=================================================
Snow
1
[ 1 .. 12 ] Group( () ) [ 1, 1 ]
2
[ 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6 ] Group( [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 2, 1 ]
3
[ 1, 2, 3, 4, 5, 6, -1, -2, -3, -4, -5, -6 ] Group( [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 2, 1 ]
4
[ 1, 1, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 11, 11 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12) ] ) [ 2, 1 ]
[ 1, 2, 3, 3, 2, 1, 7, 8, 9, 9, 8, 7 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10) ] ) [ 2, 1 ]
5
[ 1, 2, -2, -1, 5, 6, 7, 8, -8, -7, -6, -5 ] Group( [ ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,14) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, -6, -5, -4, -3, -2, -1 ] Group( [ ( 1,12)( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,14) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, -4, -3, -2, -1, 9, 10, -10, -9 ] Group( [ ( 1, 8)( 2, 7)( 3, 6)( 4, 5)( 9,12)(10,11)(13,14) ] ) [ 2, 1 ]
6
[ 1, -1, 3, 4, 5, 6, 7, -7, -6, -5, -4, -3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, -5, -4, -3, -2, -1, 11, -11 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12)(13,14) ] ) [ 2, 1 ]
[ 1, 2, 3, -3, -2, -1, 7, 8, 9, -9, -8, -7 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10)(13,14) ] ) [ 2, 1 ]
7
[ 1, 2, 2, 1, 5, 6, 7, 8, 8, 7, 6, 5 ] Group( [ ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1,12)( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 4, 3, 2, 1, 9, 10, 10, 9 ] Group( [ ( 1, 8)( 2, 7)( 3, 6)( 4, 5)( 9,12)(10,11) ] ) [ 2, 1 ]
8
[ 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12) ] ) [ 3, 1 ]
9
[ 1, -1, 3, 4, -4, -3, 1, -1, 3, 4, -4, -3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
[ 1, 2, -2, -1, 5, -5, 1, 2, -2, -1, 5, -5 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
[ 1, 2, 3, -3, -2, -1, 1, 2, 3, -3, -2, -1 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
10
[ 1, 1, 3, 4, 4, 3, 1, 1, 3, 4, 4, 3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
[ 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
[ 1, 2, 3, 3, 2, 1, 1, 2, 3, 3, 2, 1 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 4, 2 ]
11
[ 1, 1, 3, 4, -4, -3, -1, -1, -3, -4, 4, 3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
[ 1, 2, -2, -1, 5, 5, -1, -2, 2, 1, -5, -5 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
[ 1, 2, 3, 3, 2, 1, -1, -2, -3, -3, -2, -1 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
12
[ 1, -1, 3, 4, 4, 3, -1, 1, -3, -4, -4, -3 ] Group( [ ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
[ 1, 2, 2, 1, 5, -5, -1, -2, -2, -1, -5, 5 ] Group( [ ( 1,10)( 2, 9)( 3, 8)( 4, 7)( 5, 6)(11,12)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
[ 1, 2, 3, -3, -2, -1, -1, -2, -3, 3, 2, 1 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10)(13,14), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 4, 2 ]
13
[ 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8) ] ) [ 6, 1 ]
14
[ 1, -1, 3, -3, 1, -1, 3, -3, 1, -1, 3, -3 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14) ] ) [ 6, 1 ]
15
[ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9) ] ) [ 6, 1 ]
16
[ 1, 2, -2, -1, 1, 2, -2, -1, 1, 2, -2, -1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,14) ] ) [ 6, 1 ]
17
[ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12) ] ) [ 6, 2 ]
18
[ 1, 2, -1, -2, 1, 2, -1, -2, 1, 2, -1, -2 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,14) ] ) [ 6, 2 ]
19
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9) ] ) [ 12, 4 ]
20
[ 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,14) ] ) [ 12, 4 ]
21
[ 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9) ] ) [ 12, 4 ]
22
[ 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1 ] Group( [ ( 1, 5, 9)( 2, 6,10)( 3, 7,11)( 4, 8,12), ( 1, 2)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(13,14), ( 1, 4)( 2, 3)( 5,12)( 6,11)( 7,10)( 8, 9)(13,14) ] ) [ 12, 4 ]
23
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Group( [ ( 1, 3, 5, 7, 9,11)( 2, 4, 6, 8,10,12), ( 1, 6)( 2, 5)( 3, 4)( 7,12)( 8,11)( 9,10), (13,14) ] ) [ 24, 14 ]
Subgroup structure
[ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23 ],
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1 ],
[ 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1 ],
[ 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 5, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1 ],
[ 6, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ],
[ 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1 ],
[ 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1 ],
[ 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1 ],
[ 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1 ],
[ 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1 ],
[ 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1 ],
[ 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 ],
[ 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 ],
[ 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ] ]
Symmetry type S1 [ 1, 1 ]
Representation 1, dimension of U_i = 1
1, dim Fix_P(U) K = 12, dim Fix_U_i K = 1, N_H(K)/K [ 1, 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 = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
2, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 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 = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
3, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 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 = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 4 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
4, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 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 = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 5 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
5, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 5 ], maximals 1
Possible jumps from S5 [ 1 ]
Symmetry type S6 [ 2, 1 ]
Representation 1, dimension of U_i = 1
6, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 6 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 6 ], maximals 1
Possible jumps from S6 [ 1 ]
Symmetry type S7 [ 2, 1 ]
Representation 1, dimension of U_i = 1
7, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7 ], maximals
Representation 2, dimension of U_i = 1
1, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
7, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 7 ], maximals 1
Possible jumps from S7 [ 1 ]
Symmetry type S8 [ 3, 1 ]
Representation 1, dimension of U_i = 1
8, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8 ], maximals
Representation 2, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 8 ], maximals 1
Representation 3, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 8 ], maximals 1
Possible jumps from S8 [ 1, 1 ]
Symmetry type S9 [ 4, 2 ]
Representation 1, dimension of U_i = 1
9, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 9 ], maximals
Representation 2, dimension of U_i = 1
6, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 6, 9 ], maximals 6
Representation 3, dimension of U_i = 1
2, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 9 ], maximals 2
Representation 4, dimension of U_i = 1
5, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 5, 9 ], maximals 5
Possible jumps from S9 [ 2, 5, 6 ]
Symmetry type S10 [ 4, 2 ]
Representation 1, dimension of U_i = 1
10, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 10 ], maximals
Representation 2, dimension of U_i = 1
4, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 4, 10 ], maximals 4
Representation 3, dimension of U_i = 1
2, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 10 ], maximals 2
Representation 4, dimension of U_i = 1
7, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7, 10 ], maximals 7
Possible jumps from S10 [ 2, 4, 7 ]
Symmetry type S11 [ 4, 2 ]
Representation 1, dimension of U_i = 1
11, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 11 ], maximals
Representation 2, dimension of U_i = 1
4, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 4, 11 ], maximals 4
Representation 3, dimension of U_i = 1
3, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 11 ], maximals 3
Representation 4, dimension of U_i = 1
5, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 5, 11 ], maximals 5
Possible jumps from S11 [ 3, 4, 5 ]
Symmetry type S12 [ 4, 2 ]
Representation 1, dimension of U_i = 1
12, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 12 ], maximals
Representation 2, dimension of U_i = 1
6, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 6, 12 ], maximals 6
Representation 3, dimension of U_i = 1
3, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 12 ], maximals 3
Representation 4, dimension of U_i = 1
7, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7, 12 ], maximals 7
Possible jumps from S12 [ 3, 6, 7 ]
Symmetry type S13 [ 6, 1 ]
Representation 1, dimension of U_i = 1
13, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 13 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
13, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 13 ], maximals 8
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
4, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
13, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 4, 13 ], maximals 4
Possible jumps from S13 [ 4, 8 ]
Symmetry type S14 [ 6, 1 ]
Representation 1, dimension of U_i = 1
14, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 14 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
14, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 14 ], maximals 8
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
6, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
14, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 6, 14 ], maximals 6
Possible jumps from S14 [ 6, 8 ]
Symmetry type S15 [ 6, 1 ]
Representation 1, dimension of U_i = 1
15, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 15 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
15, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 15 ], maximals 8
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
7, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
15, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 7, 15 ], maximals 7
Possible jumps from S15 [ 7, 8 ]
Symmetry type S16 [ 6, 1 ]
Representation 1, dimension of U_i = 1
16, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 16 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
16, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 16 ], maximals 8
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
5, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
16, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 5, 16 ], maximals 5
Possible jumps from S16 [ 5, 8 ]
Symmetry type S17 [ 6, 2 ]
Representation 1, dimension of U_i = 1
17, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 17 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
17, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 17 ], maximals 8
Representation 3, dimension of U_i = 1
NON-REAL projection
2, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
17, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 17 ], maximals 2
Representation 4, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 6, 2 ]
17, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 17 ], maximals 1
Representation 5, dimension of U_i = 1
NON-REAL projection
2, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
17, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 17 ], maximals 2
Representation 6, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 6, 2 ]
17, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 17 ], maximals 1
Possible jumps from S17 [ 1, 1, 2, 2, 8 ]
Symmetry type S18 [ 6, 2 ]
Representation 1, dimension of U_i = 1
18, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 18 ], maximals
Representation 2, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
18, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8, 18 ], maximals 8
Representation 3, dimension of U_i = 1
NON-REAL projection
3, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
18, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 18 ], maximals 3
Representation 4, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 6, 2 ]
18, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 18 ], maximals 1
Representation 5, dimension of U_i = 1
NON-REAL projection
3, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
18, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 18 ], maximals 3
Representation 6, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 6, 2 ]
18, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 18 ], maximals 1
Possible jumps from S18 [ 1, 1, 3, 3, 8 ]
Symmetry type S19 [ 12, 4 ]
Representation 1, dimension of U_i = 1
19, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 19 ], maximals
Representation 2, dimension of U_i = 1
15, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
19, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 15, 19 ], maximals 15
Representation 3, dimension of U_i = 1
13, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
19, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 13, 19 ], maximals 13
Representation 4, dimension of U_i = 1
17, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
19, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 17, 19 ], maximals 17
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
4, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
19, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 4, 7, 19 ], maximals 4 7
Representation 6, dimension of U_i = 2
2, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
10, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
19, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 10, 19 ], maximals 10
Possible jumps from S19 [ 4, 7, 10, 13, 15, 17 ]
Symmetry type S20 [ 12, 4 ]
Representation 1, dimension of U_i = 1
20, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 20 ], maximals
Representation 2, dimension of U_i = 1
16, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 16, 20 ], maximals 16
Representation 3, dimension of U_i = 1
13, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 13, 20 ], maximals 13
Representation 4, dimension of U_i = 1
18, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 18, 20 ], maximals 18
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
5, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
4, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 4, 5, 20 ], maximals 4 5
Representation 6, dimension of U_i = 2
3, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
11, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 11, 20 ], maximals 11
Possible jumps from S20 [ 4, 5, 11, 13, 16, 18 ]
Symmetry type S21 [ 12, 4 ]
Representation 1, dimension of U_i = 1
21, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 21 ], maximals
Representation 2, dimension of U_i = 1
15, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 15, 21 ], maximals 15
Representation 3, dimension of U_i = 1
14, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 14, 21 ], maximals 14
Representation 4, dimension of U_i = 1
18, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 18, 21 ], maximals 18
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 6, 7, 21 ], maximals 6 7
Representation 6, dimension of U_i = 2
3, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
12, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 12, 21 ], maximals 12
Possible jumps from S21 [ 6, 7, 12, 14, 15, 18 ]
Symmetry type S22 [ 12, 4 ]
Representation 1, dimension of U_i = 1
22, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 22 ], maximals
Representation 2, dimension of U_i = 1
16, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
22, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 16, 22 ], maximals 16
Representation 3, dimension of U_i = 1
14, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
22, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 14, 22 ], maximals 14
Representation 4, dimension of U_i = 1
17, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
22, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 17, 22 ], maximals 17
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
5, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
22, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 5, 6, 22 ], maximals 5 6
Representation 6, dimension of U_i = 2
2, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
9, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
22, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 9, 22 ], maximals 9
Possible jumps from S22 [ 5, 6, 9, 14, 16, 17 ]
Symmetry type S23 [ 24, 14 ]
Representation 5, dimension of U_i = 1
19, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 19, 23 ], maximals 19
Representation 6, dimension of U_i = 1
20, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 20, 23 ], maximals 20
Representation 7, dimension of U_i = 1
22, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 22, 23 ], maximals 22
Representation 8, dimension of U_i = 1
21, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 21, 23 ], maximals 21
Representation 9, dimension of U_i = 2
2, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
10, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
9, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 2, 9, 10, 23 ], maximals 9 10
Representation 10, dimension of U_i = 2
3, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
11, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
12, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
23, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 11, 12, 23 ], maximals 11 12
Possible jumps from S23 [ 9, 10, 11, 12, 19, 20, 21, 22 ]
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 [ 1 ]
Possible jumps from S7 [ 1 ]
Possible jumps from S8 [ 1, 1 ]
Possible jumps from S9 [ 2, 5, 6 ]
Possible jumps from S10 [ 2, 4, 7 ]
Possible jumps from S11 [ 3, 4, 5 ]
Possible jumps from S12 [ 3, 6, 7 ]
Possible jumps from S13 [ 4, 8 ]
Possible jumps from S14 [ 6, 8 ]
Possible jumps from S15 [ 7, 8 ]
Possible jumps from S16 [ 5, 8 ]
Possible jumps from S17 [ 1, 1, 2, 2, 8 ]
Possible jumps from S18 [ 1, 1, 3, 3, 8 ]
Possible jumps from S19 [ 4, 7, 10, 13, 15, 17 ]
Possible jumps from S20 [ 4, 5, 11, 13, 16, 18 ]
Possible jumps from S21 [ 6, 7, 12, 14, 15, 18 ]
Possible jumps from S22 [ 5, 6, 9, 14, 16, 17 ]
Possible jumps from S23 [ 9, 10, 11, 12, 19, 20, 21, 22 ]