Direct sum of irreducible representation

A1	A2	E
6	2	6

Properties of derivatives and isotopomers by single substitution, h(C_3v)=6

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C3v	6	1	C	no	yes	13C	131.0816	0.9942
2	C3v	6	1	H	no	yes	2H	131.0845	0.013947
3	Cs	2	3	C	no	yes	13C	131.0816	2.9827
4	C1	1	6	C	yes	yes	13C	131.0816	5.9653
5	Cs	2	3	H	no	yes	2H	131.0845	0.041841
6	C1	1	6	H	yes	yes	2H	131.0845	0.083681
Total Number of Atoms:			20	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C_3v
***Calculated as h( C_3v)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	4	2
Double	X2	14	25
Double	XY	12	58
Triple	X3	36	174
Triple	X2Y	44	548
Triple	XYZ	24	1.128
Quadruple	X4	77	773
Quadruple	X3Y	100	3.184
Quadruple	X2Y2	158	4.766
Quadruple	X2YZ	108	9.636
Quadruple	WXYZ	24	19.368
Quintuple	X5	144	2.514
Quintuple	VWXYZ	0	310.080
Sextuple	X6	232	6.349
Sextuple	UVWXYZ	0	4.651.200

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