Direct sum of irreducible representation

A1g	A2g	B1g	B2g	E1g	E2g	A1u	A2u	B1u	B2u	E1u	E2u
3	0	0	2	2	2	0	2	2	0	2	2

Properties of derivatives and isotopomers by single substitution, h(D_6h)=24

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	D6h	24	1	Cr	no	no	53Cr 50Cr 54Cr	209.0345 206.0399 210.0328	8.3045 3.7978 2.0672
2	Cs	2	12	C	no	yes	13C	209.0378	9.7748
3	Cs	2	12	H	no	yes	2H	209.0407	0.1371
Total Number of Atoms:			25	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_6h
***Calculated as h( D_6h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	3	0
Double	X2	16	8
Double	XY	18	16
Triple	X3	44	78
Triple	X2Y	86	248
Triple	XYZ	126	512
Quadruple	X4	138	478
Quadruple	X3Y	270	1.974
Quadruple	X2Y2	402	3.000
Quadruple	X2YZ	522	6.064
Quadruple	WXYZ	756	12.272
Quintuple	X5	290	2.088
Quintuple	VWXYZ	3.780	263.760
Sextuple	X6	632	7.130
Sextuple	UVWXYZ	15.120	5.305.440

Further Reading

• P.W. Fowler, J. Chem. Soc. Faraday Trans. 91(15) 2241 (1995)
  Isomer Counting using Point Group Symmetry
  
  

---

Representation Γ_3N