Direct sum of irreducible representation

A	B1	B2	B3
7	4	4	7

Properties of derivatives and isotopomers by single substitution, h(D₂)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C2	2	2	C	yes	yes	13C	155.0816	1.9449
2	C1	1	4	C	yes	yes	13C	155.0816	3.8899
3	C1	1	4	C	yes	yes	13C	155.0816	3.8899
4	C2	2	2	C	yes	yes	13C	155.0816	1.9449
5	C2	2	2	H	yes	yes	2H	155.0845	0.027284
6	C1	1	4	H	yes	yes	2H	155.0845	0.054567
7	C1	1	4	H	yes	yes	2H	155.0845	0.054567
Total Number of Atoms:			22	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D₂
***Calculated as h( D₂)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Chiral Isomers
Single	X	7
Double	X2	69
Double	XY	123
Triple	X3	402
Triple	X2Y	1.182
Triple	XYZ	2.340
Quadruple	X4	1.897
Quadruple	X3Y	7.390
Quadruple	X2Y2	11.124
Quadruple	X2YZ	22.050
Quadruple	WXYZ	43.980
Quintuple	X5	6.667
Quintuple	VWXYZ	790.200
Sextuple	X6	18.885
Sextuple	UVWXYZ	13.430.520

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