What is a non-alternating simple group with big order, but relatively few conjugacy classes? ...
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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
$begingroup$
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, $operatorname{SL}(2,3)$, 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 1 hour ago
Shaun
10.6k113687
asked 1 hour 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, $operatorname{SL}(2,3)$, 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 1 hour ago
Shaun
10.6k113687
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
$endgroup$
3
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
1
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour 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
1 hour 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
16 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, $operatorname{SL}(2,3)$, 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 1 hour ago
Shaun
10.6k113687
asked 1 hour 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, $operatorname{SL}(2,3)$, 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 1 hour ago
Shaun
10.6k113687
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
edited 1 hour ago
Shaun
10.6k113687
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
edited 1 hour ago
Shaun
10.6k113687
edited 1 hour ago
Shaun
10.6k113687
edited 1 hour ago
Shaun
10.6k113687
10.6k113687
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
asked 1 hour ago
Máté KadlicskóMáté Kadlicskó
1999
1999
3
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
1
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour 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
1 hour 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
16 mins ago
add a comment |
3
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
1
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour 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
1 hour 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
16 mins ago
3
3
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
1
1
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour ago
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour 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
1 hour 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
1 hour 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
16 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
16 mins ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I'm a big fan of the group $operatorname{PSL}(2,7)$, also known as $operatorname{GL}(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.
answered 1 hour 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
43 mins ago
add a comment |
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1 Answer
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$begingroup$
I'm a big fan of the group $operatorname{PSL}(2,7)$, also known as $operatorname{GL}(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.
answered 1 hour 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
43 mins ago
add a comment |
$begingroup$
I'm a big fan of the group $operatorname{PSL}(2,7)$, also known as $operatorname{GL}(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.
answered 1 hour 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
43 mins ago
add a comment |
$begingroup$
I'm a big fan of the group $operatorname{PSL}(2,7)$, also known as $operatorname{GL}(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.
answered 1 hour ago
ServaesServaes
30.7k342101
$endgroup$
I'm a big fan of the group $operatorname{PSL}(2,7)$, also known as $operatorname{GL}(3,2)$, which is finite, simple, not isomorphic to an alternating group, and has precisely $6$ conjugacy classes.
answered 1 hour ago
ServaesServaes
30.7k342101
answered 1 hour ago
ServaesServaes
30.7k342101
answered 1 hour ago
ServaesServaes
30.7k342101
answered 1 hour 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
43 mins 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
43 mins 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
43 mins 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
43 mins ago
add a comment |
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3
$begingroup$
No, you will be arrested shortly.
$endgroup$
– Shaun
1 hour ago
1
$begingroup$
the StackExchange police are on their way already?
$endgroup$
– Máté Kadlicskó
1 hour 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
1 hour 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
16 mins ago