A347371 Number of isomorphism types of automorphism groups of Riemann surfaces of genus n.

19, 37, 44, 64, 59, 86, 65, 154, 119, 118, 98, 206, 99, 176, 139, 346, 117, 290, 136, 368, 187, 193, 171, 621, 184, 276, 306, 483, 187, 404, 189, 1014, 255, 332, 253, 880, 205, 381, 341, 1163, 244, 549, 244, 788, 436, 401, 273

Offset: 2

Author

Eric M. Schmidt, Aug 29 2021

Keywords

• nonn
• hard

Comments

This includes subgroups of the full automorphism group.

Breuer's book erroneously gives a(33) = 1013. (See errata.)

Examples

			The 19 automorphism groups for Riemann surfaces of genus 2 are the trivial group, C2, C3, C4, C2 X C2, C5, C6, S3, Q8, C8, D8, C10, C6 . C2, C2 X C6, D12, QD16, SL_2(3), (C2 X C6) . C2, and GL_2(3). [Breuer, Table 9 on p. 77]
		

References

• Thomas Breuer, Characters and automorphism groups of compact Riemann surfaces, Cambridge University Press, 2000, p. 91.

Links

• Thomas Breuer, Errata et Addenda for Characters and Automorphism Groups of Compact Riemann Surfaces.
• Jen Paulhus, Branching data for curves up to genus 48.

Crossrefs

Cf. A179982, A346293, A347368, A347369, A347370, A347372, A347373.