String C-groups from groups of order 2^m and exponent at least 2^(m - 3)

Abstract: This work provides a classification of string C-groups of order 2m and exponent at least 2^m - 3. Prior to the classification, we complete the list of groups of exponent 2^m - 3 and rank at least 3. The main result states that, aside from the cyclic and dihedral groups, only two groups of exponent at least 2^m - 3 are connected string C-groups. Both have rank 3 and are quotients of the string Coxeter group W = [4, 2^m - 3].