Direct sum of irreducible representation

A1g	A2g	B1g	B2g	E1g	E2g	E3g	A1u	A2u	B1u	B2u	E1u	E2u	E3u
3	0	2	0	2	2	2	0	2	0	2	2	2	2

Properties of derivatives and isotopomers by single substitution, h(D_8h)=32

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	D8h	32	1	U	no	no	235U 234U	443.1691 442.1662	0.6017 0.004596
2	Cs	2	16	C	no	yes	13C	447.1793	14.7642
3	Cs	2	16	H	no	yes	2H	447.1823	0.2071
Total Number of Atoms:			33	✅ Correct Number of Atoms found

*Atom Orbit
**Subgroup of point group D_8h
***Calculated as h( D_8h)/h(Site Symmetry)
****Natural Abundance of single substituted Isotopomer in %

Numbers of isomers by substitution

Replacement	Pattern	Achiral Isomers	Chiral Isomer Pairs
Single	X	3	0
Double	X2	18	12
Double	XY	18	24
Triple	X3	54	148
Triple	X2Y	96	468
Triple	XYZ	126	960
Quadruple	X4	202	1.212
Quadruple	X3Y	342	4.944
Quadruple	X2Y2	528	7.476
Quadruple	X2YZ	594	15.048
Quadruple	WXYZ	756	30.312
Quintuple	X5	478	7.212
Quintuple	VWXYZ	3.780	888.120
Sextuple	X6	1.258	34.140
Sextuple	UVWXYZ	15.120	24.912.720

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