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A characteristic factor is a factor in a particular factorization of the Totient Function 
such that the
product of characteristic factors gives the representation of a corresponding abstract Group as a Direct
Product. By computing the characteristic factors, any Abelian Group can be expressed as a
Direct Product of Cyclic Subgroups, for
example, Finite Group Z2Z4 or Finite Group Z2Z2Z2. There
is a simple algorithm for determining the characteristic factors of Modulo Multiplication Groups.
See also Cyclic Group, Direct Product (Group), Modulo Multiplication Group, Totient Function
References
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 94, 1993.