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IsConjugate does not try cheap invariants that may yield a false result #6266

@ThomasBreuer

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@ThomasBreuer

(The problem has been described in oscar-system/Oscar.jl#5838.)

gap> g:= AtlasGroup( "HN" );
<permutation group of size 273030912000000 with 2 generators>
gap> h:= AtlasSubgroup( g, 1 );
<permutation group of size 239500800 with 2 generators>
gap> k:= AtlasSubgroup( g, 2 );
<permutation group of size 177408000 with 2 generators>
gap> IsConjugate( g, h, k );

The last question takes a long time. It could be answered immediately, using that the orders of the two subgroups are known and different, but GAP does not use such shortcuts.

I think the natural place where necessary conditions could/should be checked is RepresentativeAction.

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