What is a non-alternating simple group with big order, but relatively few conjugacy classes? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Surprising but simple group theory result on conjugacy classesConjugacy classes of non-Abelian group of order $p^3$Character formula for $S_n$ and $GL(V)$Estimates on conjugacy classes of a finite group.On Conjugacy Classes of Alternating Group $A_n$Can a group have a subset that is stable under all automorphisms, but not under inverse?Degrees of Irreducible Characters of $GL(n,q)$Conjugacy classes splitting in alternating groupFinding square of an element from a character tableSize of Conjugacy Classes group of order 168

Is it ethical to give a final exam after the professor has quit before teaching the remaining chapters of the course?

Should I use a zero-interest credit card for a large one-time purchase?

Should I discuss the type of campaign with my players?

What causes the vertical darker bands in my photo?

Generate an RGB colour grid

In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?

Why am I getting the error "non-boolean type specified in a context where a condition is expected" for this request?

How to bypass password on Windows XP account?

3 doors, three guards, one stone

ListPlot join points by nearest neighbor rather than order

Dating a Former Employee

Check which numbers satisfy the condition [A*B*C = A! + B! + C!]

Short Story with Cinderella as a Voo-doo Witch

What LEGO pieces have "real-world" functionality?

What does this icon in iOS Stardew Valley mean?

Why didn't this character "real die" when they blew their stack out in Altered Carbon?

Using et al. for a last / senior author rather than for a first author

Use BFD on a Virtual-Template Interface

Is there a program I can run on the C64 to speed up booting of a game?

Book where humans were engineered with genes from animal species to survive hostile planets

Why was the term "discrete" used in discrete logarithm?

How to deal with a team lead who never gives me credit?

Why is my conclusion inconsistent with the van't Hoff equation?

What is the role of the transistor and diode in a soft start circuit?



What is a non-alternating simple group with big order, but relatively few conjugacy classes?



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Surprising but simple group theory result on conjugacy classesConjugacy classes of non-Abelian group of order $p^3$Character formula for $S_n$ and $GL(V)$Estimates on conjugacy classes of a finite group.On Conjugacy Classes of Alternating Group $A_n$Can a group have a subset that is stable under all automorphisms, but not under inverse?Degrees of Irreducible Characters of $GL(n,q)$Conjugacy classes splitting in alternating groupFinding square of an element from a character tableSize of Conjugacy Classes group of order 168










3












$begingroup$


I'm not sure if this question is legal.


I'm writing my BsC thesis on character theoretical calculations and I have already calculated a lot of character tables (a few alternating, symmetric, $operatornameSL(2,3)$, etc..), but I still have some space, so I thought I could choose a group, with not too many conjugacy classes (around $7$ still fit in nicely), that is preferably not monomial.



What do you suggest?



Thanks in advance!






group-theory representation-theory examples-counterexamples characters







share|cite|improve this question











$endgroup$







  • 5




    $begingroup$
    No, you will be arrested shortly.
    $endgroup$
    – Shaun
    2 hours ago






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    2 hours ago






  • 1




    $begingroup$
    Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
    $endgroup$
    – Shaun
    2 hours ago











  • $begingroup$
    $A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
    $endgroup$
    – Derek Holt
    41 mins ago















3












$begingroup$


I'm not sure if this question is legal.


I'm writing my BsC thesis on character theoretical calculations and I have already calculated a lot of character tables (a few alternating, symmetric, $operatornameSL(2,3)$, etc..), but I still have some space, so I thought I could choose a group, with not too many conjugacy classes (around $7$ still fit in nicely), that is preferably not monomial.



What do you suggest?



Thanks in advance!






group-theory representation-theory examples-counterexamples characters







share|cite|improve this question











$endgroup$







  • 5




    $begingroup$
    No, you will be arrested shortly.
    $endgroup$
    – Shaun
    2 hours ago






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    2 hours ago






  • 1




    $begingroup$
    Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
    $endgroup$
    – Shaun
    2 hours ago











  • $begingroup$
    $A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
    $endgroup$
    – Derek Holt
    41 mins ago













3












3








3





$begingroup$


I'm not sure if this question is legal.


I'm writing my BsC thesis on character theoretical calculations and I have already calculated a lot of character tables (a few alternating, symmetric, $operatornameSL(2,3)$, etc..), but I still have some space, so I thought I could choose a group, with not too many conjugacy classes (around $7$ still fit in nicely), that is preferably not monomial.



What do you suggest?



Thanks in advance!






group-theory representation-theory examples-counterexamples characters







share|cite|improve this question











$endgroup$




I'm not sure if this question is legal.


I'm writing my BsC thesis on character theoretical calculations and I have already calculated a lot of character tables (a few alternating, symmetric, $operatornameSL(2,3)$, etc..), but I still have some space, so I thought I could choose a group, with not too many conjugacy classes (around $7$ still fit in nicely), that is preferably not monomial.



What do you suggest?



Thanks in advance!






group-theory representation-theory examples-counterexamples characters




group-theory representation-theory examples-counterexamples characters






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 hours ago









Shaun

10.6k113687




10.6k113687










asked 2 hours ago









Máté KadlicskóMáté Kadlicskó

1999




1999







  • 5




    $begingroup$
    No, you will be arrested shortly.
    $endgroup$
    – Shaun
    2 hours ago






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    2 hours ago






  • 1




    $begingroup$
    Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
    $endgroup$
    – Shaun
    2 hours ago











  • $begingroup$
    $A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
    $endgroup$
    – Derek Holt
    41 mins ago












  • 5




    $begingroup$
    No, you will be arrested shortly.
    $endgroup$
    – Shaun
    2 hours ago






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    2 hours ago






  • 1




    $begingroup$
    Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
    $endgroup$
    – Shaun
    2 hours ago











  • $begingroup$
    $A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
    $endgroup$
    – Derek Holt
    41 mins ago







5




5




$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
2 hours ago




$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
2 hours ago




1




1




$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
2 hours ago




$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
2 hours ago




1




1




$begingroup$
Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
$endgroup$
– Shaun
2 hours ago





$begingroup$
Anywho, you could try something fancy like a semidirect product (other than a dihedral group) or maybe even a Wreath product. Pick your poison. There's plenty of small groups to build'm from.
$endgroup$
– Shaun
2 hours ago













$begingroup$
$A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
$endgroup$
– Derek Holt
41 mins ago




$begingroup$
$A_5$, $A_6$ and $rm PSL(2,7) cong rm PSL(3,2)$ are the only finite nonabelian simple groups with at most $7$ conjugacy classes.
$endgroup$
– Derek Holt
41 mins ago










1 Answer
1






active

oldest

votes


















5












$begingroup$

I'm a big fan of the group $operatornamePSL(2,7)$, also known as $operatornameGL(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you for your answer! What makes you a fan of it?
    $endgroup$
    – Máté Kadlicskó
    1 hour ago






  • 1




    $begingroup$
    @MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
    $endgroup$
    – Servaes
    1 hour ago












Your Answer








StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3190340%2fwhat-is-a-non-alternating-simple-group-with-big-order-but-relatively-few-conjug%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









5












$begingroup$

I'm a big fan of the group $operatornamePSL(2,7)$, also known as $operatornameGL(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you for your answer! What makes you a fan of it?
    $endgroup$
    – Máté Kadlicskó
    1 hour ago






  • 1




    $begingroup$
    @MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
    $endgroup$
    – Servaes
    1 hour ago
















5












$begingroup$

I'm a big fan of the group $operatornamePSL(2,7)$, also known as $operatornameGL(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.






share|cite|improve this answer









$endgroup$












  • $begingroup$
    Thank you for your answer! What makes you a fan of it?
    $endgroup$
    – Máté Kadlicskó
    1 hour ago






  • 1




    $begingroup$
    @MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
    $endgroup$
    – Servaes
    1 hour ago














5












5








5





$begingroup$

I'm a big fan of the group $operatornamePSL(2,7)$, also known as $operatornameGL(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.






share|cite|improve this answer









$endgroup$



I'm a big fan of the group $operatornamePSL(2,7)$, also known as $operatornameGL(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 hours ago









ServaesServaes

30.7k342101




30.7k342101











  • $begingroup$
    Thank you for your answer! What makes you a fan of it?
    $endgroup$
    – Máté Kadlicskó
    1 hour ago






  • 1




    $begingroup$
    @MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
    $endgroup$
    – Servaes
    1 hour ago

















  • $begingroup$
    Thank you for your answer! What makes you a fan of it?
    $endgroup$
    – Máté Kadlicskó
    1 hour ago






  • 1




    $begingroup$
    @MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
    $endgroup$
    – Servaes
    1 hour ago
















$begingroup$
Thank you for your answer! What makes you a fan of it?
$endgroup$
– Máté Kadlicskó
1 hour ago




$begingroup$
Thank you for your answer! What makes you a fan of it?
$endgroup$
– Máté Kadlicskó
1 hour ago




1




1




$begingroup$
@MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
$endgroup$
– Servaes
1 hour ago





$begingroup$
@MátéKadlicskó The fact that it describes two seemingly different geometries, and that it is small enough to allow any calculations to be done manually.
$endgroup$
– Servaes
1 hour ago


















draft saved

draft discarded
















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3190340%2fwhat-is-a-non-alternating-simple-group-with-big-order-but-relatively-few-conjug%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Which organization defines CJK Unified Ideographs? The Next CEO of Stack OverflowCharacters which have several different shapesHow useful are the kanji in reading Chinese?Can Chinese readers scan large amounts of text faster/more accurately than their alphabet-using counterparts?丼: why is “well” also “bowl of food”?What Does Unicode 8.0 Mean For Chinese?How are blanks indicated for placeholders in Chinese (like ???)Is there a dictionary of standard character variants?How to display CJK Extension F?How is it decided as to which character is used on the tech terminology?How does 子 come to mean 'midnight'?

Image
Apart from "berlinern", do any other German dialects have a corresponding verb? Horror movie/show or scene where a horse creature opens its mouth really wide and devours a man in a stables I believe this to be a fraud - hired, then asked to cash check and send cash as Bitcoin How do I construct this japanese bowl? How to Reset Passwords on Multiple Websites Easily? If I blow insulation everywhere in my attic except the door trap, will heat escape through it? How do I go from 300 unfinished/half written blog posts, to published posts? What happens if you roll doubles 3 times then land on "Go to jail?" Text adventure game code Can a caster that cast Polymorph on themselves stop concentrating at any point even if their Int is low? How did people program for Consoles with multiple CPUs? Is it my responsibility to learn a new technology in my own time my employer wants to implement? Unreliable Magic - Is it worth it? What is the point of a new v...
Read more

Shenzhen Football Club Índice Elenco atual | Títulos | Referências Ligações externas | Menu de navegaçãoGooglenotíciaslivrosacadêmicoeditar«"Elenco"»Site oficialexpandindo-oeee

Image
Clubes de futebol da ChinaClubes de futebol fundados em 1994 Chinês simplificadoclube de futebolShenzhenGuangdongSuperliga Chinesa Sven-Göran Eriksson Esta página ou secção cita fontes confiáveis e independentes, mas que não cobrem todo o conteúdo, o que compromete a verificabilidade (desde agosto de 2009) . Por favor, insira mais referências no texto. Material sem fontes poderá ser removido. — Encontre fontes: Google (notícias, livros e acadêmico) Shenzhen FC 深圳 Nome Shenzhen Football Club 深圳市足球俱乐部 Alcunhas Youth Army , Phoenix Mascote Touro Fundação 26 de janeiro de 1994 (25 anos) Estádio Shenzhen Stadium Localização Shenzhen, Guangdong Presidente Deng Junjie (邓俊杰) Treinador Sven-Göran Eriksson Material (d)esportivo Nike Competição China League One Copa FA da China editar Sh...
Read more

When We Were Young (canção de Adele) Índice Antecedentes e lançamento | Faixas e formatos | Performances e covers | Desempenho nas tabelas musicais | Créditos | Histórico de lançamento | Referências Menu de navegação«Best albums of 2015»«Adele - When We Were Young (Radio Date: 22-01-2016)»«When We Were Young - Single by Adele»«Adele: Inside Her Private Life and Triumphant Return»«adele interview: world exclusive first interview in three years»«Tobias Jesso Jr: since Adele tweeted his song, he's even bigger than his dad»«Adele interviews Tobias Jesso Jr: 'I think that a couple of the ideas we had could be rap songs'»«Adele on Her Return: 'I Was So Frightened That No One Cared'»«Tobias Jesso Jr. on working with Adele: 'I was as nervous as shit'»«How Ariel Rechtshaid Pushed Adele To Her Limit»«Adele Previews 'When We Were Young' on '60 Minutes' Teaser, Tops Trending 140»«Adele Performs New '25' Ballad, "When We Were Young" Live: Watch»«Which '25' Song Should Be Adele's Next Single?»«Adele's 'When We Were Young' Confirmed As Second Single From '25'»«Adele's new single artwork for 'When We Were Young' is perfectly adorable»«Adele at the BBC review: honest, funny and spectacular – Celebrity News News»«'Saturday Night Live': Adele Sings 'Hello' and 'When We Were Young'»«'Adele: Live in New York City' NBC Special – Set List Revealed!»«Adele Closes Out the 2016 Brit Awards With 'When We Were Young'»«What Is The Adele Live Tour Set List? There's No Way She'd Leave Out These 8 Songs»«See Demi Lovato's Soaring Cover of Adele's 'When We Were Young'»«'The Voice': 5 Best Moments From Week 1 Blind Auditions»«Adele – When We Were Young (Media Control Charts)»«Adele – When We Were Young (Entertainment Monitoring Africa)»«Adele – When We Were Young (ARIA Charts)»«Adele – When We Were Young (Ö3 Austria Top 40)»«Adele – When We Were Young (Ultratop 50)»«Adele – When We Were Young (Ultratop 40)»«Adele – When We Were Young (Canadian Hot 100)»«Adele – When We Were Young (Tracklisten)»«Adele – When We Were Young (The Official Charts Company)»«Adele – Hello (IFPI Slovenská Republika)»«Adele – When We Were Young (Productores de Música de España)»«Adele – When We Were Young (Billboard Hot 100)»«Adele – When We Were Young (Pop Songs)»«Adele – When We Were Young (Adult Pop Songs)»«Adele – When We Were Young (Hot Adult Contemporary Charts)»«Adele – When We Were Young (Hot Dance Club Songs)»«Adele – When We Were Young (Rock Airplay)»«Adele – When We Were Young (IFPI Finlândia)»«Adele – When We Were Young (Syndicat National de l'Éditon Phonographique)»«Adele – When We Were Young (Magyar Hanglemezkiadók Szövetsége)»«Adele – When We Were Young (Irish Recorded Music Association)»«Adele – When We Were Young (Mexico Airplay)»«Adele – When We Were Young (VG-lista)»«Adele – When We Were Young (NZ Top 40 Singles)»«Adele – When We Were Young (MegaCharts)»«Adele – When We Were Young (Związek Producentów Audio Video)»«Adele – When We Were Young (Portugal Digital Songs)»«Adele – When We Were Young (UK Indie Singles Chart)»«Adele – When We Were Young (UK Singles Chart)»«Adele – When We Were Young (Sverigetopplistan)»«Adele – When We Were Young (Schweizer Hitparade)»«Adele – When We Were Young (Portugal Digital Songs)»«Music Canada – Gold/Platinum – When We Were Young»«NZ Top 40 Singles Chart»«Certified Awards»e

Image
Singles de AdeleCanções compostas por AdeleSingles de 2016Singles de balada cançãoinglesaAdeleálbum de estúdioTobias Jesso, Jr.LondresXL Recordingsdigitalmentebloqueio de escritorLos AngelesTobias Jesso Jr.Philip GlassAriel RechtshaidBillboardColumbia RecordsAdele at the BBCBBC OneAdele Live in New York CityNBCGlastonbury FestivalAdele Live 2016Demi LovatoRolling StoneLuke Evans "When We Were Young" Single de Adele do álbum 25 Lançamento 22 de janeiro de 2016  ( 2016-01-22 ) Formato(s) Download digital Gravação 2015; Dean Street Studios (Londres, Inglaterra) Gênero(s) Soul [ 1 ] Duração 4 : 50 Gravadora(s) XL Composição Adele Adkins, Tobias Jesso, Jr. Produção Ariel Rechtshaid Cronologia de singles de Adele "Hello" (2015) "Send My Love (To Your New Lover)" (2016) ...
Read more