Direct sum of irreducible representation

A	B	E*
4	4	4

Properties of derivatives and isotopomers by single substitution, h(S₄)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C1	1	4	C	yes	yes	13C	240.9101	1.3407
2	C1	1	4	C	yes	yes	13C	240.9101	1.3407
3	C1	1	4	Cl	yes	yes	37Cl	241.9038	38.5666
4	C1	1	4	H	yes	yes	2H	240.9130	0.018807
Total Number of Atoms:			16	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group S₄
***Calculated as h( S₄)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	0	4
Double	X2	0	32
Double	XY	0	60
Triple	X3	0	140
Triple	X2Y	0	420
Triple	XYZ	0	840
Quadruple	X4	4	460
Quadruple	X3Y	0	1.820
Quadruple	X2Y2	0	2.744
Quadruple	X2YZ	0	5.460
Quadruple	WXYZ	0	10.920
Quintuple	X5	0	1.092
Quintuple	VWXYZ	0	131.040
Sextuple	X6	0	2.016
Sextuple	UVWXYZ	0	1.441.440

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