Magma V2.20-3     Fri Mar 18 2016 11:03:51 on Fordham-David-Swinarski [Seed = 
2184760335]
Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv10c.txt";
Loading "autcv10c.txt"
> G:=SmallGroup(48,30);
> RunExample(G,5,[3,4,4]);
Set seed to 0.


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


--------------------------------------
Class |   1  2  3  4  5  6  7  8  9 10
Size  |   1  1  3  3  8  6  6  6  6  8
Order |   1  2  2  2  3  4  4  4  4  6
--------------------------------------
p  =  2   1  1  1  1  5  4  4  2  2  5
p  =  3   1  2  3  4  1  7  6  9  8  2
--------------------------------------
X.1   +   1  1  1  1  1  1  1  1  1  1
X.2   +   1  1  1  1  1 -1 -1 -1 -1  1
X.3   0   1 -1  1 -1  1 -I  I -I  I -1
X.4   0   1 -1  1 -1  1  I -I  I -I -1
X.5   -   2 -2  2 -2 -1  0  0  0  0  1
X.6   +   2  2  2  2 -1  0  0  0  0 -1
X.7   +   3  3 -1 -1  0  1  1 -1 -1  0
X.8   +   3  3 -1 -1  0 -1 -1  1  1  0
X.9   0   3 -3 -1  1  0  I -I -I  I  0
X.10  0   3 -3 -1  1  0 -I  I  I -I  0


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

I = RootOfUnity(4)


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

[2]     Order 2       Length 1      
        Rep G.2

[3]     Order 2       Length 3      
        Rep G.4

[4]     Order 2       Length 3      
        Rep G.2 * G.4

[5]     Order 3       Length 8      
        Rep G.3

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

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

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

[9]     Order 4       Length 6      
        Rep G.1

[10]    Order 6       Length 8      
        Rep G.2 * G.3


Surface kernel generators:  [ G.3^2 * G.4 * G.5, G.1 * G.2 * G.3^2, G.1 * G.4 ]
Is hyperelliptic?  true
Curve is hyperelliptic
> G;
GrpPC : G of order 48 = 2^4 * 3
PC-Relations:
    G.1^2 = G.2, 
    G.2^2 = Id(G), 
    G.3^3 = Id(G), 
    G.4^2 = Id(G), 
    G.5^2 = Id(G), 
    G.3^G.1 = G.3^2, 
    G.4^G.1 = G.5, 
    G.4^G.3 = G.5, 
    G.5^G.1 = G.4, 
    G.5^G.3 = G.4 * G.5
> FP,f:=FPGroup(G);
> PermG,g:=PermutationGroup(FP);
> g(Inverse(f)(G.3^2 * G.4 * G.5));
(1, 11, 4)(2, 14, 7)(3, 15, 9)(6, 16, 12)
> g(Inverse(f)(G.1 * G.2 * G.3^2));                                            
(1, 6, 3, 2)(4, 12, 9, 7)(5, 16, 10, 14)(8, 11, 13, 15)
> PermG;
Permutation group PermG acting on a set of cardinality 16
Order = 48 = 2^4 * 3
    (1, 2, 3, 6)(4, 8, 9, 13)(5, 7, 10, 12)(11, 14, 15, 16)
    (1, 3)(2, 6)(4, 9)(5, 10)(7, 12)(8, 13)(11, 15)(14, 16)
    (4, 5, 11)(7, 8, 14)(9, 10, 15)(12, 13, 16)
    (1, 4)(2, 7)(3, 9)(5, 11)(6, 12)(8, 14)(10, 15)(13, 16)
    (1, 5)(2, 8)(3, 10)(4, 11)(6, 13)(7, 14)(9, 15)(12, 16)