Orthogonal C2

[TristanPfersdorff]

At this point it really should be obvious what this PR is :)

Checklist for the reviewer

General

• [ ] All functions have unit tests

Functions constructing generators of maximal subgroups

• [ ] The code which computes and then stores the sizes is correct. To do this one confers to the tables referenced by the code.
• [ ] The test suite checks whether all constructed generators are sensible. That is it tests the generators'
  • [ ] determinants (and if applicable also the spinor norms are correct), and
  • [ ] compatibility with the correct form,
  • [ ] DefaultFieldOfMatrixGroup returns the correct field.

Functions assembling the list of all maximal subgroups of a certain group

• [ ] The code agrees with the tables in section 8.2 of the book "The Maximal Subgroups of the Low-dimensional Finite Classical Groups".

The reviewer doesn't need to compare our results to magma's results. That's the job of the person implementing the code.

[codecov[bot]]

Codecov Report

Merging #111 (8953ddc) into main (fceaf27) will decrease coverage by 1.48%. The diff coverage is 71.62%.

@@            Coverage Diff             @@
##             main     #111      +/-   ##
==========================================
- Coverage   91.85%   90.37%   -1.49%     
==========================================
  Files          14       14              
  Lines        3673     3939     +266     
==========================================
+ Hits         3374     3560     +186     
- Misses        299      379      +80     

Impacted Files	Coverage Δ
gap/ClassicalMaximals.gi	70.68% <2.38%> (-7.20%)	:arrow_down:
gap/Utils.gi	94.00% <93.75%> (+0.44%)	:arrow_up:
gap/Forms.gi	88.11% <100.00%> (ø)
gap/ImprimitiveMatrixGroups.gi	99.13% <100.00%> (+0.86%)	:arrow_up:
gap/ReducibleMatrixGroups.gi	98.75% <100.00%> (-0.04%)	:arrow_down:

[TristanPfersdorff]

RECOG FUN! The group OmegaNonIsometricImprimitives(-1, 6, 9) causes some really fishy issues, here's the file to reproduce it.

Edit: [KL90] disallows this case because it assumes QuoInt(n, 2) >= 5, probably because orthogonal groups with n < 7 are evil (in case n = 6, Omega is isomorphic to some quotient of another classical group). However, tables 8.31 and 8.33 in [BHR13] do list these groups for n = 6, so maybe we should care? I'm not sure what to make of this, so I'll just leave this here and hope that someone else does.

[fingolfin]

Needs conflict resolution

[TristanPfersdorff]

Yeah the whole conflict resolution thing is a little annoying, it's really just trivial conflicts with a couple of overlapping lines in gap/ClassicalMaximals.gi. Anyway it's done now.