swinarski@MAB-OptiPlex-790:~$ magma
Magma V2.20-1     Sun Jan 19 2014 14:25:13 on MAB-OptiPlex-790 [Seed = 
3512706390]
Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv6.txt";
Loading "autcv6.txt"
> RunExample(SmallGroup(16,7),4,[2,2,2,8]);


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


-------------------------------
Class |   1  2  3  4  5   6   7
Size  |   1  1  4  4  2   2   2
Order |   1  2  2  2  4   8   8
-------------------------------
p  =  2   1  1  1  1  2   5   5
-------------------------------
X.1   +   1  1  1  1  1   1   1
X.2   +   1  1 -1  1  1  -1  -1
X.3   +   1  1  1 -1  1  -1  -1
X.4   +   1  1 -1 -1  1   1   1
X.5   +   2  2  0  0 -2   0   0
X.6   +   2 -2  0  0  0  Z1 -Z1
X.7   +   2 -2  0  0  0 -Z1  Z1


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 
]


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

[2]     Order 2       Length 1      
        Rep G.4

[3]     Order 2       Length 4      
        Rep G.1

[4]     Order 2       Length 4      
        Rep G.2

[5]     Order 4       Length 2      
        Rep G.3

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

[7]     Order 8       Length 2      
        Rep G.1 * G.2


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