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As J.D.Dixon noted in his great books, there are just 5 proper primitive groups of degree 8, $P(8)=5$. I wanted to examine it with GAP, so wrote the following small program:

 > G:=[];; > for k in [1..7] do G[k]:=PrimitiveGroup( 8,k ); od; > G[1]; G[2]; G[3]; G[4];  G[5];  G[6];  G[7];  

Clearly, since $S_8$ and $A_8$ are not proper, so it works as we want. My question is how to "List all groups", for example as I called them above without writing the third line of the program? I examined some List commend line in the GAP, and could't list the groups not in the form I did above ( G[1]; G[2]; G[3]; G[4]; G[5]; G[6]; G[7]; ). Thanks for any help.

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    I'm not sure I understand your question... do you ask for a GAP command to display a list? If that is the case: As far as I know, there is no possibility to display arbitrary lists in a readable format. In your case, however, the following should work fine: `n := 8;; List( [1..NrPrimitiveGroups(n)], i -> PrimitiveGroup(n,i) );`2012-05-11
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    Also, I just noticed that `AllPrimitiveGroups(NrMovedPoints,[8])` yields identical output. Moreover, to use GAP libraries efficiently, you may want to learn about [selection functions](http://www.gap-system.org/Manuals/doc/htm/ref/CHAP048.htm#SECT005).2012-05-11
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    @m_l: Thanks for the help. You kindly gave me what I should to know. Thanks again.2012-05-11
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    @AlexanderKonovalov: Thanks for the edit. May I ask you a question about GAP?2013-04-22
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    @BabakS.: yes, sure - just here or by email, please.2013-04-22
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    @AlexanderKonovalov: How can I command GAP to write a*b as ab while I am working on a free group. In fact this makes my output so easy to study. Thanks.2013-04-22
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    What about `Print(ReplacedString(String(a*b),"*",""),"\n")` ? Note, however, that `a*b` **IS** the output which may be correctly parsed back by GAP, while `ab` is not - for example, what if `ab` is already a name of another global variable?2013-04-22
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    @m_l: Thanks for sharing the link about selection functions, but it points to the old GAP 4.4.12 manual and does not work any more. Apparently the new link should point [here](http://www.gap-system.org/Manuals/doc/ref/chap50.html#X81B00B667D2BD022). This is why it's more reliable to advice to type in GAP e.g. `?SmallGroup` to invoke the documentation from the GAP command line (`SetHelpViewer` may be configured to open the HTML version of the manual in a browser instead of showing the text version directly in the GAP session).2013-04-23
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    @AlexanderKonovalov: Are you online?2013-04-24
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    @AlexanderKonovalov: What about using GAP for this one? http://math.stackexchange.com/q/370476/8581. Thanks for your time. You are very Welcome to me, friend.2013-04-24
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    @BabakS.: yes, GAP will easily handle computations described at http://math.stackexchange.com/questions/370476/let-g-gl2-mathbbz-5-mathbbz-the-general-linear-group-of-2-times-2. It is also easy to guess the names of functions to use.2013-04-24
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    @AlexanderKonovalov: Thanks friend for the edit.2013-04-29

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Thanks to m_l, this has been answered in the comments. I'm posting a formal answer in order to clean up unanswered questions with the gap tag in view of "http://meta.math.stackexchange.com/questions/1559/dealing-with-answers-in-comments?" discussion on Meta.

I will try to cover a bit wider topic for a reader who will discover this page in a search for an answer on a similar question. GAP contains several Data Libraries listed on this page. In GAP 4.6, Group Libraries are covered in Chapter 50 of the Reference Manual (chapter numbering may change in future versions), and this includes the Small Groups Library, Primitive and Transtive Permutation Groups libraries, and more. From the GAP command line this chapter may be viewed by entering ?Group Libraries. Look there for functions like AllLibraryGroups and OneLibraryGroup, where "Library" denotes the appropriate library.