Orthogonal group over finite field

rsg

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Let O(n,F_q) be the orthogonal group over finite field F_q. The question is how to calculate the order of the group.
The answer is given in http://en.wikipedia.org/wiki/Orthogonal_group#Over_finite_fields". This seems to be a standard result, but I could not find a proof for this in the basic representation theory books that I have. Neither could I solve it myself from the (direct sum) construction they have given.
Can someone please help me? It is enough if you give some references (books/papers) where it is solved.
 
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