     ... ... ..... ....... ......... ........... .............
E24     2.00000 -1.05065 -0.89613  1.99217 -1.19694 -0.73460  1.96876 -1.33387 -0.56732  1.92993 -1.46036 -0.39560  1.87600 -1.57542 -0.22079  1.80739 -1.67814 -0.04424  1.72463 -1.76774  0.13265  1.62837 -1.84350  0.30850  1.51937 -1.90483  0.48194  1.39848 -1.95125  0.65160  1.26665 -1.98241  0.81617  1.12490 -1.99804  0.97435  0.00000     ... ... ..... ....... ......... ........... .............
E25     2.00000 -1.19694 -0.56732  1.87600 -1.67814  0.13265  1.51937 -1.95125  0.81617  0.97435 -1.98241  1.39848  0.30850 -1.76774  1.80739 -0.39560 -1.33387  1.99217 -1.05065 -0.73460  1.92993 -1.57542 -0.04424  1.62837 -1.90483  0.65160  1.12490 -1.99804  1.26665  0.48194 -1.84350  1.72463 -0.22079 -1.46036  1.96876 -0.89613  0.00000     ... ... ..... ....... ......... ........... .............
E26     2.00000 -1.33387 -0.22079  1.62837 -1.95125  0.97435  0.65160 -1.84350  1.80739 -0.56732 -1.05065  1.96876 -1.57542  0.13265  1.39848 -1.99804  1.26665  0.30850 -1.67814  1.92993 -0.89613 -0.73460  1.87600 -1.76774  0.48194  1.12490 -1.98241  1.51937 -0.04424 -1.46036  1.99217 -1.19694 -0.39560  1.72463 -1.90483  0.81617  0.00000     ... ... ..... ....... ......... ........... .............
E27     2.00000 -1.46036  0.13265  1.26665 -1.98241  1.62837 -0.39560 -1.05065  1.92993 -1.76774  0.65160  0.81617 -1.84350  1.87600 -0.89613 -0.56732  1.72463 -1.95125  1.12490  0.30850 -1.57542  1.99217 -1.33387 -0.04424  1.39848 -1.99804  1.51937 -0.22079 -1.19694  1.96876 -1.67814  0.48194  0.97435 -1.90483  1.80739 -0.73460  0.00000     ... ... ..... ....... ......... ........... .............
E28     2.00000 -1.57542  0.48194  0.81617 -1.76774  1.96876 -1.33387  0.13265  1.12490 -1.90483  1.87600 -1.05065 -0.22079  1.39848 -1.98241  1.72463 -0.73460 -0.56732  1.62837 -1.99804  1.51937 -0.39560 -0.89613  1.80739 -1.95125  1.26665 -0.04424 -1.19694  1.92993 -1.84350  0.97435  0.30850 -1.46036  1.99217 -1.67814  0.65160  0.00000     ... ... ..... ....... ......... ........... .............
E29     2.00000 -1.67814  0.81617  0.30850 -1.33387  1.92993 -1.90483  1.26665 -0.22079 -0.89613  1.72463 -1.99804  1.62837 -0.73460 -0.39560  1.39848 -1.95125  1.87600 -1.19694  0.13265  0.97435 -1.76774  1.99217 -1.57542  0.65160  0.48194 -1.46036  1.96876 -1.84350  1.12490 -0.04424 -1.05065  1.80739 -1.98241  1.51937 -0.56732  0.00000     ... ... ..... ....... ......... ........... .............
E30     2.00000 -1.76774  1.12490 -0.22079 -0.73460  1.51937 -1.95125  1.92993 -1.46036  0.65160  0.30850 -1.19694  1.80739 -1.99804  1.72463 -1.05065  0.13265  0.81617 -1.57542  1.96876 -1.90483  1.39848 -0.56732 -0.39560  1.26665 -1.84350  1.99217 -1.67814  0.97435 -0.04424 -0.89613  1.62837 -1.98241  1.87600 -1.33387  0.48194  0.00000     ... ... ..... ....... ......... ........... .............
E31     2.00000 -1.84350  1.39848 -0.73460 -0.04424  0.81617 -1.46036  1.87600 -1.99804  1.80739 -1.33387  0.65160  0.13265 -0.89613  1.51937 -1.90483  1.99217 -1.76774  1.26665 -0.56732 -0.22079  0.97435 -1.57542  1.92993 -1.98241  1.72463 -1.19694  0.48194  0.30850 -1.05065  1.62837 -1.95125  1.96876 -1.67814  1.12490 -0.39560  0.00000     ... ... ..... ....... ......... ........... .............
E32     2.00000 -1.90483  1.62837 -1.19694  0.65160 -0.04424 -0.56732  1.12490 -1.57542  1.87600 -1.99804  1.92993 -1.67814  1.26665 -0.73460  0.13265  0.48194 -1.05065  1.51937 -1.84350  1.99217 -1.95125  1.72463 -1.33387  0.81617 -0.22079 -0.39560  0.97435 -1.46036  1.80739 -1.98241  1.96876 -1.76774  1.39848 -0.89613  0.30850  0.00000     ... ... ..... ....... ......... ........... .............
E33     2.00000 -1.95125  1.80739 -1.57542  1.26665 -0.89613  0.48194 -0.04424 -0.39560  0.81617 -1.19694  1.51937 -1.76774  1.92993 -1.99804  1.96876 -1.84350  1.62837 -1.33387  0.97435 -0.56732  0.13265  0.30850 -0.73460  1.12490 -1.46036  1.72463 -1.90483  1.99217 -1.98241  1.87600 -1.67814  1.39848 -1.05065  0.65160 -0.22079  0.00000     ... ... ..... ....... ......... ........... .............
E34     2.00000 -1.98241  1.92993 -1.84350  1.72463 -1.57542  1.39848 -1.19694  0.97435 -0.73460  0.48194 -0.22079 -0.04424  0.30850 -0.56732  0.81617 -1.05065  1.26665 -1.46036  1.62837 -1.76774  1.87600 -1.95125  1.99217 -1.99804  1.96876 -1.90483  1.80739 -1.67814  1.51937 -1.33387  1.12490 -0.89613  0.65160 -0.39560  0.13265  0.00000     ... ... ..... ....... ......... ........... .............
E35     2.00000 -1.99804  1.99217 -1.98241  1.96876 -1.95125  1.92993 -1.90483  1.87600 -1.84350  1.80739 -1.76774  1.72463 -1.67814  1.62837 -1.57542  1.51937 -1.46036  1.39848 -1.33387  1.26665 -1.19694  1.12490 -1.05065  0.97435 -0.89613  0.81617 -0.73460  0.65160 -0.56732  0.48194 -0.39560  0.30850 -0.22079  0.13265 -0.04424  0.00000     ... ... ..... ....... ......... ........... .............

 Irrational character values:  1.992173644150 = 2*cos(2*π/71)
                               1.968755828445 = 2*cos(4*π/71)
                               1.929929829046 = 2*cos(6*π/71)
                               1.875999512038 = 2*cos(8*π/71)
                               1.807386955274 = 2*cos(10*π/71)
                               1.724629145040 = 2*cos(12*π/71)
                               1.628373773407 = 2*cos(14*π/71)
                               1.519374169167 = 2*cos(16*π/71)
                               1.398483402009 = 2*cos(18*π/71)
                               1.266647606096 = 2*cos(20*π/71)
                               1.124898575282 = 2*cos(22*π/71)
                               0.974345687922 = 2*cos(24*π/71)
                               0.816167224487 = 2*cos(26*π/71)
                               0.651601145920 = 2*cos(28*π/71)
                               0.481935404913 = 2*cos(30*π/71)
                               0.308497865931 = 2*cos(32*π/71)
                               0.132645912870 = 2*cos(34*π/71)
                              -0.044244174306 = 2*cos(36*π/71)
                              -0.220787990831 = 2*cos(38*π/71)
                              -0.395603841971 = 2*cos(40*π/71)
                              -0.567323556669 = 2*cos(42*π/71)
                              -0.734603195330 = 2*cos(44*π/71)
                              -0.896133567975 = 2*cos(46*π/71)
                              -1.050650480429 = 2*cos(48*π/71)
                              -1.196944628348 = 2*cos(50*π/71)
                              -1.333871061673 = 2*cos(52*π/71)
                              -1.460358145412 = 2*cos(54*π/71)
                              -1.575415946635 = 2*cos(56*π/71)
                              -1.678143982049 = 2*cos(58*π/71)
                              -1.767738265491 = 2*cos(60*π/71)
                              -1.843497600218 = 2*cos(62*π/71)
                              -1.904829066716 = 2*cos(64*π/71)
                              -1.951252663105 = 2*cos(66*π/71)
                              -1.982405061799 = 2*cos(68*π/71)
                              -1.998042453040 = 2*cos(70*π/71)



 Symmetry of Rotations and Cartesian products

A1   p+d+f+g+h+i+j+k+l+m    z, z2, z3, z4, z5, z6 
A2   R                      Rz 
E1   R+p+d+f+g+h+i+j+k+l+m  {Rx, Ry}, {x, y}, {xz, yz}, {xz2, yz2}, {xz3, yz3}, {xz4, yz4}, {xz5, yz5} 
E2   d+f+g+h+i+j+k+l+m      {x2y2, xy}, {z(x2y2), xyz}, {z2(x2y2), xyz2}, {z3(x2y2), xyz3}, {z4(x2y2), xyz4} 
E3   f+g+h+i+j+k+l+m        {x(x2−3y2), y(3x2y2)}, {xz(x2−3y2), yz(3x2y2)}, {xz2(x2−3y2), yz2(3x2y2)}, {xz3(x2−3y2), yz3(3x2y2)} 
E4   g+h+i+j+k+l+m          {(x2y2)2−4x2y2, xy(x2y2)}, {z((x2y2)2−4x2y2), xyz(x2y2)}, {z2((x2y2)2−4x2y2), xyz2(x2y2)} 
E5   h+i+j+k+l+m            {x(x2−(5+2√5)y2)(x2−(5−2√5)y2), y((5+2√5)x2y2)((5−2√5)x2y2)}, {xz(x2−(5+2√5)y2)(x2−(5−2√5)y2), yz((5+2√5)x2y2)((5−2√5)x2y2)} 
E6   i+j+k+l+m              {x2(x2−3y2)2y2(3x2y2)2, xy(x2−3y2)(3x2y2)} 
E7   j+k+l+m 
E8   k+l+m 
E9   l+m 
E10  m 

 Notes:

    α  The order of the C71v point group is 142, and the order of the principal axis (C71) is 71. The group has 37 irreducible representations.

    β  The C71v point group is isomorphic to D71.

    γ  The C71v point group is generated by two symmetry elements, C71 and any σv.
       Also, the group may be generated from any two σv planes.

    δ  The group contains one set of symmetry planes σv intersecting in the principal (z) axis. The xz plane (but not the yz plane) is a member of that set.

    ε  The lowest nonvanishing multipole moment in C71v is 2 (dipole moment).

    ζ  This point group is non-Abelian (some symmetry operations are not commutative).
       Therefore, the character table contains multi-membered classes and degenerate irreducible representations.

    η  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 just 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 C71v point group was created by Gernot Katzer.

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