Geodesic
Quasi-permutation representations ofSL(2,q) and PSL(2,q)
Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 393-408

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By a quasi-permutation matrix we meana square matrix over the complex field [Copf] with non-negative integraltrace. Thus every permutation matrix over [Copf] is a quasi-permutationmatrix. For a given finite group G, let p(G) denote the minimal degreeof a faithful permutation representation of G (or a faithfulrepresentation of G by permutation matrices), let q(G) denote theminimal degree of a faithful representation of G by quasi-permutationmatrices over the rational field Q, and let c(G) be the minimaldegree of a faithful representation of G by complex quasi-permutationmatrices. See [1]. 
Behravesh, Houshang. Quasi-permutation representations ofSL(2,q) and PSL(2,q). Glasgow mathematical journal, Tome 41 (1999) no. 3, pp. 393-408. doi: 10.1017/S0017089599000567
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     author = {Behravesh, Houshang},
     title = {Quasi-permutation representations {ofSL(2,q)} and {PSL(2,q)}},
     journal = {Glasgow mathematical journal},
     pages = {393--408},
     year = {1999},
     volume = {41},
     number = {3},
     doi = {10.1017/S0017089599000567},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089599000567/}
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