Direct sum of irreducible representation

A1	A2	E
7	4	11

Properties of derivatives and isotopomers by single substitution, h(C_3v)=6

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C1	1	6	C	yes	yes	13C	265.0973	5.2803
2	C1	1	6	C	yes	yes	13C	265.0973	5.2803
3	C1	1	6	C	yes	yes	13C	265.0973	5.2803
4	Cs	2	3	C	no	yes	13C	265.0973	2.6401
5	Cs	2	3	H	no	yes	2H	265.1002	0.037036
6	Cs	2	3	H	no	yes	2H	265.1002	0.037036
7	C1	1	6	H	yes	yes	2H	265.1002	0.074072
Total Number of Atoms:			33	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_3v
***Calculated as h( C_3v)/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	4
Double	X2	18	79
Double	XY	6	173
Triple	X3	46	890
Triple	X2Y	48	2.704
Triple	XYZ	6	5.453
Quadruple	X4	150	6.745
Quadruple	X3Y	90	27.235
Quadruple	X2Y2	300	40.770
Quadruple	X2YZ	90	81.795
Quadruple	WXYZ	0	163.680
Quintuple	X5	330	39.391
Quintuple	VWXYZ	0	4.746.720
Sextuple	X6	770	184.228
Sextuple	UVWXYZ	0	132.908.160

Further Reading

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

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Representation Γ_3N