[dchanin@ace-math01 ~]$ magma
Magma V2.21-4     Tue Sep  1 2015 20:48:22 on ace-math01 [Seed = 1173772051]
Type ? for help.  Type <Ctrl>-D to quit
> load "autcv9.txt";
Loading "autcv9.txt"
> Mmats,Gmats,Q,C:=RunExample(SmallGroup(24,12),4,[2,2,2,4]);


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


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



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

[2]     Order 2       Length 3      
        Rep G.3

[3]     Order 2       Length 6      
        Rep G.1

[4]     Order 3       Length 8      
        Rep G.2

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


SKGs:  [ G.1, G.1 * G.2 * G.4, G.1 * G.3 * G.4, G.1 * G.2^2 * G.3 * G.4 ]
Is hyperelliptic?  false
Is cyclic trigonal?  false
Multiplicities of irreducibles in relevant G-modules:
I_1      =[ 0, 0, 0, 0, 0 ]
S_1      =[ 0, 1, 0, 1, 0 ]
H^0(C,1K)=[ 0, 1, 0, 1, 0 ]
I_2      =[ 1, 0, 0, 0, 0 ]
S_2      =[ 2, 0, 1, 0, 2 ]
H^0(C,2K)=[ 1, 0, 1, 0, 2 ]
I_3      =[ 0, 2, 0, 1, 0 ]
S_3      =[ 0, 3, 1, 4, 1 ]
H^0(C,3K)=[ 0, 1, 1, 3, 1 ]
I2timesS1=[ 0, 1, 0, 1, 0 ]
Is clearly not generated by quadrics? true
Matrix generators for action on H^0(C,K):
Field K Cyclotomic Field of order 24 and degree 8
[
    [-1  0  0  0]
    [ 0 -1 -1  0]
    [ 0  0  1  0]
    [ 0  0  1 -1],

    [ 1  0  0  0]
    [ 0  1  0  1]
    [ 0  0  0 -1]
    [ 0  0  1 -1],

    [ 1  0  0  0]
    [ 0  0 -1  1]
    [ 0 -1  0 -1]
    [ 0  0  0 -1],

    [ 1  0  0  0]
    [ 0 -1  0  0]
    [ 0  1  0  1]
    [ 0  1  1  0]
]
Surface Kernel Generators:
[
    [-1  0  0  0]
    [ 0 -1 -1  0]
    [ 0  0  1  0]
    [ 0  0  1 -1],

    [-1  0  0  0]
    [ 0  1  0  0]
    [ 0 -1 -1  0]
    [ 0 -1  0 -1],

    [-1  0  0  0]
    [ 0  0  0  1]
    [ 0  0 -1  0]
    [ 0  1  0  0],

    [-1  0  0  0]
    [ 0  1  0  1]
    [ 0 -1  0  0]
    [ 0 -1 -1  0]
]
Finding quadrics:
I2 contains a 1-dimensional subspace of CharacterRow 1
Dimension 2
Multiplicity 2
[
    a^2,
    b^2 - b*c - b*d + c^2 + c*d + d^2
]
Finding cubics:
I3 contains a 2-dimensional subspace of CharacterRow 2
Dimension 3
Multiplicity 3
[
    a^3,
    a*b^2 - a*b*c - a*b*d + a*c^2 + a*c*d + a*d^2,
    b^2*c + b^2*d - b*c^2 - 2*b*c*d - b*d^2 + c^2*d + c*d^2
]
I3 contains a 3-dimensional subspace of CharacterRow 4
Dimension 12
Multiplicity 4
[
    a^2*b,
    a^2*c,
    a^2*d,
    a*b^2 - a*d^2,
    a*b*c + a*b*d - a*c*d - a*d^2,
    a*c^2 - a*d^2,
    b^3 + d^3,
    b^2*c - b*c^2 + 2/3*d^3,
    b^2*d - b*d^2 + 2/3*d^3,
    b*c*d + 1/3*d^3,
    c^3 - d^3,
    c^2*d + c*d^2 + 2/3*d^3
]
> K<z>:=CyclotomicField(24);
> P3<a,b,c,d>:=ProjectiveSpace(K,3);
> mu3:=z^3;
> X:=Scheme(P3,[a^2+b^2 - b*c - b*d + c^2 + c*d + d^2,(a^3-(a*b^2 - a*b*c - a*\
b*d + a*c^2 + a*c*d + a*d^2)) + mu2*(b^2*c + b^2*d - b*c^2 -2*b*c*d - b*d^2 + \
c^2*d + c*d^2)]);
> Dimension(X);
1
> IsSingular(X);
false
> Automorphism(X,Mmats[1]);
Mapping from: Sch: X to Sch: X
with equations : 
-a
-b
-b + c + d
-d
and inverse
-a
-b
-b + c + d
-d
> Automorphism(X,Mmats[2]);
Mapping from: Sch: X to Sch: X
with equations : 
a
b
d
b - c - d
and inverse
a
b
b - c - d
c
> Automorphism(X,Mmats[3]);
Mapping from: Sch: X to Sch: X
with equations : 
a
-c
-b
b - c - d
and inverse
a
-c
-b
b - c - d
> Automorphism(X,Mmats[4]);
Mapping from: Sch: X to Sch: X
with equations : 
a
-b + c + d
d
c
and inverse
a
-b + c + d
d
c