Direct sum of irreducible representation

Ag	Bg	Au	Bu
15	0	0	15

Properties of derivatives and isotopomers by single substitution, h(C_2h)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	2	C	no	yes	13C	229.0973	1.8195
2	Cs	2	2	C	no	yes	13C	229.0973	1.8195
3	Cs	2	2	C	no	yes	13C	229.0973	1.8195
4	Cs	2	2	C	no	yes	13C	229.0973	1.8195
5	Cs	2	2	C	no	yes	13C	229.0973	1.8195
6	Cs	2	2	C	no	yes	13C	229.0973	1.8195
7	Cs	2	2	C	no	yes	13C	229.0973	1.8195
8	Cs	2	2	C	no	yes	13C	229.0973	1.8195
9	Cs	2	2	C	no	yes	13C	229.0973	1.8195
10	Cs	2	2	H	no	yes	2H	229.1002	0.025524
11	Cs	2	2	H	no	yes	2H	229.1002	0.025524
12	Cs	2	2	H	no	yes	2H	229.1002	0.025524
13	Cs	2	2	H	no	yes	2H	229.1002	0.025524
14	Cs	2	2	H	no	yes	2H	229.1002	0.025524
15	Cs	2	2	H	no	yes	2H	229.1002	0.025524
Total Number of Atoms:			30	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_2h
***Calculated as h( C_2h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	15	0
Double	X2	225	0
Double	XY	435	0
Triple	X3	2.030	0
Triple	X2Y	6.090	0
Triple	XYZ	12.180	0
Quadruple	X4	13.755	0
Quadruple	X3Y	54.810	0
Quadruple	X2Y2	82.320	0
Quadruple	X2YZ	164.430	0
Quadruple	WXYZ	328.860	0
Quintuple	X5	71.253	0
Quintuple	VWXYZ	8.550.360	0
Sextuple	X6	297.115	0
Sextuple	UVWXYZ	213.759.000	0

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