Talk:List of small groups

message: The reference at the end of the page is a dead link. Would anybody fix it?--131.215.134.104 21:09, 2 August 2007 (UTC)
thread_title: Dead link

message: What is Dn when n is odd?? I mean, given you're using the 2n-convention. What is D3, for instance? Is it just the cyclic group? What else could it be? It must have exactly 3 elements, if D3 × C2 is really isomorphic to D6. But then it must be C3. The ordinary definition doesn't make sense. We can't let one element have order "1.5" and the other order 2. Revolver 02:25, 10 Sep 2004 (UTC)
replies: text: It looks as if these were added by someone using the other convention, where Dn is the dihedral group of order 2n. The isomorphisms given (e.g., D6 = D3 × C2) then make sense, though they are for groups of twice the stated size. But as it stands, they make no sense at all, so I'm removing them. --Zundark 10:32, 31 Oct 2004 (UTC)
thread_title: D<sub>''n''</sub>

message: Considering the confusion it would be better to use, at least in Wikipedia, a uniform notation. Is  Dn for order 2n more common?--Patrick 12:27, 5 August 2005 (UTC)
thread_title: Notation

message: Isn't there an edge missing from the "topmost" element to the neutral element? (June 19, 2006)
:There would be an edge there if we were drawing all the cycles, but we are not. From Cycle graph (algebra): Cycles which contain a non-prime number of elements will implicitly have cycles which are not connected in the graph. For the group Dih4 above, we might want to draw a line between a2 and e  since (a2)2=e  but since a2 is part of a larger cycle, this is not done. —Keenan Pepper 04:27, 20 June 2006 (UTC)
thread_title:  Error in cycle graph of Dih_4xZ_2? 

message: The table for groups of order 16 has a format error. The last line is misaligned. Albmont 11:43, 3 May 2007 (UTC)
replies: text: Fixed. Someone had messed up the template that this page uses. --Zundark 11:55, 3 May 2007 (UTC)
thread_title:  Format error in the table for order 16 

message: Shouldn't there be 3 pairs of 4-cycles which share the square element? i.e. take the diagram for Z4 × Z2, cut off its two "legs", make three copies, and glue them together at the identity. --192.75.48.150 21:00, 14 May 2007 (UTC)
thread_title:  Cycle diagram for {{SubSup|Z|4|2}}  

message: Why no cycle graphs for Z3 = A3 and S3 = Dih3? I'd add them if I knew how... LaQuilla (talk) 13:10, 8 November 2008 (UTC)
thread_title:  Missing cycle graphs 

message: What is meant by "The order 16 modular group"? The page linked doesn't describe a finite group at all. --Octavo (talk) 12:15, 11 January 2009 (UTC)
replies: text: I think it's meant in the sense of M-group, in which case the link should be changed. The group in question seems to be the one with exactly two non-normal subgroups, and in this group all subgroups are permutable, so the subgroup lattice is modular. --Zundark (talk) 16:13, 11 January 2009 (UTC)
thread_title:  Modular group 

message: This article says, under "Small group library": "except for order 1024 (423164062 groups; the ones of order 1024 had to be skipped, there are alone 49487365422 nonisomorphic 2-groups of order 1024.)," which seems inconsistent on its face as the first number is smaller than the second.  Our article on p-group says "For instance, of the 49 910 529 484 different groups of order at most 2000, 49 487 365 422, or just over 99%, are 2-groups of order 1024 (Besche, Eick & O'Brien 2002)." Am I missing something here?--agr (talk) 15:59, 5 August 2010 (UTC)
replies: text: 423,164,062 is the number of groups of the given type (order at most 2000 and not 1024) in the library. Together with the 49,487,365,422 groups of order 1024, this makes 49,910,529,484 groups of order at most 2000, as the other article says. --Zundark (talk) 16:16, 5 August 2010 (UTC)
replies: text: Thanks for the clarification, but I do find the language used unnecessarily confusing.  It might be clearer to say: "those of order at most 2000, except for order 1024 (423 164 062 groups, the excluded groups of order 1024 comprise an additional 49 487 365 422 nonisomorphic 2-groups.)"--agr (talk) 17:22, 5 August 2010 (UTC)
thread_title:  How many groups of order 1024? 

message: Under groups of order 16, there is a group listed as "the group generated by the Pauli matrices". However on our article Pauli group, this group is stated to be isomorphic to the generalised quaternion group of order 16, which is listed separately on the page.
This is clearly contradictory - the two groups are shown to have different cycle graphs. Further, this would give just eight isomorphism classes of non-Abelian groups of order 16, meaning we're missing one. (This would possibly be the group with GAP ID 3 or 13). Kidburla (talk) 16:15, 8 December 2010 (UTC)
thread_title:  Pauli group - contradiction? 

message: In the citation for Marshal Hall's book on groups of order dividing 64, the link goes to http://en.wikipedia.org/wiki/Marshall_Hall which is a disambiguation page.
I believe the correct link should be to http://en.wikipedia.org/wiki/Marshall_Hall_(mathematician) but I can't figure out how to make the citation point there.
Somebody who is expert at Wiki please fix it.
198.144.192.45 (talk) 08:20, 27 November 2011 (UTC)
replies: text: I've fixed it. --Zundark (talk) 09:20, 27 November 2011 (UTC)
replies: text: Ah, thanks. 198.144.192.45 (talk) 19:35, 6 January 2013 (UTC)
thread_title:  Ambiguous link to Marshal Hall 

message: Is this simply because we've managed to find sources for all the groups of orders up to 16, but not for 18?  Or is there some other reason?
Obviously we can trivially extend it to 17.  By the fundamental theorem of finite abelian groups we can extend the abelian section as far as we like.  Of course, we would need to find a source for the non-abelian groups of orders 18 and 20 if we're going to extend it this far.  (It would be nice if we could run a program to generate all the possible group tables for these orders and publish the results here.  But that would be OR.)
But 21 is interesting as it's the smallest odd order of a non-abelian group.  So it would be nice if we can extend it at least as far as this. — Smjg (talk) 17:49, 1 January 2014 (UTC)
replies: text: I'd like to extend this list to order 24, not so many more, and useful since that covers tetrahedral group symmetry, and a few more crystalographic dihedral groups. Tom Ruen (talk) 19:41, 16 December 2014 (UTC)
thread_title:  Why stop at 16? 

message: The second column in the table has been introduced with notation that seems obscure (Goi), and explanation in the article seems appropriate. —Quondum 22:15, 16 December 2014 (UTC)
replies: text: I added a sentence to the Glossary. The naming is used in this paper  with cycle graphics up to order 36. I've seen other indexing systems used, so if I (or someone) find other sources with different indexing, we can can cross-reference them also. Tom Ruen (talk) 22:40, 16 December 2014 (UTC)
replies: text:  I'm not convinced that indexing to an individual reference's (or in this case actually the small groups library's) indexing scheme is warranted in this table, since this article is not about the small groups library; it only uses it as a reference (though I'm not specifically opposing it).  Also, I notice the two indices have been swapped on the non-abelian groups of order 18 and higher. —Quondum 23:27, 16 December 2014 (UTC)

text: Agreed it is excessive and I don't know what might be warrented in the long term, but given my lack of familiarity, and the ease of errors, for the moment, I find it necessary to help me, at least until all the table entries are filled, and like the cycle graphs completed. Tom Ruen (talk) 00:47, 17 December 2014 (UTC)
replies: text:  Makes sense.  Happy editing.  —Quondum 06:54, 17 December 2014 (UTC)
thread_title:  Notation needs explanation 

message: Hello fellow Wikipedians,
I have just modified 3 external links on List of small groups. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added  tag to http://groupprops.subwiki.org/wiki/Direct_product_of_Z3_and_Z3
*Added  tag to http://groupprops.subwiki.org/wiki/Direct_product_of_Z4_and_Z2_and_Z2
*Added  tag to http://groupprops.subwiki.org/wiki/Direct_product_of_Z12_and_Z2
*Added archive https://web.archive.org/web/20060923012610/http://math.sun.ac.za/~wild/Marcel%20Wild%20-%20Home%20Page_files/Groups16AMM.pdf to http://math.sun.ac.za/~wild/Marcel%20Wild%20-%20Home%20Page_files/Groups16AMM.pdf
*Added archive https://web.archive.org/web/20120305020857/http://www.icm.tu-bs.de/ag_algebra/software/small/ to http://www.icm.tu-bs.de/ag_algebra/software/small/
*Added archive https://web.archive.org/web/20120305020857/http://www.icm.tu-bs.de/ag_algebra/software/small/ to http://www.icm.tu-bs.de/ag_algebra/software/small/
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 12:09, 2 January 2018 (UTC)
thread_title:  External links modified 

message: The first number given is 0. It is not clear if this is for n=1 or n=0.
:This is in the paragraph called "Counts".  — Preceding unsigned comment added by 2A00:23C0:7C80:8401:E46B:CCC4:EA04:5A30 (talk) 15:06, 18 October 2018 (UTC)
replies: text: Fixed. —David Eppstein (talk) 16:20, 18 October 2018 (UTC)
thread_title:  Low order 

message: What does ⋊ mean? 31.48.245.78 (talk) 13:19, 19 February 2020 (UTC)
replies: text: Semidirect product. Double sharp (talk) 18:01, 19 February 2020 (UTC)
thread_title:  Symbol 

message: o Particular groups in the Group Properties Wiki
o Groups of given order
have no links, external or otherwise. 31.48.245.78 (talk) 13:36, 19 February 2020 (UTC)
thread_title:  External links 

message: This section says that the smallest order for which the Small Groups Library does not have any information is 2048. That matches neither my experience (OR) nor the GAP documentationhttps://www.gap-system.org/Manuals/pkg/SmallGrp-1.4.1/doc/chap1.html#X7C16EA1580AC7586.
Both OR and the documentation say that order 1024 is not included.
What is the reason for the discrepancy? Is there something that I'm missing here?
Mstemper (talk) 21:04, 26 June 2020 (UTC)
thread_title:  Small Groups Library 

message: What are Goi in the tables, and would someone add a paragraph in the article to explain? Thanks. --Rockyunited (talk) 20:45, 27 December 2020 (UTC)
thread_title: What are G<sub>''o''</sub><sup>''i''</sup> in the tables?

message: This page (2021) states that there are 49487367289 groups of order 1024. Should the number 49487365422 in the section "Small Groups Library" be corrected? See also this Math Stack Exchange question. 129.104.240.174 (talk) 00:26, 28 August 2023 (UTC)
replies: text: Yes, per comment at Talk:1024_(number)#Number_of_groups_of_order_1024. Barnards.tar.gz (talk) 15:20, 28 August 2023 (UTC)
thread_title:  Number of groups of order 1024 

message: For the semidirect product  \mathbb{Z}_4 \rtimes \mathbb{Z}_4  table lists 3 subgroups  \mathbb{Z}^{2}_2 \times \mathbb{Z}_2  , which seems to be wrong, and instead there should be 3 subgroups  \mathbb{Z}_4 \times \mathbb{Z}_2  , as for example in this table. Can someone check that? Serpens 2 (talk) 16:27, 29 January 2024 (UTC)
replies: text: I also see the similar issue with  Q_8 \times \mathbb{Z}_2  Serpens 2 (talk) 17:42, 29 January 2024 (UTC)
replies: text: and with Iwasawa modular group Serpens 2 (talk) 10:03, 30 January 2024 (UTC)
thread_title:  Possible error in semidirect Z4 x Z4