The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 6 (Q1742913)

Non-orientable unbordered Klein surfaces are the non-orientable versions of compact Riemann surfaces. The groups which occur as the full automorphism groups of non-orientable Klein surfaces are known up to genus 5, and in the present paper the author gives such a classification for genus 6 (in a sequel to the present paper, [\textit{A. Bacelo}, Rev. Mat. Complut. 31, No. 1, 247--261 (2018; Zbl 1383.57024)], he obtained a classification also for genus 7). A basic concept here is the \textit{symmetric crosscap number} of a finite group which is defined as the minimum genus of an unbordered non-orientable Klein surface on which the group acts, and basic for the present paper are the known groups of crosscap number up to 6 (there are 11 groups of symmetric crosscap number 6; by computer-algebra methods, Conder classified the groups of symmetric crosscap number up to 65, publishing the results on his homepage).