A list of all non-abelian groups of orders upto 30 is given in Table 1 on page 134 of ‘Generators and Relations for Discrete Groups’ — Coxeter and Moser (Springer, 1972). Of course the abelian groups are easily dealt with using the structure theory of Chapter 5. Elementary methods of obtaining low-order groups along similar lines to those used in Chapter 7 are given in sections 126 and 127 of the classic ‘Theory of Groups of Finite Order’ by Burnside, 1911 (republished by Dover, 1955). In sections 112 to 118 of the same book elementary methods are given for determining all groups of orders p2, p3, and p4 for a prime p.
KeywordsAbelian Group Normal Subgroup Finite Group Simple Group Factor Group
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