SUtree: A Mathematica-based software package and database for the investigation of discrete subgroups of SU(3). It accompanies the paper 1110.4891 [hep-ph]. In case you use SUtree (or parts of it) to produce a scientific publication or a talk, then please give proper academic credit to us by citing our paper (and not this homepage).

Download: You can download SUtree here. Put the file into the directory you like, extract it, and then open the example file "ExampleNotebookSUtree.mb" with Mathematica to explore SUtree (note that we have used Mathematica 7 and do not guarantee the package to work perfectly with other versions of Mathematica).


  • Numerical lists of sixty-one SU(3) subgroups with 3D irreps (crystallographic groups and groups with order<512)
  • Molien & generating functions
  • Primary and secondary invariant polynomials
  • Syzygies for (nearly) all secondary invariants
  • Translations between invariants and VEVs in SO(3) and SU(3)-bases
  • Character tables
  • Kronecker products
  • Branching rules

SUtree is maintained by Alexander Merle and Roman Zwicky. It is distributed under the terms of the GNU General Public Licence. Updates: We will continuously update SUtree. See the Logbook below for recent changes. Bugs: The authors take no responsibility for any wrong results obtained when using SUtree. The user him/herself must check the reliability of any results obtained! Please report any errors that you discover in the program and/or database to A.Merle (AT) instead of blaming us, we will be happy to receive your feedback! Your input is welcome! Please contact us if you find one of the remaining 5 syzygies, or if you can trade a numerical syzygy for an analytic one. The same applies if you manage to determine the remaining generating functions.


  • February 24, 2012: Paper published as JHEP 1202: 128, 2012.
  • January 23, 2012: Paper accepted by JHEP!
  • November 30, 2011: Version 1.1 online. This version should work with Mathematica 8 as well.
  • October 20, 2011: SUtree is now online!