Avoid IdGroup in IsSymmetricGroup

[fingolfin]

Based on experiments, just testing the order seemed to be fastest. Though of course it also depends on the representation used for the group.

With this many more packages pass test with gap --bare.

In my experiments the new code was never slower and sometimes faster than IdGroup. For example, in master (the three groups used here are the ones of order 720 which contains an A6 of index 2)

gap> G:=SmallGroup(720, 763);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
271
gap> G:=SmallGroup(720, 764);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
1212
gap> G:=SmallGroup(720, 765);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
994

With this PR:

gap> G:=SmallGroup(720, 763);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
273
gap> G:=SmallGroup(720, 764);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
943
gap> G:=SmallGroup(720, 765);; for i in [1..1000] do IsSymmetricGroup(Group(GeneratorsOfGroup(G))); od; time;
715

[ThomasBreuer]

Iterating over the group looks horrible. What about stopping at the first element of order 6 (then we are sure the group is S6) or of order 8 or 10 (then we are sure the group is not S6)?

[codecov]

Codecov Report

❌ Patch coverage is 88.88889% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 78.69%. Comparing base (fc1bbdf) to head (ea50863).
⚠️ Report is 5 commits behind head on master.

Files with missing lines	Patch %	Lines
lib/grpnames.gi	88.88%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #6383   +/-   ##
=======================================
  Coverage   78.69%   78.69%           
=======================================
  Files         684      684           
  Lines      292891   292897    +6     
  Branches     8686     8660   -26     
=======================================
+ Hits       230497   230505    +8     
+ Misses      60581    60577    -4     
- Partials     1813     1815    +2     

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[fingolfin]

@ThomasBreuer good idea, done now