Character table for dirhenium decacarbonyl of full non-rigid molecule group

Table 1.
Character table of dirhenium decacarbonyl.
1a
4a
2a
4b
2b
4c
2c
4d
2P
1a
2a
1a
2a
1a
2a
1a
2a
3P
1a
4b
2a
4a
2b
4d
2c
4c
÷1 1
1 1
1 1
1 1
1
÷2 1
−1 1
−1
−1 1
−1 1
÷3 1
−1 1
−1 1
−1 1
−1
÷4 1
1 1
1
−1
−1
−1
−1
÷5 1
A
−1
−A
−1
−A
1
A
÷6 1
−A
−1
�
−1
A
1
−A
÷7 1
A
−1
−A
1
A
−1
−A
÷8 1
−A
−1
A
1
−A
−1
A
A = −E(4) = −sqrt(−1) = −i.
Remark: From Table 1
, we see that there are 8 conjugacy classes and 8 irreducible character, namely [()], [(1,2,3,4)(6,7,8,9)], [(1,3)(2,4)(6,8)(7,9)],
[(1,4,3,2)(6,9,8,7)], [(1,6)(2,7)(3,8)(4,9)(5,10)], [(1,7,3,9)(2,8,4,6)(5,10)],
[(1,8)(2,9)(3,6)(4,7)(5,10)], [(1,9,3,7)(2,6,4,8)(5,10)].