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

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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!










share|cite|improve this question











$endgroup$







  • 5




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






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    4 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
    4 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
    2 hours 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!










share|cite|improve this question











$endgroup$







  • 5




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






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    4 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
    4 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
    2 hours 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!










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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 4 hours ago









Shaun

10.6k113687




10.6k113687










asked 4 hours ago









Máté KadlicskóMáté Kadlicskó

1999




1999







  • 5




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






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    4 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
    4 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
    2 hours ago












  • 5




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






  • 1




    $begingroup$
    the StackExchange police are on their way already?
    $endgroup$
    – Máté Kadlicskó
    4 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
    4 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
    2 hours ago







5




5




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




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




1




1




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




$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
4 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
4 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
4 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
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
2 hours ago










1 Answer
1






active

oldest

votes


















6












$begingroup$

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
    3 hours 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
    2 hours ago












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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









6












$begingroup$

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
    3 hours 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
    2 hours ago
















6












$begingroup$

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
    3 hours 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
    2 hours ago














6












6








6





$begingroup$

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 3 hours ago









ServaesServaes

30.7k342101




30.7k342101











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

















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
















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




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


















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