Direct sum of irreducible representation

A'	A''
17	0

Properties of derivatives and isotopomers by single substitution, h(C_s)=2

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	Cs	2	1	C	no	yes	13C	130.0612	1.0021
2	Cs	2	1	C	no	yes	13C	130.0612	1.0021
3	Cs	2	1	C	no	yes	13C	130.0612	1.0021
4	Cs	2	1	C	no	yes	13C	130.0612	1.0021
5	Cs	2	1	C	no	yes	13C	130.0612	1.0021
6	Cs	2	1	C	no	yes	13C	130.0612	1.0021
7	Cs	2	1	N	no	yes	15N	130.0549	0.3310
8	Cs	2	1	C	no	yes	13C	130.0612	1.0021
9	Cs	2	1	C	no	yes	13C	130.0612	1.0021
10	Cs	2	1	C	no	yes	13C	130.0612	1.0021
11	Cs	2	1	H	no	yes	2H	130.0641	0.014057
12	Cs	2	1	H	no	yes	2H	130.0641	0.014057
13	Cs	2	1	H	no	yes	2H	130.0641	0.014057
14	Cs	2	1	H	no	yes	2H	130.0641	0.014057
15	Cs	2	1	H	no	yes	2H	130.0641	0.014057
16	Cs	2	1	H	no	yes	2H	130.0641	0.014057
17	Cs	2	1	H	no	yes	2H	130.0641	0.014057
Total Number of Atoms:			17	✅ Correct Number of Atoms found

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

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	17	0
Double	X2	136	0
Double	XY	272	0
Triple	X3	680	0
Triple	X2Y	2.040	0
Triple	XYZ	4.080	0
Quadruple	X4	2.380	0
Quadruple	X3Y	9.520	0
Quadruple	X2Y2	14.280	0
Quadruple	X2YZ	28.560	0
Quadruple	WXYZ	57.120	0
Quintuple	X5	6.188	0
Quintuple	VWXYZ	742.560	0
Sextuple	X6	12.376	0
Sextuple	UVWXYZ	8.910.720	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