Direct sum of irreducible representation

A1	A2	E
2	2	2

Properties of derivatives and isotopomers by single substitution, h(D₃)=6

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C3	3	2	C	yes	yes	13C	31.0503	2.1738
2	C1	1	6	H	yes	yes	2H	31.0532	0.091481
Total Number of Atoms:			8	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D₃
***Calculated as h( D₃)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Chiral Isomers
Single	X	2
Double	X2	7
Double	XY	10
Triple	X3	10
Triple	X2Y	28
Triple	XYZ	56
Quadruple	X4	16
Quadruple	X3Y	48
Quadruple	X2Y2	76
Quadruple	X2YZ	140
Quadruple	WXYZ	280
Quintuple	X5	10
Quintuple	VWXYZ	1.120
Sextuple	X6	7
Sextuple	UVWXYZ	3.360

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