Direct-Product Tables - Group Theory Applied to Chemistry - page 216

Appendix E
Direct-Product Tables

Extensive direct-product tables are provided by Herzberg [ 10 ]. Antisymmetrized
and symmetrized parts of direct squares are indicated by braces and brackets, re-
spectively.

D 3 A 1 A 2 E

A 1 A 1 A 2 E

A 2 A 2 A 1 E

E E E [ A 1 + E ]+{ A 2 }

D 4 A 1 A 2 B 1 B 2 E

A 1 A 1 A 2 B 1 B 2 E

A 2 A 2 A 1 B 2 B 1 E

B 1 B 1 B 2 A 1 A 2 E

B 2 B 2 B 1 A 2 A 1 E

E E E E E [ A 1 + B 1 + B 2 ]+{ A 2 }

D 5 A 1 A 2 E 1 E 2

A 1 A 1 A 2 E 1 E 2

A 2 A 2 A 1 E 1 E 2

E 1 E 1 E 1 [ A 1 + E 2 ]+{ A 2 } E 1 + E 2

E 2 E 2 E 2 E 1 + E 2 [ A 1 + E 1 ]+{ A 2 }

D 6 A 1 A 2 B 1 B 2 E 1 E 2

A 1 A 1 A 2 B 1 B 2 E 1 E 2

A 2 A 2 A 1 B 2 B 1 E 1 E 2

B 1 B 1 B 2 A 1 A 2 E 2 E 1

B 2 B 2 B 1 A 2 A 1 E 2 E 1

E 1 E 1 E 1 E 2 E 2 [ A 1 + E 2 ]+{ A 2 } B 1 + B 2 + E 1

E 2 E 2 E 2 E 1 E 1 B 1 + B 2 + E 1 [ A 1 + E 2 ]+{ A 2 }