THE 2-GROUPS OF ODD STRONG SYMMETRIC GENUS.

Let G be a finite group. The strong symmetric genusσ0(G) is the minimum genus of any Riemann surface on which G acts preserving orientation. We show that a 2-group G has strong symmetric genus congruent to 3 (mod 4) if and only if G is in one of 14 families of groups. A consequence of this classification is that almost all positive integers that are the genus of a 2-group are congruent to 1 (mod 4). [ABSTRACT FROM AUTHOR]