On $\pi$-solvable irreducible linear groups with a Hall $TI$-subgroup of odd order. II

$\pi$-solvable finite irreducible complex linear groups whose Hall $\pi$-subgroups are $TI$-subgroups and the degree of the group is small with respect to the order of such subgroup, are investigated. This is the second one in the series of the author's papers aimed on determining the possible values of the degree n if a Hall $\pi$-subgroup $H$ is not normal, $|H|$ is odd, and $n<2|H|$. The proof of a theorem that yields the complete list of these values is continued, it was started in the first paper of the series (Trudy Instituta Matematiki, 2008, v. 16, № 2, p. 118–130). A number of properties of a minimal counterexample to the theorem is established.