Direct sum of irreducible representation

A	B	E*
12	11	11

Properties of derivatives and isotopomers by single substitution, h(S₄)=4

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	C1	1	4	C	yes	yes	13C	321.1599	3.3636
2	S4	4	1	C	no	no	13C	321.1599	0.8409
3	C1	1	4	C	yes	yes	13C	321.1599	3.3636
4	C1	1	4	C	yes	yes	13C	321.1599	3.3636
5	C1	1	4	C	yes	yes	13C	321.1599	3.3636
6	C1	1	4	C	yes	yes	13C	321.1599	3.3636
7	C1	1	4	C	yes	yes	13C	321.1599	3.3636
8	C1	1	4	H	yes	yes	2H	321.1628	0.047185
9	C1	1	4	H	yes	yes	2H	321.1628	0.047185
10	C1	1	4	H	yes	yes	2H	321.1628	0.047185
11	C1	1	4	H	yes	yes	2H	321.1628	0.047185
12	C1	1	4	H	yes	yes	2H	321.1628	0.047185
Total Number of Atoms:			45	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group S₄
***Calculated as h( S₄)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	1	11
Double	X2	0	253
Double	XY	0	495
Triple	X3	0	3.553
Triple	X2Y	0	10.648
Triple	XYZ	0	21.285
Quadruple	X4	11	37.301
Quadruple	X3Y	0	148.995
Quadruple	X2Y2	0	223.608
Quadruple	X2YZ	0	446.985
Quadruple	WXYZ	0	893.970
Quintuple	X5	11	305.492
Quintuple	VWXYZ	0	36.652.770
Sextuple	X6	0	2.036.650
Sextuple	UVWXYZ	0	1.466.110.800

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