================================================= C4 [ [ -1, 1, -1, 1 ], [ 0, -1, 0, 1 ], [ -1, 0, 1, 0 ], [ 1, 1, 1, 1 ] ] 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 ] ] 4 11 1 1 2 2 2 1 2 2 1 1 1 1 2 2 2 2 4 4 4 8 8 16 1 2 3 4 1 2 3 4 -3 -4 -1 -2 1 2 3 4 2 1 4 3 1 2 3 4 4 3 2 1 1 2 3 4 -2 -1 -4 -3 1 2 3 4 -4 -3 -2 -1 1 2 3 4 1 4 3 2 1 2 3 4 3 2 1 4 1 2 3 4 3 2 1 4 1 4 3 2 3 4 1 2 1 2 3 4 2 1 4 3 -3 -4 -1 -2 -4 -3 -2 -1 1 2 3 4 4 3 2 1 -3 -4 -1 -2 -2 -1 -4 -3 1 2 3 4 -3 -2 -1 -4 1 4 3 2 -3 -4 -1 -2 1 2 3 4 -1 -4 -3 -2 3 2 1 4 -3 -4 -1 -2 1 2 3 4 3 2 1 4 4 3 2 1 4 1 2 3 1 4 3 2 3 4 1 2 2 3 4 1 2 1 4 3 1 2 3 4 -4 -3 -2 -1 3 2 1 4 -4 -1 -2 -3 1 4 3 2 -2 -3 -4 -1 3 4 1 2 -2 -1 -4 -3 1 2 3 4 2 3 4 1 3 4 1 2 4 1 2 3 1 4 3 2 4 3 2 1 3 2 1 4 2 1 4 3 -1 -2 -3 -4 -2 -3 -4 -1 -3 -4 -1 -2 -4 -1 -2 -3 -1 -4 -3 -2 -4 -3 -2 -1 -3 -2 -1 -4 -2 -1 -4 -3 Symmetry H=H1, Symmetry type S1, Id(H)=[ 1, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1 ], maximals , factor group id(H/H')=[ 1, 1 ] Jumps from H1 to H[ ] Typejumps from S1 to S[ ] Symmetry H=H2, Symmetry type S2, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H2, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H2, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 2 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H2 to H[ 1 ] Typejumps from S2 to S[ 1 ] Symmetry H=H3, Symmetry type S3, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H3, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 3 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H3, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 3 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H3 to H[ 1 ] Typejumps from S3 to S[ 1 ] Symmetry H=H4, Symmetry type S3, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H4, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 4 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H4, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 4 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H4 to H[ 1 ] Typejumps from S3 to S[ 1 ] Symmetry H=H5, Symmetry type S4, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H5, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 5 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H5, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 5 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H5 to H[ 1 ] Typejumps from S4 to S[ 1 ] Symmetry H=H6, Symmetry type S4, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H6, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 6 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H6, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 6 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H6 to H[ 1 ] Typejumps from S4 to S[ 1 ] Symmetry H=H7, Symmetry type S5, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H7, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 7 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H7, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 7 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H7 to H[ 1 ] Typejumps from S5 to S[ 1 ] Symmetry H=H8, Symmetry type S5, Id(H)=[ 2, 1 ] Representation 1, dimension of irred subspace U_i = 1 K=H8, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 8 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H1, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 8 ], maximals 1 , factor group id(H/H')=[ 2, 1 ] Jumps from H8 to H[ 1 ] Typejumps from S5 to S[ 1 ] Symmetry H=H9, Symmetry type S6, Id(H)=[ 4, 2 ] Representation 1, dimension of irred subspace U_i = 1 K=H9, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 9 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H7, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 7, 9 ], maximals 7 , factor group id(H/H')=[ 2, 1 ] Representation 3, dimension of irred subspace U_i = 1 K=H8, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H9, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 8, 9 ], maximals 8 , factor group id(H/H')=[ 2, 1 ] Jumps from H9 to H[ 7, 8 ] Typejumps from S6 to S[ 5, 5 ] Symmetry H=H10, Symmetry type S7, Id(H)=[ 4, 2 ] Representation 1, dimension of irred subspace U_i = 1 K=H10, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 10 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H3, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 3, 10 ], maximals 3 , factor group id(H/H')=[ 2, 1 ] Representation 3, dimension of irred subspace U_i = 1 K=H2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2, 10 ], maximals 2 , factor group id(H/H')=[ 2, 1 ] Representation 4, dimension of irred subspace U_i = 1 K=H6, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H10, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 6, 10 ], maximals 6 , factor group id(H/H')=[ 2, 1 ] Jumps from H10 to H[ 2, 3, 6 ] Typejumps from S7 to S[ 2, 3, 4 ] Symmetry H=H11, Symmetry type S7, Id(H)=[ 4, 2 ] Representation 1, dimension of irred subspace U_i = 1 K=H11, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 11 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H4, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 4, 11 ], maximals 4 , factor group id(H/H')=[ 2, 1 ] Representation 3, dimension of irred subspace U_i = 1 K=H2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2, 11 ], maximals 2 , factor group id(H/H')=[ 2, 1 ] Representation 4, dimension of irred subspace U_i = 1 K=H5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 5, 11 ], maximals 5 , factor group id(H/H')=[ 2, 1 ] Jumps from H11 to H[ 2, 4, 5 ] Typejumps from S7 to S[ 2, 3, 4 ] Symmetry H=H12, Symmetry type S8, Id(H)=[ 4, 2 ] Representation 1, dimension of irred subspace U_i = 1 K=H12, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 12 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H7, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 7, 12 ], maximals 7 , factor group id(H/H')=[ 2, 1 ] Representation 4, dimension of irred subspace U_i = 1 K=H2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2, 12 ], maximals 2 , factor group id(H/H')=[ 2, 1 ] Jumps from H12 to H[ 2, 7 ] Typejumps from S8 to S[ 2, 5 ] Symmetry H=H13, Symmetry type S8, Id(H)=[ 4, 2 ] Representation 1, dimension of irred subspace U_i = 1 K=H13, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 13 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 2, dimension of irred subspace U_i = 1 K=H8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H13, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 8, 13 ], maximals 8 , factor group id(H/H')=[ 2, 1 ] Representation 4, dimension of irred subspace U_i = 1 K=H2, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H13, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2, 13 ], maximals 2 , factor group id(H/H')=[ 2, 1 ] Jumps from H13 to H[ 2, 8 ] Typejumps from S8 to S[ 2, 5 ] Symmetry H=H14, Symmetry type S9, Id(H)=[ 8, 3 ] Representation 1, dimension of irred subspace U_i = 1 K=H14, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 14 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 3, dimension of irred subspace U_i = 1 K=H9, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H14, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 9, 14 ], maximals 9 , factor group id(H/H')=[ 2, 1 ] Representation 5, dimension of irred subspace U_i = 2 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, id(N_H(K)/K)=[ 8, 3 ] K=H7, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H3, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H14, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 3, 7, 14 ], maximals 3 7 , factor group id(H/H')=[ 8, 3 ] Jumps from H14 to H[ 3, 7, 9 ] Typejumps from S9 to S[ 3, 5, 6 ] Symmetry H=H15, Symmetry type S10, Id(H)=[ 8, 3 ] Representation 1, dimension of irred subspace U_i = 1 K=H15, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 15 ], maximals , factor group id(H/H')=[ 1, 1 ] Representation 3, dimension of irred subspace U_i = 1 K=H9, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H15, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 9, 15 ], maximals 9 , factor group id(H/H')=[ 2, 1 ] Representation 5, dimension of irred subspace U_i = 2 K=H1, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, id(N_H(K)/K)=[ 8, 3 ] K=H7, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H15, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 1, 5, 7, 15 ], maximals 5 7 , factor group id(H/H')=[ 8, 3 ] Jumps from H15 to H[ 5, 7, 9 ] Typejumps from S10 to S[ 4, 5, 6 ] Symmetry H=H16, Symmetry type S11, Id(H)=[ 16, 11 ] Representation 5, dimension of irred subspace U_i = 1 K=H14, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H16, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 14, 16 ], maximals 14 , factor group id(H/H')=[ 2, 1 ] Representation 6, dimension of irred subspace U_i = 1 K=H15, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H16, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 15, 16 ], maximals 15 , factor group id(H/H')=[ 2, 1 ] Representation 9, dimension of irred subspace U_i = 2 K=H2, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, id(N_H(K)/K)=[ 8, 3 ] K=H13, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H11, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, id(N_H(K)/K)=[ 2, 1 ] K=H16, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, id(N_H(K)/K)=[ 1, 1 ] isotropy subgroups H[ 2, 11, 13, 16 ], maximals 11 13 , factor group id(H/H')=[ 8, 3 ] Jumps from H16 to H[ 11, 13, 14, 15 ] Typejumps from S11 to S[ 7, 8, 9, 10 ] fromH : fromS : toK size(N_H(K)/K) ... 1 : 1 : 2 : 2 : 1 2 3 : 3 : 1 2 4 : 3 : 1 2 5 : 4 : 1 2 6 : 4 : 1 2 7 : 5 : 1 2 8 : 5 : 1 2 9 : 6 : 7 2 8 2 10 : 7 : 2 2 3 2 6 2 11 : 7 : 2 2 4 2 5 2 12 : 8 : 2 2 7 2 13 : 8 : 2 2 8 2 14 : 9 : 3 2 7 2 9 2 15 : 10 : 5 2 7 2 9 2 16 : 11 : 11 2 13 2 14 2 15 2 fromH toK size(N_H(K)/K) ... one from each type 1 2 1 2 3 1 2 4 1 2 5 1 2 6 1 2 7 1 2 8 1 2 9 7 2 10 2 2 3 2 6 2 11 2 2 4 2 5 2 12 2 2 7 2 13 2 2 8 2 14 3 2 7 2 9 2 15 5 2 7 2 9 2 16 11 2 13 2 14 2 15 2 fromS : toS size(N_H(K)/K) id(H/H')... 1 : 2 : 1 2 Z2 3 : 1 2 Z2 4 : 1 2 Z2 5 : 1 2 Z2 6 : 5 2 Z2 7 : 2 2 Z2 3 2 Z2 4 2 Z2 8 : 2 2 Z2 5 2 Z2 9 : 3 2 D4 5 2 D4 6 2 Z2 10 : 4 2 D4 5 2 D4 6 2 Z2 11 : 7 2 D4 8 2 D4 9 2 Z2 10 2 Z2 Typejumps from S1 to S[ ] Typejumps from S2 to S[ 1 ] Typejumps from S3 to S[ 1 ] Typejumps from S3 to S[ 1 ] Typejumps from S4 to S[ 1 ] Typejumps from S4 to S[ 1 ] Typejumps from S5 to S[ 1 ] Typejumps from S5 to S[ 1 ] Typejumps from S6 to S[ 5, 5 ] Typejumps from S7 to S[ 2, 3, 4 ] Typejumps from S7 to S[ 2, 3, 4 ] Typejumps from S8 to S[ 2, 5 ] Typejumps from S8 to S[ 2, 5 ] Typejumps from S9 to S[ 3, 5, 6 ] Typejumps from S10 to S[ 4, 5, 6 ] Typejumps from S11 to S[ 7, 8, 9, 10 ]