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This article describes the linear representation theory of the [[projective general linear group of degree two]] over a [[finite field]]. The order (size) of the field is <math>q</math>, and the characteristic prime is <math>p</math>. <math>q</math> is a power of <math>p</math>. The group is denoted <math>PGL(2,q)</math> or <math>PGL_2(q)</math>.

See also the linear representation theory for: [[linear representation theory of special linear group of degree two over a finite field|special linear group]], [[linear representation theory of projective special linear group of degree two over a finite field|projective special linear group]], and [[linear representation theory of general linear group of degree two over a finite field|general linear group]].

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