Direct sum of irreducible representation

A	B1	B2	B3
7	6	6	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	137.1286	1.9866
2	C1	1	4	C	yes	yes	13C	137.1286	3.9732
3	C1	1	4	C	yes	yes	13C	137.1286	3.9732
4	C1	1	4	H	yes	yes	2H	137.1315	0.055735
5	C1	1	4	H	yes	yes	2H	137.1315	0.055735
6	C1	1	4	H	yes	yes	2H	137.1315	0.055735
7	C1	1	4	H	yes	yes	2H	137.1315	0.055735
Total Number of Atoms:			26	✅ 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	91
Double	XY	163
Triple	X3	656
Triple	X2Y	1.956
Triple	XYZ	3.900
Quadruple	X4	3.796
Quadruple	X3Y	14.956
Quadruple	X2Y2	22.542
Quadruple	X2YZ	44.856
Quadruple	WXYZ	89.700
Quintuple	X5	16.478
Quintuple	VWXYZ	1.973.400
Sextuple	X6	57.772
Sextuple	UVWXYZ	41.441.400

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