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Use ClassicalMaximals package to systematically test RecogniseClassical and later also RecogniseGroup #455

Description

@fingolfin

I envision a .tst file or multiple which basically is wrapped in one big #@if LoadPackage("classicalmaximals") so that it only runs if ClassicalMaximals is available.

Then one would call ClassicalMaximalsGeneric with various parameters; and the on each of the return groups, invoke RecogniseClassical and check that its return value is consistent with a maximal subgroup; so if e.g. we are looking at SO+ type then make sure that isOmegatContained is false

Excerpt from its docs:

ClassicalMaximalsGeneric( type, n, q[, classes] )

Return representatives of the conjugacy classes of maximal subgroups of the classical group with the given parameters. Here, type must be a string equal to one of "L", "U", "S", "O-", "O", or "O+".

The optional argument classes must be a subset of the range [1..9], corresponding to the Aschbacher classes C1 to C9. If given, it restricts which classes of maximal subgroups are computed.

Right now ClassicalMaximalsGeneric does not necessarily return the full result, but that shouldn't stop us from using what's already there.

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