Direct sum of irreducible representation

A	E*
13	11

Properties of derivatives and isotopomers by single substitution, h(C₃)=3

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C3	3	1	C	yes	yes	13C	245.1286	0.8992
2	C3	3	1	H	yes	yes	2H	245.1315	0.012614
3	C1	1	3	C	yes	yes	13C	245.1286	2.6975
4	C1	1	3	C	yes	yes	13C	245.1286	2.6975
5	C1	1	3	C	yes	yes	13C	245.1286	2.6975
6	C1	1	3	C	yes	yes	13C	245.1286	2.6975
7	C1	1	3	C	yes	yes	13C	245.1286	2.6975
8	C1	1	3	C	yes	yes	13C	245.1286	2.6975
9	C1	1	3	H	yes	yes	2H	245.1315	0.037841
10	C1	1	3	H	yes	yes	2H	245.1315	0.037841
11	C1	1	3	H	yes	yes	2H	245.1315	0.037841
12	C1	1	3	H	yes	yes	2H	245.1315	0.037841
13	C1	1	3	H	yes	yes	2H	245.1315	0.037841
Total Number of Atoms:			35	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group C₃
***Calculated as h( C₃)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Chiral Isomers
Single	X	13
Double	X2	199
Double	XY	398
Triple	X3	2.189
Triple	X2Y	6.545
Triple	XYZ	13.090
Quadruple	X4	17.468
Quadruple	X3Y	69.828
Quadruple	X2Y2	104.720
Quadruple	X2YZ	209.440
Quadruple	WXYZ	418.880
Quintuple	X5	108.218
Quintuple	VWXYZ	12.985.280
Sextuple	X6	541.090
Sextuple	UVWXYZ	389.558.400

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