  We give an $AB$-factorization of the supercharacter table of the group of
$n\times n$ unipotent upper triangular matrices over $\FF_q$, where $A$ is a
lower-triangular matrix with entries in $\ZZ[q]$ and $B$ is a unipotent
upper-triangular matrix with entries in $\ZZ[q^{-1}]$. To this end we introduce
a $q$ deformation of a new power-sum basis of the Hopf algebra of symmetric
functions in noncommutative variables. The factorization is obtain from the
transition matrices between the supercharacter basis, the $q$-power-sum basis
and the superclass basis. This is similar to the decomposition of the character
table of the symmetric group $S_n$ given by the transition matrices between
Schur functions, monomials and power-sums.
  We deduce some combinatorial results associated to this decomposition. In
particular we compute the determinant of the supercharacter table.
