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C4
1
[ 1 .. 4 ] Group( () ) [ 1, 1 ]
2
[ 1, 2, -1, -2 ] Group( [ (1,3)(2,4)(5,6) ] ) [ 2, 1 ]
3
[ 1, 1, 3, 3 ] Group( [ (1,2)(3,4) ] ) [ 2, 1 ]
[ 1, 2, 2, 1 ] Group( [ (1,4)(2,3) ] ) [ 2, 1 ]
4
[ 1, -1, 3, -3 ] Group( [ (1,2)(3,4)(5,6) ] ) [ 2, 1 ]
[ 1, 2, -2, -1 ] Group( [ (1,4)(2,3)(5,6) ] ) [ 2, 1 ]
5
[ 1, 2, 3, 2 ] Group( [ (2,4) ] ) [ 2, 1 ]
[ 1, 2, 1, 4 ] Group( [ (1,3) ] ) [ 2, 1 ]
6
[ 1, 2, 1, 2 ] Group( [ (2,4), (1,3) ] ) [ 4, 2 ]
7
[ 1, 1, -1, -1 ] Group( [ (1,2)(3,4), (1,3)(2,4)(5,6) ] ) [ 4, 2 ]
[ 1, -1, -1, 1 ] Group( [ (1,4)(2,3), (1,3)(2,4)(5,6) ] ) [ 4, 2 ]
8
[ 1, 0, -1, 0 ] Group( [ (2,4), (1,3)(5,6) ] ) [ 4, 2 ]
[ 0, 2, 0, -2 ] Group( [ (1,3), (2,4)(5,6) ] ) [ 4, 2 ]
9
[ 1, 1, 1, 1 ] Group( [ (2,4), (1,3), (1,2)(3,4) ] ) [ 8, 3 ]
10
[ 1, -1, 1, -1 ] Group( [ (2,4), (1,3), (1,2)(3,4)(5,6) ] ) [ 8, 3 ]
11
[ 0, 0, 0, 0 ] Group( [ (1,2,3,4), (1,2)(3,4), (5,6) ] ) [ 16, 11 ]
Subgroup structure
[ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 3, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 4, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1 ],
[ 5, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1 ],
[ 6, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1 ],
[ 7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ]
[ [ -1, 1, -1, 1 ], [ 0, -1, 0, 1 ], [ -1, 0, 1, 0 ], [ 1, 1, 1, 1 ] ]
Symmetry type S1
Group( [ () ] )
[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]
Symmetry type S2
Group( [ (1,3)(2,4)(5,6) ] )
[ [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ] ]
Symmetry type S3
Group( [ (1,2)(3,4) ] )
[ [ 0, 1, 1, 0 ], [ 0, 0, 0, 1 ] ]
Group( [ (1,4)(2,3) ] )
[ [ 0, 1, -1, 0 ], [ 0, 0, 0, 1 ] ]
Symmetry type S4
Group( [ (1,2)(3,4)(5,6) ] )
[ [ 1, 0, 0, 0 ], [ 0, 1, -1, 0 ] ]
Group( [ (1,4)(2,3)(5,6) ] )
[ [ 1, 0, 0, 0 ], [ 0, 1, 1, 0 ] ]
Symmetry type S5
Group( [ (2,4) ] )
[ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]
Group( [ (1,3) ] )
[ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ] ]
Symmetry type S6
Group( [ (2,4), (1,3) ] )
[ [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ] ]
Symmetry type S7
Group( [ (1,2)(3,4), (1,3)(2,4)(5,6) ] )
[ [ 0, 1, 1, 0 ] ]
Group( [ (1,4)(2,3), (1,3)(2,4)(5,6) ] )
[ [ 0, 1, -1, 0 ] ]
Symmetry type S8
Group( [ (2,4), (1,3)(5,6) ] )
[ [ 0, 0, 1, 0 ] ]
Group( [ (1,3), (2,4)(5,6) ] )
[ [ 0, 1, 0, 0 ] ]
Symmetry type S9
Group( [ (2,4), (1,3), (1,2)(3,4) ] )
[ [ 0, 0, 0, 1 ] ]
Symmetry type S10
Group( [ (2,4), (1,3), (1,2)(3,4)(5,6) ] )
[ [ 1, 0, 0, 0 ] ]
Symmetry type S11
Group( [ (1,2,3,4), (1,2)(3,4), (5,6) ] )
[ ]
Symmetry type S1 [ 1, 1 ]
Representation 1, dimension of U_i = 1
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ]
isotropy subgroups [ 1 ], maximals
Possible jumps from S1 [ ]
Symmetry type S2 [ 2, 1 ]
Representation 1, dimension of U_i = 1
2, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 2 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ] ]
2, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ] ]
isotropy subgroups [ 1, 2 ], maximals 1
Possible jumps from S2 [ 1 ]
Symmetry type S3 [ 2, 1 ]
Representation 1, dimension of U_i = 1
3, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 0, 0 ], [ 0, 0, 1, 1 ] ]
isotropy subgroups [ 3 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, -1, 0, 0 ], [ 0, 0, 1, -1 ] ]
3, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 0, 0 ], [ 0, 0, 1, -1 ] ]
isotropy subgroups [ 1, 3 ], maximals 1
Possible jumps from S3 [ 1 ]
Symmetry type S4 [ 2, 1 ]
Representation 1, dimension of U_i = 1
4, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 0, 0 ], [ 0, 0, 1, -1 ] ]
isotropy subgroups [ 4 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 1, 0, 0 ], [ 0, 0, 1, 1 ] ]
4, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 0, 0 ], [ 0, 0, 1, 1 ] ]
isotropy subgroups [ 1, 4 ], maximals 1
Possible jumps from S4 [ 1 ]
Symmetry type S5 [ 2, 1 ]
Representation 1, dimension of U_i = 1
5, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 1 ], [ 0, 0, 1, 0 ] ]
isotropy subgroups [ 5 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
5, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 1, 5 ], maximals 1
Possible jumps from S5 [ 1 ]
Symmetry type S6 [ 4, 2 ]
Representation 1, dimension of U_i = 1
6, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ] ]
isotropy subgroups [ 6 ], maximals
Representation 2, dimension of U_i = 1
5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ] ]
6, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ] ]
isotropy subgroups [ 5, 6 ], maximals 5
Representation 3, dimension of U_i = 1
5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
6, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 5, 6 ], maximals 5
Possible jumps from S6 [ 5, 5 ]
Symmetry type S7 [ 4, 2 ]
Representation 1, dimension of U_i = 1
7, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, -1, -1 ] ]
isotropy subgroups [ 7 ], maximals
Representation 2, dimension of U_i = 1
3, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
7, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
isotropy subgroups [ 3, 7 ], maximals 3
Representation 3, dimension of U_i = 1
2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, -1, -1, 1 ] ]
7, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, -1, 1 ] ]
isotropy subgroups [ 2, 7 ], maximals 2
Representation 4, dimension of U_i = 1
4, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
7, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
isotropy subgroups [ 4, 7 ], maximals 4
Possible jumps from S7 [ 2, 3, 4 ]
Symmetry type S8 [ 4, 2 ]
Representation 1, dimension of U_i = 1
8, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ] ]
isotropy subgroups [ 8 ], maximals
Representation 2, dimension of U_i = 1
5, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ] ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, 1, 0 ], [ 0, 1, 0, 1 ] ]
isotropy subgroups [ 5, 8 ], maximals 5
Representation 4, dimension of U_i = 1
2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 2, 8 ], maximals 2
Possible jumps from S8 [ 2, 5 ]
Symmetry type S9 [ 8, 3 ]
Representation 1, dimension of U_i = 1
9, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
isotropy subgroups [ 9 ], maximals
Representation 3, dimension of U_i = 1
6, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
isotropy subgroups [ 6, 9 ], maximals 6
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
3, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 1, 3, 5, 9 ], maximals 3 5
Possible jumps from S9 [ 3, 5, 6 ]
Symmetry type S10 [ 8, 3 ]
Representation 1, dimension of U_i = 1
10, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
isotropy subgroups [ 10 ], maximals
Representation 3, dimension of U_i = 1
6, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
isotropy subgroups [ 6, 10 ], maximals 6
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
4, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 1, 4, 5, 10 ], maximals 4 5
Possible jumps from S10 [ 4, 5, 6 ]
Symmetry type S11 [ 16, 11 ]
Representation 5, dimension of U_i = 1
9, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 1, 1, 1 ] ]
isotropy subgroups [ 9, 11 ], maximals 9
Representation 6, dimension of U_i = 1
10, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, -1, 1, -1 ] ]
isotropy subgroups [ 10, 11 ], maximals 10
Representation 9, dimension of U_i = 2
2, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
8, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
7, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
Base for P(Psi) [ [ 1, 0, -1, 0 ], [ 0, 1, 0, -1 ] ]
isotropy subgroups [ 2, 7, 8, 11 ], maximals 7 8
Possible jumps from S11 [ 7, 8, 9, 10 ]
Possible jumps from S1 [ ]
Possible jumps from S2 [ 1 ]
Possible jumps from S3 [ 1 ]
Possible jumps from S4 [ 1 ]
Possible jumps from S5 [ 1 ]
Possible jumps from S6 [ 5, 5 ]
Possible jumps from S7 [ 2, 3, 4 ]
Possible jumps from S8 [ 2, 5 ]
Possible jumps from S9 [ 3, 5, 6 ]
Possible jumps from S10 [ 4, 5, 6 ]
Possible jumps from S11 [ 7, 8, 9, 10 ]