Davids-MacBook-Pro-2:aut dswinarski$ magma
Magma V2.21-7     Tue Mar 22 2016 07:09:33 on Davids-MacBook-Pro-2 [Seed = 
662722192]

+-------------------------------------------------------------------+
|       This copy of Magma has been made available through a        |
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+-------------------------------------------------------------------+

Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv10d.txt";
Loading "autcv10d.txt"
> G:=SmallGroup(48,6);
> RunExample(G,6,[2,4,24]);
Set seed to 0.


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


-----------------------------------------------------------------
Class |   1  2  3  4  5  6  7   8   9  10  11   12   13   14   15
Size  |   1  1 12  2  2 12  2   2   2   2   2    2    2    2    2
Order |   1  2  2  3  4  4  6   8   8  12  12   24   24   24   24
-----------------------------------------------------------------
p  =  2   1  1  1  4  2  2  4   5   5   7   7   10   11   11   10
p  =  3   1  2  3  1  5  6  2   8   9   5   5    9    9    8    8
-----------------------------------------------------------------
X.1   +   1  1  1  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    1    1    1    1
X.3   +   1  1  1  1  1 -1  1  -1  -1   1   1   -1   -1   -1   -1
X.4   +   1  1 -1  1  1  1  1  -1  -1   1   1   -1   -1   -1   -1
X.5   +   2  2  0 -1  2  0 -1   2   2  -1  -1   -1   -1   -1   -1
X.6   +   2  2  0 -1  2  0 -1  -2  -2  -1  -1    1    1    1    1
X.7   +   2  2  0  2 -2  0  2   0   0  -2  -2    0    0    0    0
X.8   0   2 -2  0  2  0  0 -2  Z1 -Z1   0   0  -Z1  -Z1   Z1   Z1
X.9   0   2 -2  0  2  0  0 -2 -Z1  Z1   0   0   Z1   Z1  -Z1  -Z1
X.10  +   2  2  0 -1 -2  0 -1   0   0   1   1   Z2  -Z2  -Z2   Z2
X.11  +   2  2  0 -1 -2  0 -1   0   0   1   1  -Z2   Z2   Z2  -Z2
X.12  0   2 -2  0 -1  0  0  1  Z1 -Z1  Z2 -Z2   Z3-Z3#5 Z3#5  -Z3
X.13  0   2 -2  0 -1  0  0  1 -Z1  Z1  Z2 -Z2  -Z3 Z3#5-Z3#5   Z3
X.14  0   2 -2  0 -1  0  0  1  Z1 -Z1 -Z2  Z2-Z3#5   Z3  -Z3 Z3#5
X.15  0   2 -2  0 -1  0  0  1 -Z1  Z1 -Z2  Z2 Z3#5  -Z3   Z3-Z3#5


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(12: Sparse := true)) ! [ RationalField() | 0, 1, 0, 2 
]

Z3     = (CyclotomicField(24: Sparse := true)) ! [ RationalField() | 0, -1, 0, 
0, 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 12     
        Rep G.1

[4]     Order 3       Length 2      
        Rep G.5

[5]     Order 4       Length 2      
        Rep G.3

[6]     Order 4       Length 12     
        Rep G.1 * G.2 * G.3

[7]     Order 6       Length 2      
        Rep G.4 * G.5

[8]     Order 8       Length 2      
        Rep G.2

[9]     Order 8       Length 2      
        Rep G.2 * G.4

[10]    Order 12      Length 2      
        Rep G.3 * G.5^2

[11]    Order 12      Length 2      
        Rep G.3 * G.5

[12]    Order 24      Length 2      
        Rep G.2 * G.4 * G.5

[13]    Order 24      Length 2      
        Rep G.2 * G.4 * G.5^2

[14]    Order 24      Length 2      
        Rep G.2 * G.5^2

[15]    Order 24      Length 2      
        Rep G.2 * G.5


Surface kernel generators:  [ G.1 * G.4 * G.5, G.1 * G.2 * G.4, G.2 * G.3 * G.4 
* G.5 ]
Is hyperelliptic?  true
Curve is hyperelliptic
> FP,f:=FPGroup(G);
> PermG,g:=PermutationGroup(FP);
> g(Inverse(f)(G.1 * G.4 * G.5));
(1, 11)(2, 22)(3, 10)(4, 5)(6, 15)(7, 14)(8, 13)(9, 18)(12, 21)(16, 24)(17, 23)
> g(Inverse(f)(G.1 * G.2 * G.4));
(1, 7, 4, 2)(3, 6, 9, 13)(5, 24, 11, 17)(8, 12, 15, 21)(10, 16, 18, 23)(14, 19, 
    22, 20)