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 = pe, where p is a prime. The order of GLn(q) is
The order of GLn(q) is
When n is even, the order of Spn(q) is