swinarski@MAB-OptiPlex-790:~$ magma
Magma V2.20-1     Sun Jan 19 2014 13:22:10 on MAB-OptiPlex-790 [Seed = 
2129673141]
Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv6.txt";
Loading "autcv6.txt"
> RunExample(SmallGroup(32,19),4,[2,4,16]);


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


---------------------------------------------------
Class |   1  2  3  4  5   6   7    8    9   10   11
Size  |   1  1  8  2  8   2   2    2    2    2    2
Order |   1  2  2  4  4   8   8   16   16   16   16
---------------------------------------------------
p  =  2   1  1  1  2  2   4   4    6    7    6    7
---------------------------------------------------
X.1   +   1  1  1  1  1   1   1    1    1    1    1
X.2   +   1  1  1  1 -1   1   1   -1   -1   -1   -1
X.3   +   1  1 -1  1 -1   1   1    1    1    1    1
X.4   +   1  1 -1  1  1   1   1   -1   -1   -1   -1
X.5   +   2  2  0  2  0  -2  -2    0    0    0    0
X.6   +   2  2  0 -2  0   0   0  -Z1   Z1  -Z1   Z1
X.7   +   2  2  0 -2  0   0   0   Z1  -Z1   Z1  -Z1
X.8   0   2 -2  0  0  0  Z1 -Z1   Z2-Z2#3  -Z2 Z2#3
X.9   0   2 -2  0  0  0 -Z1  Z1-Z2#3  -Z2 Z2#3   Z2
X.10  0   2 -2  0  0  0  Z1 -Z1  -Z2 Z2#3   Z2-Z2#3
X.11  0   2 -2  0  0  0 -Z1  Z1 Z2#3   Z2-Z2#3  -Z2


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

# denotes algebraic conjugation, that is,
#k indicates replacing the root of unity w by w^k

Z1     = (CyclotomicField(8: Sparse := true)) ! [ RationalField() | 0, -1, 0, 1 
]

Z2     = (CyclotomicField(16: Sparse := true)) ! [ RationalField() | 0, 0, 0, 1,
0, 1, 0, 0 ]


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

[2]     Order 2       Length 1      
        Rep G.5

[3]     Order 2       Length 8      
        Rep G.2

[4]     Order 4       Length 2      
        Rep G.4

[5]     Order 4       Length 8      
        Rep G.1

[6]     Order 8       Length 2      
        Rep G.3

[7]     Order 8       Length 2      
        Rep G.3 * G.5

[8]     Order 16      Length 2      
        Rep G.1 * G.2 * G.4 * G.5

[9]     Order 16      Length 2      
        Rep G.1 * G.2 * G.5

[10]    Order 16      Length 2      
        Rep G.1 * G.2 * G.4

[11]    Order 16      Length 2      
        Rep G.1 * G.2


SKGs:  [ G.2 * G.4, G.1 * G.4 * G.5, G.1 * G.2 ]
Is hyperelliptic?  true
Curve is hyperelliptic
> G:=SmallGroup(32,19);
> FP,f:=FPGroup(G);
> PermG,g:=PermutationGroup(FP);
> g(Inverse(f)(G.2 * G.4));
(1, 4)(2, 14)(3, 12)(5, 11)(6, 8)(7, 9)(13, 15)
> g(Inverse(f)(G.1 * G.4*G.5));
(1, 13, 5, 8)(2, 4, 9, 11)(3, 7, 12, 14)(6, 10, 15, 16)