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
If a contract sometimes uses the wrong name, is it still valid?
Identify plant with long narrow paired leaves and reddish stems
In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?
Can an alien society believe that their star system is the universe?
How to tell that you are a giant?
What does this icon in iOS Stardew Valley mean?
Why did the IBM 650 use bi-quinary?
Denied boarding although I have proper visa and documentation. To whom should I make a complaint?
How to bypass password on Windows XP account?
How come Sam didn't become Lord of Horn Hill?
The logistics of corpse disposal
How to deal with a team lead who never gives me credit?
Short Story with Cinderella as a Voo-doo Witch
Apollo command module space walk?
What's inside the kernel part of virtual memory of 64 bit linux processes?
How to call a function with default parameter through a pointer to function that is the return of another function?
How discoverable are IPv6 addresses and AAAA names by potential attackers?
What does the word "veer" mean here?
What is the role of the transistor and diode in a soft start circuit?
Is there a program I can run on the C64 to speed up booting of a game?
What does the "x" in "x86" represent?
Extract all GPU name, model and GPU ram
Are two submodules (where one is contained in the other) isomorphic if their quotientmodules are isomorphic?
Fundamental Solution of the Pell Equation
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
$begingroup$
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
edited 2 hours ago
Shaun
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
$endgroup$
add a comment |
$begingroup$
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
edited 2 hours ago
Shaun
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
$endgroup$
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
58 mins ago
add a comment |
$begingroup$
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
edited 2 hours ago
Shaun
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
$endgroup$
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
edited 2 hours ago
Shaun
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
edited 2 hours ago
Shaun
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
edited 2 hours ago
Shaun
10.6k113687
edited 2 hours ago
Shaun
10.6k113687
edited 2 hours ago
Shaun
10.6k113687
10.6k113687
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
asked 2 hours ago
Máté KadlicskóMáté Kadlicskó
1999
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
58 mins ago
add a comment |
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
58 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
58 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
58 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
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.
answered 2 hours ago
ServaesServaes
30.7k342101
$endgroup$
$begingroup$
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
add a comment |
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
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
$begingroup$
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.
answered 2 hours ago
ServaesServaes
30.7k342101
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered 2 hours ago
ServaesServaes
30.7k342101
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
answered 2 hours ago
ServaesServaes
30.7k342101
$endgroup$
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.
answered 2 hours ago
ServaesServaes
30.7k342101
answered 2 hours ago
ServaesServaes
30.7k342101
answered 2 hours ago
ServaesServaes
30.7k342101
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
add a comment |
$begingroup$
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
add a comment |
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.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
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
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
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
58 mins ago