Center for Theoretical Physics and Mathematics, AEOI, Tehran, Iran Department of Mathematics, University of Tehran, Teheran, IranInstitute for Advanced Studies in Basic Sciences, Gava Zang, Zanjan, Iran Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran

**Abstract:** In this paper we classify some of the homogeneous integral table algebras of degree 5 containing a faithful element of width 3 such that in a given basis of the algebra the basis elements are standard. This work is towards classifing homogeneous integral table algebras of degree 5.

**Classification (MSC2000):** 20C05, 20C99, 16P10

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