Direct sum of irreducible representation

A1	A2	B1	B2	E1	E2	E3	E4	E5	E6	E7
3	0	0	2	2	2	2	2	2	2	2

Properties of derivatives and isotopomers by single substitution, h(D_8d)=32

Atom Set*	Site Symmetry**	h(Site Symmetry)	Identical Atoms***	Element	Chrial	Polar	Isotopomer
							Isotope	Mass	Abundance****
1	D8d	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_8d
***Calculated as h( D_8d)/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	12	15
Double	XY	10	28
Triple	X3	40	155
Triple	X2Y	50	491
Triple	XYZ	30	1.008
Quadruple	X4	118	1.254
Quadruple	X3Y	150	5.040
Quadruple	X2Y2	246	7.617
Quadruple	X2YZ	170	15.260
Quadruple	WXYZ	60	30.660
Quintuple	X5	298	7.302
Quintuple	VWXYZ	60	889.980
Sextuple	X6	672	34.433
Sextuple	UVWXYZ	0	24.920.280

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