Direct sum of irreducible representation

A'	E'*	A''	E''*
8	6	5	3

Properties of derivatives and isotopomers by single substitution, h(C_3h)=6

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	3	C	no	yes	13C	153.1599	2.9452
2	C3	3	2	C	yes	yes	13C	153.1599	1.9635
3	C3	3	2	H	yes	yes	2H	153.1628	0.027544
4	C1	1	6	C	yes	yes	13C	153.1599	5.8905
5	Cs	2	3	H	no	yes	2H	153.1628	0.041316
6	Cs	2	3	H	no	yes	2H	153.1628	0.041316
7	C1	1	6	H	yes	yes	2H	153.1628	0.082632
8	C1	1	6	H	yes	yes	2H	153.1628	0.082632
Total Number of Atoms:			31	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_3h
***Calculated as h( C_3h)/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	5
Double	X2	17	71
Double	XY	24	147
Triple	X3	63	722
Triple	X2Y	117	2.193
Triple	XYZ	168	4.419
Quadruple	X4	193	5.160
Quadruple	X3Y	432	20.774
Quadruple	X2Y2	554	31.190
Quadruple	X2YZ	768	62.550
Quadruple	WXYZ	1.008	125.364
Quintuple	X5	519	28.077
Quintuple	VWXYZ	5.040	3.395.700
Sextuple	X6	1.209	122.133
Sextuple	UVWXYZ	20.160	88.343.640

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