The Class Structure and Irreducible Representations of Semi-direct Product Groups
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In Chapter 3, we have shown how semi-direct product structure may arise in NRM groups. Apart from its formal significance, the presence of semi-direct product structure is of great practical utililty. Thus, as discussed in detail by Altmann  (cf. also [139, 147, 151]), both the class structure and the irreducible representations of a semi-direct product group can be calculated using systematic procedures that exploit the (known) properties of the smaller component groups to the maximum extent. Such techniques represent an optimal use of purely group-theoretical information in the NRM problem and, as shown by the applications described in Chapter 4, can provide an effective approach to the classification of large NRM symmetry groups.
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