Magma V2.21-4     Fri Sep  4 2015 05:12:08 on ace-math01 [Seed = 1491365218]
Type ? for help.  Type <Ctrl>-D to quit.
> load "autcv10.txt";
Loading "autcv10.txt"
> MatrixGens,MatrixSKG,Q,C:=RunExample(SmallGroup(120,35),5,[2,3,10]);
Set seed to 0.


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


----------------------------------------------
Class |   1  2  3  4  5    6    7  8    9   10
Size  |   1  1 15 15 20   12   12 20   12   12
Order |   1  2  2  2  3    5    5  6   10   10
----------------------------------------------
p  =  2   1  1  1  1  5    7    6  5    6    7
p  =  3   1  2  3  4  1    7    6  2   10    9
p  =  5   1  2  3  4  5    1    1  8    2    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   +   3  3 -1 -1  0   Z1 Z1#2  0 Z1#2   Z1
X.4   +   3  3 -1 -1  0 Z1#2   Z1  0   Z1 Z1#2
X.5   +   3 -3  1 -1  0   Z1 Z1#2  0-Z1#2  -Z1
X.6   +   3 -3  1 -1  0 Z1#2   Z1  0  -Z1-Z1#2
X.7   +   4  4  0  0  1   -1   -1  1   -1   -1
X.8   +   4 -4  0  0  1   -1   -1 -1    1    1
X.9   +   5  5  1  1 -1    0    0 -1    0    0
X.10  +   5 -5 -1  1 -1    0    0  1    0    0


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

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

Z1     = (CyclotomicField(5: Sparse := true)) ! [ RationalField() | 0, 0, -1, -1
]


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

[2]     Order 2       Length 1      
        Rep (6, 7)

[3]     Order 2       Length 15     
        Rep (1, 3)(2, 4)(6, 7)

[4]     Order 2       Length 15     
        Rep (1, 5)(2, 4)

[5]     Order 3       Length 20     
        Rep (1, 5, 4)

[6]     Order 5       Length 12     
        Rep (1, 2, 3, 5, 4)

[7]     Order 5       Length 12     
        Rep (1, 3, 4, 2, 5)

[8]     Order 6       Length 20     
        Rep (1, 4, 5)(6, 7)

[9]     Order 10      Length 12     
        Rep (1, 4, 3, 5, 2)(6, 7)

[10]    Order 10      Length 12     
        Rep (1, 5, 4, 2, 3)(6, 7)


Surface kernel generators:  [
    (1, 4)(3, 5)(6, 7),
    (2, 4, 5),
    (1, 4, 2, 3, 5)(6, 7)
]
Is hyperelliptic?  true