Is there any reference where I can find the character table of the symmetric group $S\_7$? A simple search in google gave me a GAP program that computes the character table, but I don't understand the table that the program produces, since it does not tell me each column in the table is associated to which conjugacy class. I would like to have a table like
[enter link description here](http://books.google.ca/books?id=ly88AAAAIAAJ&pg=PA140&dq=character%20table%20of%20S6&hl=en&sa=X&ei=d0E_U-zxJObQsASwy4GAAQ&ved=0CEQQ6AEwBA#v=onepage&q=character%20table%20of%20S6&f=false)


I would be extremely thankful if you provide me reference. 



Character table of $S_7$
As you already discovered, GAP can easily compute this. The character table looks like this:



```
gap> G:=SymmetricGroup(7);
Sym( [ 1 .. 7 ] )
gap> ct := CharacterTable(G);;
CharacterTable( Sym( [ 1 .. 7 ] ) )
gap> Display(ct);
CT2

      2  4  4  4  4  3  2  3  1  3  3   2  1   1  1  .
      3  2  1  1  1  2  1  1  2  1  .   1  .   .  1  .
      5  1  1  .  .  .  .  .  .  .  .   .  1   1  .  .
      7  1  .  .  .  .  .  .  .  .  .   .  .   .  .  1

        1a 2a 2b 2c 3a 6a 6b 3b 4a 4b 12a 5a 10a 6c 7a
     2P 1a 1a 1a 1a 3a 3a 3a 3b 2b 2b  6b 5a  5a 3b 7a
     3P 1a 2a 2b 2c 1a 2a 2b 1a 4a 4b  4a 5a 10a 2c 7a
     5P 1a 2a 2b 2c 3a 6a 6b 3b 4a 4b 12a 1a  2a 6c 7a
     7P 1a 2a 2b 2c 3a 6a 6b 3b 4a 4b 12a 5a 10a 6c 1a

X.1      1 -1  1 -1  1 -1  1  1 -1  1  -1  1  -1 -1  1
X.2      6 -4  2  .  3 -1 -1  . -2  .   1  1   1  . -1
X.3     14 -6  2 -2  2  .  2 -1  .  .   . -1  -1  1  .
X.4     14 -4  2  . -1 -1 -1  2  2  .  -1 -1   1  .  .
X.5     15 -5 -1  3  3  1 -1  . -1 -1  -1  .   .  .  1
X.6     35 -5 -1 -1 -1  1 -1 -1  1  1   1  .   . -1  .
X.7     21 -1  1  3 -3 -1  1  .  1 -1   1  1  -1  .  .
X.8     21  1  1 -3 -3  1  1  . -1 -1  -1  1   1  .  .
X.9     20  . -4  .  2  .  2  2  .  .   .  .   .  . -1
X.10    35  5 -1  1 -1 -1 -1 -1 -1  1  -1  .   .  1  .
X.11    14  4  2  . -1  1 -1  2 -2  .   1 -1  -1  .  .
X.12    15  5 -1 -3  3 -1 -1  .  1 -1   1  .   .  .  1
X.13    14  6  2  2  2  .  2 -1  .  .   . -1   1 -1  .
X.14     6  4  2  .  3  1 -1  .  2  .  -1  1  -1  . -1
X.15     1  1  1  1  1  1  1  1  1  1   1  1   1  1  1

```

In order to understand how to read this, one needs to know (e.g. by a quick look at the documentation) that the rows labelled X.1 to X.15 correspond to the irreducible characters, while the columns correspond to the conjugacy classes of the group. So, let's ask GAP for the classes and a representative of each:



```
gap> cc:=ConjugacyClasses(ct);
[ ()^G, (1,2)^G, (1,2)(3,4)^G, (1,2)(3,4)(5,6)^G, (1,2,3)^G, (1,2,3)(4,5)^G, (1,2,3)(4,5)(6,7)^G,
  (1,2,3)(4,5,6)^G, (1,2,3,4)^G, (1,2,3,4)(5,6)^G, (1,2,3,4)(5,6,7)^G, (1,2,3,4,5)^G, (1,2,3,4,5)(6,7)^G,
  (1,2,3,4,5,6)^G, (1,2,3,4,5,6,7)^G ]
gap> for i in [1..15] do Print(i, ": ", Representative(cc[i]), "\n"); od;
1: ()
2: (1,2)
3: (1,2)(3,4)
4: (1,2)(3,4)(5,6)
5: (1,2,3)
6: (1,2,3)(4,5)
7: (1,2,3)(4,5)(6,7)
8: (1,2,3)(4,5,6)
9: (1,2,3,4)
10: (1,2,3,4)(5,6)
11: (1,2,3,4)(5,6,7)
12: (1,2,3,4,5)
13: (1,2,3,4,5)(6,7)
14: (1,2,3,4,5,6)
15: (1,2,3,4,5,6,7) 

```

Of course you can get a lot more information from this, too. More on this can be found in the GAP manual.


