swinarski@MAB-OptiPlex-790:~$ magma
Magma V2.20-1     Sun Jan 19 2014 13:24:36 on MAB-OptiPlex-790 [Seed = 
1929132047]
Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv6.txt";
Loading "autcv6.txt"
> RunExample(SmallGroup(24,3),4,[3,4,6]);


Character Table of Group G
--------------------------


---------------------------------
Class |   1  2   3   4  5   6   7
Size  |   1  1   4   4  6   4   4
Order |   1  2   3   3  4   6   6
---------------------------------
p  =  2   1  1   4   3  2   4   3
p  =  3   1  2   1   1  5   2   2
---------------------------------
X.1   +   1  1   1   1  1   1   1
X.2   0   1  1-1-J   J  1-1-J   J
X.3   0   1  1   J-1-J  1   J-1-J
X.4   -   2 -2  -1  -1  0   1   1
X.5   0   2 -2  -J 1+J  0   J-1-J
X.6   0   2 -2 1+J  -J  0-1-J   J
X.7   +   3  3   0   0 -1   0   0


Explanation of Character Value Symbols
--------------------------------------

J = RootOfUnity(3)


Conjugacy Classes of group G
----------------------------
[1]     Order 1       Length 1      
        Rep Id(G)

[2]     Order 2       Length 1      
        Rep G.4

[3]     Order 3       Length 4      
        Rep G.1

[4]     Order 3       Length 4      
        Rep G.1^2

[5]     Order 4       Length 6      
        Rep G.2

[6]     Order 6       Length 4      
        Rep G.1 * G.4

[7]     Order 6       Length 4      
        Rep G.1^2 * G.4


SKGs:  [ G.1, G.3 * G.4, G.1^2 * G.2 ]
Is hyperelliptic?  true
Curve is hyperelliptic

> G:=SmallGroup(24,3);
> FP,f:=FPGroup(G);
> PermG,g:=PermutationGroup(FP);
> g(Inverse(f)(G.1));
(2, 3, 5)(6, 8, 7)
> g(Inverse(f)(G.3*G.4));
(1, 8, 4, 3)(2, 7, 6, 5)
> G;