Group Theory Tables

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Atkins, Child, & Phillips: Tables for Group Theory

Tables for Group Theory By P. W. ATKINS, M. S. CHILD, and C. S. G. PHILLIPS This provides the essential tables (character tables, direct products, descent in symmetry and subgroups) required for those using group theory, together with general formulae, examples, and other relevant information. Character Tables: 1 2 3 4 5 6 7 8 9

10 11 12

The Groups C1, Cs, Ci The Groups Cn (n = 2, 3, …, 8) The Groups Dn (n = 2, 3, 4, 5, 6) The Groups Cnv (n = 2, 3, 4, 5, 6) The Groups Cnh (n = 2, 3, 4, 5, 6) The Groups Dnh (n = 2, 3, 4, 5, 6) The Groups Dnd (n = 2, 3, 4, 5, 6) The Groups Sn (n = 4, 6, 8) The Cubic Groups: T, Td, Th O, Oh The Groups I, Ih The Groups C∞ v and D∞ h The Full Rotation Group (SU2 and R3)

3 4 6 7 8 10 12 14 15

17 18 19

Direct Products: 1 2 3 4 5 6 7 8 9 10 11

General Rules C2, C3, C6, D3, D6, C2v, C3v, C6v, C2h, C3h, C6h, D3h, D6h, D3d, S6 D2, D2h C4, D4, C4v, C4h, D4h, D2d, S4 C5, D5, C5v, C5h, D5h, D5d D4d, S8 T, O, Th, Oh, Td D6d I, Ih C∞v, D∞h The Full Rotation Group (SU2 and R3)

The extended rotation groups (double groups): character tables and direct product table Descent in symmetry and subgroups

20 20 20 20 21 21 21 22 22 22 23

24 26

Notes and Illustrations: General formulae Worked examples Examples of bases for some representations Illustrative examples of point groups: I Shapes II Molecules

29 31 35 37 39

OXFORD © Oxford University Press, 2006. All rights reserved.

Higher Education 1


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