The full label of a subgroup is of the form $\mathtt{N.i.m.a}$ or $\mathtt{N.i.m.a.j}$. In either case, $\mathtt{N.i}$ is the label of the ambient group, $\mathtt{m}$ is the index of the subgroup in the ambient group, $\mathtt{a}$ distinguishes subgroups up to automorphism and $\mathtt{j}$ distinguishes subgroups up to conjugacy. Both $\mathtt{a}$ and $\mathtt{j}$ take the form of a sequence of letters followed by an ordinal. The letters are a base 26 (a=0, z=25) encoding of the ordering up to Gassmann-equivalence, and the integer following distinguishes groups in the same Gassmann class. For some ambient groups, we only compute subgroups up to automorphism (in which case the first form is used, omitting the $\mathtt{j}$.

When the ambient group is clear from context, sometimes the short label $\mathtt{m.a}$ or $\mathtt{m.a.j}$ is used instead.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by David Roe on 2021-10-11 14:47:13

**Referred to by:**

- columns.gps_char.kernel
- columns.gps_groups_cc.centralizer
- columns.gps_subgroups.centralizer
- columns.gps_subgroups.contained_in
- columns.gps_subgroups.contains
- columns.gps_subgroups.core
- columns.gps_subgroups.label
- columns.gps_subgroups.normal_closure
- columns.gps_subgroups.normalizer
- group.label
- lmfdb/groups/abstract/main.py (line 921)

**History:**(expand/hide all)

- 2021-10-11 14:47:13 by David Roe (Reviewed)