Abstract :
In this paper, we consider the Artin exponent of the Groups of unitriangular matrices U(eta,F) from the principal character of its cyclic subgroups and denoted by A(U(eta,F)) WHERE eta=4 and F=ZP p is prime number, and we found that A(U(4,ZP)) =p8 Furthermore, we found that, the order of this group / U(4,ZP)/ =rho^4 its exponent exrho (U(4,ZP))=rho and found general forms of all conjugacy classes.
