Direct sum of irreducible representation

A'	E'*	A''	E''*
7	6	4	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	151.1442	2.9462
2	C3	3	2	C	yes	yes	13C	151.1442	1.9641
3	C1	1	6	C	yes	yes	13C	151.1442	5.8923
4	Cs	2	3	H	no	yes	2H	151.1471	0.041329
5	Cs	2	3	H	no	yes	2H	151.1471	0.041329
6	C1	1	6	H	yes	yes	2H	151.1471	0.082658
7	C1	1	6	H	yes	yes	2H	151.1471	0.082658
Total Number of Atoms:			29	✅ 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	4
Double	X2	16	60
Double	XY	24	124
Triple	X3	60	582
Triple	X2Y	114	1.770
Triple	XYZ	168	3.570
Quadruple	X4	177	3.876
Quadruple	X3Y	408	15.636
Quadruple	X2Y2	522	23.490
Quadruple	X2YZ	744	47.130
Quadruple	WXYZ	1.008	94.500
Quintuple	X5	459	19.566
Quintuple	VWXYZ	5.040	2.372.580
Sextuple	X6	1.032	78.666
Sextuple	UVWXYZ	20.160	56.992.320

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