Direct sum of irreducible representation

A	B
8	7

Properties of derivatives and isotopomers by single substitution, h(C₂)=2

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C2	2	1	C	yes	yes	13C	71.0816	1.0508
2	C1	1	2	C	yes	yes	13C	71.0816	2.1015
3	C1	1	2	C	yes	yes	13C	71.0816	2.1015
4	C1	1	2	H	yes	yes	2H	71.0845	0.029480
5	C1	1	2	H	yes	yes	2H	71.0845	0.029480
6	C1	1	2	H	yes	yes	2H	71.0845	0.029480
7	C1	1	2	H	yes	yes	2H	71.0845	0.029480
8	C1	1	2	H	yes	yes	2H	71.0845	0.029480
Total Number of Atoms:			15	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C₂
***Calculated as h( C₂)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Chiral Isomers
Single	X	8
Double	X2	56
Double	XY	105
Triple	X3	231
Triple	X2Y	686
Triple	XYZ	1.365
Quadruple	X4	693
Quadruple	X3Y	2.730
Quadruple	X2Y2	4.116
Quadruple	X2YZ	8.190
Quadruple	WXYZ	16.380
Quintuple	X5	1.512
Quintuple	VWXYZ	180.180
Sextuple	X6	2.520
Sextuple	UVWXYZ	1.801.800

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