The orders of the classical groups are well known; see for example [108, p19, p118, p70, p141] for derivations of the orders of the general groups, and [66, Tables 2.1.C, 2.1.D] (reproduced here as Table 1.3) for a convenient summary of the indices of groups in Series 1.1 and 1.2.

Theorem 1.6.22 Let *q* = *p*^{e}, where *p* is a prime. The order of GL_{n}(*q*) is

The order of GL_{n}(*q*) is

When *n* is even, the order of Sp_{n}(*q*) is

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