  We study charged black hole solutions in Einstein-Gauss-Bonnet theory with
the dilaton field which is the low-energy effective theory of the heterotic
string. The spacetime is D-dimensional and assumed to be static and spherically
symmetric with the $(D-2)$-dimensional constant curvature space and
asymptotically flat. The system of the basic equations is complex and the
solutions are obtained numerically. We identify the allowed parameter region
where the black hole solutions exist, and show configurations of the field
functions in D=4 -- 6 and 10. We also show the relations of the physical
quantities of the black holes such as the horizon radius, the mass, the
temperature, and so on, and find several results. The forms of the allowed
parameter regions are different depending on the dimension. There is no extreme
black hole solution with T=0 that can be obtained by taking the limit of the
non-extreme solutions within the parameter range we chose. Entropy of the black
holes in the dilatonic theory is always larger than that in the non-dilatonic
theory. Our analysis includes the higher order term of the dilaton field which
is not in our previous works. Its effect remarkably appears in five dimensions
and is given in the appendix. By our analysis it is found that the properties
of the black hole solutions strongly depend on the dimension, charge, existence
of the dilaton field. Hence both the detailed analyses of the individual
systems and the investigations from the systematic point of view are important.
