\\ Left Cell Data for F4 (CC 2012, B. Binegar) \\ \\ This file contains a table of data for the 72 left cells of the Weyl \\ group W of F4. Each line below corresponds to a particular left cell \\ of W. The datums held in the (colon-delimited) columns are as follows: \\ Column Contents \\ 1 KLatlas index (order of discovery by KLatlas, counting from 0) \\ 2 number of Weyl group elements in the left cell \\ 3 Weyl group elements contained in the left cell (as enumerated by KLatlas, counting from 0) \\ 4 KLatlas indices of the left cells immediately below the left cell in the W-graph of W \\ 5 representation of W carried by left cell (in terms of partitions for the classical Weyl groups and \\ or R. Carter's notation for the irreducible representations of the exceptional Weyl groups) \\ 6 special representation of W attached to the cell \\ 7 special nilpotent orbit attached to the left cell (in terms of partitions for the nilpotent orbits of \\ classical groups or Bala-Carter notation for the nilpotent orbits of the exceptional groups \\ 8 KLatlas block index of the unique Duflo involution contained in the left cell \\ 9 KLatlas cell index of the unique Duflo involution contained in the left cell \\ 10 reduced word expression for the unique Duflo involution contained in the left cell \\ 11 A-value of the unique Duflo involution contained in the left cell \\ 12 tau-infinity invariant of primitive ideal attached to the left cell \\ 0 : 72 : 0 : [0, 0] : phi[1,0] : phi[1,0] : F4 : 0 : 0 : e : 0 : [{{}}, {}, {}, {}, {}] 1 : 72 : 1 : [1, 0] : phi[2,4,2]+phi[4,1] : phi[4,1] : F4(a1) : 1 : 0 : 4 : 1 : [{{4}}, {{3}}, {{2}, {4}}, {{1}, {3}}, {{2}, {4}}] 2 : 72 : 2 : [2, 0] : phi[2,4,2]+phi[4,1] : phi[4,1] : F4(a1) : 2 : 0 : 3 : 1 : [{{3}}, {{2}, {4}}, {{1}, {3}}, {{2}, {4}}, {{1}, {3}}] 3 : 72 : 3 : [3, 0] : phi[2,4,1]+phi[4,1] : phi[4,1] : F4(a1) : 3 : 0 : 2 : 1 : [{{2}}, {{1}, {3}}, {{2}, {4}}, {{1}, {3}}, {{2}, {4}}] 4 : 72 : 4 : [4, 0] : phi[2,4,1]+phi[4,1] : phi[4,1] : F4(a1) : 4 : 0 : 1 : 1 : [{{1}}, {{2}}, {{1}, {3}}, {{2}, {4}}, {{1}, {3}}] 5 : 72 : 8 : [5, 0] : phi[9,2] : phi[9,2] : F4(a2) : 8 : 0 : 24 : 2 : [{{2, 4}}, {{2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}] 6 : 72 : 11 : [6, 0] : phi[9,2] : phi[9,2] : F4(a2) : 11 : 0 : 14 : 2 : [{{1, 4}}, {{1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}] 7 : 72 : 12 : [7, 0] : phi[9,2] : phi[9,2] : F4(a2) : 12 : 0 : 13 : 2 : [{{1, 3}}, {{1}, {2}, {3}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}] 8 : 72 : 33 : [8, 1] : phi[9,2] : phi[9,2] : F4(a2) : 33 : 1 : 3243 : 2 : [{{3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}] 9 : 72 : 199 : [9, 5] : phi[9,2] : phi[9,2] : F4(a2) : 199 : 5 : 43213234 : 2 : [{{4}}, {{3}}, {{2}, {4}}, {{3}, {1, 3}}, {{1}, {2}, {3}, {4}, {1, 4}}] 10 : 72 : 15 : [10, 0] : phi[8,3,2] : phi[8,3,2] : B3 : 15 : 0 : 343 : 3 : [{{3, 4}}, {{3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}] 11 : 72 : 44 : [11, 1] : phi[9,2] : phi[9,2] : F4(a2) : 44 : 1 : 2132 : 2 : [{{2}}, {{3}, {1, 3}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}] 12 : 72 : 254 : [12, 6] : phi[9,2] : phi[9,2] : F4(a2) : 254 : 6 : 12324321 : 2 : [{{1}}, {{2}}, {{1}, {3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}] 13 : 72 : 29 : [13, 0] : phi[8,3,1] : phi[8,3,1] : C3 : 29 : 0 : 121 : 3 : [{{1, 2}}, {{2}, {1, 3}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}] 14 : 72 : 106 : [14, 3] : phi[9,2] : phi[9,2] : F4(a2) : 106 : 3 : 232432 : 2 : [{{2}}, {{1}, {3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}] 15 : 72 : 66 : [15, 1] : phi[8,3,2] : phi[8,3,2] : B3 : 66 : 1 : 23432 : 3 : [{{2, 4}}, {{2}, {3}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}] 16 : 72 : 101 : [16, 3] : phi[9,2] : phi[9,2] : F4(a2) : 101 : 3 : 321323 : 2 : [{{3}}, {{2}, {4}}, {{3}, {1, 3}}, {{1}, {2}, {3}, {4}, {1, 4}}, {{2}, {3}, {1, 3}, {2, 4}}] 17 : 72 : 148 : [17, 2] : phi[8,3,2] : phi[8,3,2] : B3 : 148 : 2 : 3234323 : 3 : [{{3}}, {{2, 4}}, {{2}, {3}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}] 18 : 72 : 477 : [18, 5] : phi[8,3,2] : phi[8,3,2] : B3 : 477 : 5 : 21323432132 : 3 : [{{2}}, {{3}, {1, 3}}, {{2}, {3}, {4}, {1, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}] 19 : 72 : 171 : [19, 2] : phi[8,3,1] : phi[8,3,1] : C3 : 171 : 2 : 2132132 : 3 : [{{2}}, {{1, 3}}, {{2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}] 20 : 72 : 444 : [20, 5] : phi[8,3,1] : phi[8,3,1] : C3 : 444 : 5 : 32143213243 : 3 : [{{3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {1, 4}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}] 21 : 72 : 635 : [21, 6] : phi[8,3,2] : phi[8,3,2] : B3 : 635 : 6 : 3213234321323 : 3 : [{{3}}, {{2}, {4}}, {{3}, {1, 3}}, {{2}, {3}, {4}, {1, 4}}, {{3}, {1, 3}, {2, 4}}] 22 : 72 : 643 : [22, 6] : phi[8,3,1] : phi[8,3,1] : C3 : 643 : 6 : 2321432132432 : 3 : [{{2}}, {{1}, {3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {1, 4}}, {{2}, {1, 3}, {2, 4}}] 23 : 72 : 41 : [23, 0] : phi[4,8]+phi[6,6,2]+phi[9,6,1]+phi[9,6,2]+phi[12,4]+2*phi[16,5] : phi[12,4] : F4(a3) : 41 : 0 : 2323 : 4 : [{{2, 3}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 24 : 72 : 185 : [24, 3] : phi[8,3,2] : phi[8,3,2] : B3 : 185 : 3 : 1234321 : 3 : [{{1, 4}}, {{1, 3}, {2, 4}}, {{2}, {3}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}] 25 : 72 : 173 : [25, 3] : phi[8,3,1] : phi[8,3,1] : C3 : 173 : 3 : 1432134 : 3 : [{{1, 4}}, {{1, 3}, {2, 4}}, {{2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}] 26 : 72 : 320 : [26, 4] : phi[8,3,2] : phi[8,3,2] : B3 : 320 : 4 : 132343213 : 3 : [{{1, 3}}, {{2}, {3}, {1, 4}}, {{3}, {1, 3}, {2, 4}}, {{2}, {3}, {4}, {1, 4}, {3, 4}}, {{3}, {1, 3}, {2, 4}}] 27 : 72 : 802 : [27, 7] : phi[8,3,2] : phi[8,3,2] : B3 : 802 : 7 : 432132343213234 : 3 : [{{4}}, {{3}}, {{2}, {4}}, {{3}, {1, 3}}, {{2}, {3}, {4}, {1, 4}}] 28 : 72 : 858 : [28, 7] : phi[8,3,1] : phi[8,3,1] : C3 : 858 : 7 : 123214321324321 : 3 : [{{1}}, {{2}}, {{1}, {3}}, {{2}, {2, 4}}, {{1}, {2}, {3}, {1, 4}}] 29 : 72 : 46 : [29, 0] : phi[4,7,2]+phi[6,6,1]+phi[9,6,2]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 46 : 0 : 1343 : 4 : [{{1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 30 : 72 : 300 : [30, 4] : phi[8,3,1] : phi[8,3,1] : C3 : 300 : 4 : 214321324 : 3 : [{{2, 4}}, {{2}, {3}, {1, 4}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}] 31 : 72 : 53 : [31, 0] : phi[4,7,1]+phi[6,6,1]+phi[9,6,1]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 53 : 0 : 1214 : 4 : [{{1, 2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 32 : 72 : 82 : [32, 1] : phi[8,3,1] : phi[8,3,1] : C3 : 82 : 1 : 13213 : 3 : [{{1, 3}}, {{2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}, {{1}, {2}, {3}, {1, 4}, {1, 2}}, {{2}, {1, 3}, {2, 4}}] 33 : 72 : 103 : [33, 1] : phi[4,8]+phi[6,6,2]+phi[9,6,1]+phi[9,6,2]+phi[12,4]+2*phi[16,5] : phi[12,4] : F4(a3) : 103 : 1 : 243234 : 4 : [{{2, 4}}, {{1, 4}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 34 : 72 : 133 : [34, 2] : phi[4,8]+phi[6,6,2]+phi[9,6,1]+phi[9,6,2]+phi[12,4]+2*phi[16,5] : phi[12,4] : F4(a3) : 133 : 2 : 123213 : 4 : [{{1, 3}}, {{1, 4}, {1, 2}, {2, 3}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 35 : 72 : 113 : [35, 1] : phi[4,7,2]+phi[6,6,1]+phi[9,6,2]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 113 : 1 : 213432 : 4 : [{{2, 4}}, {{2}, {3}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 36 : 72 : 123 : [36, 1] : phi[4,7,1]+phi[6,6,1]+phi[9,6,1]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 123 : 1 : 132143 : 4 : [{{1, 3}}, {{2}, {3}, {1, 2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 37 : 72 : 208 : [37, 5] : phi[1,12,2]+phi[4,7,2]+phi[6,6,2]+2*phi[9,6,2]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 208 : 5 : 32343234 : 4 : [{{3, 4}}, {{3}, {2, 4}}, {{1, 4}, {2, 4}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 38 : 72 : 251 : [38, 6] : phi[4,8]+phi[6,6,2]+phi[9,6,1]+phi[9,6,2]+phi[12,4]+2*phi[16,5] : phi[12,4] : F4(a3) : 251 : 6 : 12432134 : 4 : [{{1, 4}}, {{1, 3}, {2, 4}}, {{1, 4}, {1, 2}, {2, 3}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 39 : 72 : 269 : [39, 8] : phi[1,12,1]+phi[4,7,1]+phi[6,6,2]+2*phi[9,6,1]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 269 : 8 : 12132132 : 4 : [{{1, 2}}, {{2}, {1, 3}}, {{1, 3}, {1, 4}, {1, 2}, {2, 3}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}, {2, 3}, {3, 4}}] 40 : 72 : 210 : [40, 2] : phi[4,7,2]+phi[6,6,1]+phi[9,6,2]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 210 : 2 : 32134323 : 4 : [{{3}}, {{2, 4}}, {{2}, {3}, {1, 3, 4}}, {{1, 3}, {1, 4}, {2, 4}, {3, 4}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 41 : 72 : 232 : [41, 2] : phi[4,7,1]+phi[6,6,1]+phi[9,6,1]+phi[12,4]+phi[16,5] : phi[12,4] : F4(a3) : 232 : 2 : 21321432 : 4 : [{{2}}, {{1, 3}}, {{2}, {3}, {1, 2, 4}}, {{1, 3}, {1, 4}, {2, 4}, {1, 2}}, {{2}, {3}, {1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 42 : 72 : 294 : [42, 0] : phi[8,9,2] : phi[8,9,2] : A2 : 294 : 0 : 232343234 : 9 : [{{2, 3, 4}}, {{1, 3, 4}}, {{3, 4}, {1, 2, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}] 43 : 72 : 349 : [43, 0] : phi[8,9,1] : phi[8,9,1] : A2s : 349 : 0 : 121321323 : 9 : [{{1, 2, 3}}, {{1, 2, 4}}, {{1, 2}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}] 44 : 72 : 509 : [44, 1] : phi[8,9,2] : phi[8,9,2] : A2 : 509 : 1 : 12323432134 : 9 : [{{1, 3, 4}}, {{3, 4}, {1, 2, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}] 45 : 72 : 515 : [45, 1] : phi[8,9,1] : phi[8,9,1] : A2s : 515 : 1 : 12143213234 : 9 : [{{1, 2, 4}}, {{1, 2}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}] 46 : 72 : 708 : [46, 2] : phi[8,9,2] : phi[8,9,2] : A2 : 708 : 2 : 1213234321324 : 9 : [{{1, 2, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}] 47 : 72 : 673 : [47, 2] : phi[8,9,1] : phi[8,9,1] : A2s : 673 : 2 : 1321432132343 : 9 : [{{1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}] 48 : 72 : 852 : [48, 3] : phi[8,9,2] : phi[8,9,2] : A2 : 852 : 3 : 132132343213243 : 9 : [{{1, 3}}, {{2, 3}, {1, 2, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}] 49 : 72 : 830 : [49, 3] : phi[8,9,1] : phi[8,9,1] : A2s : 830 : 3 : 213214321323432 : 9 : [{{2, 4}}, {{2, 3}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}] 50 : 72 : 980 : [50, 5] : phi[8,9,2] : phi[8,9,2] : A2 : 980 : 5 : 13432132343213234 : 9 : [{{1, 3, 4}}, {{1, 3}, {2, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}] 51 : 72 : 979 : [51, 4] : phi[8,9,2] : phi[8,9,2] : A2 : 979 : 4 : 21321323432132432 : 9 : [{{2, 3}}, {{1, 3}, {2, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}] 52 : 72 : 1003 : [52, 5] : phi[8,9,1] : phi[8,9,1] : A2s : 1003 : 5 : 12132143213234321 : 9 : [{{1, 2, 4}}, {{1, 3}, {2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}] 53 : 72 : 966 : [53, 4] : phi[8,9,1] : phi[8,9,1] : A2s : 966 : 4 : 23213243213234323 : 9 : [{{2, 3}}, {{1, 3}, {2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}] 54 : 72 : 1069 : [54, 6] : phi[8,9,2] : phi[8,9,2] : A2 : 1069 : 6 : 2132432132343213234 : 9 : [{{2, 4}}, {{2, 3}, {3, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}] 55 : 72 : 1136 : [55, 7] : phi[8,9,1] : phi[8,9,1] : A2s : 1136 : 7 : 121321324321323432132 : 9 : [{{1, 2}}, {{1, 3}}, {{1, 2}, {2, 3}, {1, 2, 4}}, {{1, 3}, {2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}}] 56 : 72 : 951 : [56, 3] : phi[9,10] : phi[9,10] : A1+A1s : 951 : 3 : 1213213234321323 : 10 : [{{1, 2, 3}}, {{1, 3}, {1, 2, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}, {2, 3, 4}}] 57 : 72 : 1085 : [57, 6] : phi[8,9,1] : phi[8,9,1] : A2s : 1085 : 6 : 1232132432132343213 : 9 : [{{1, 3}}, {{1, 2}, {2, 3}, {1, 2, 4}}, {{1, 3}, {2, 4}}, {{1, 2}, {2, 3}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}] 58 : 72 : 1122 : [58, 7] : phi[8,9,2] : phi[8,9,2] : A2 : 1122 : 7 : 321323432132343213234 : 9 : [{{3, 4}}, {{2, 4}}, {{2, 3}, {3, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}}, {{2, 3}, {3, 4}, {1, 2, 4}, {1, 3, 4}}] 59 : 72 : 897 : [59, 2] : phi[9,10] : phi[9,10] : A1+A1s : 897 : 2 : 2321343213234323 : 10 : [{{2, 3, 4}}, {{2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}, {2, 3, 4}}] 60 : 72 : 1050 : [60, 5] : phi[9,10] : phi[9,10] : A1+A1s : 1050 : 5 : 121432132343213234 : 10 : [{{1, 2, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 61 : 72 : 1045 : [61, 5] : phi[9,10] : phi[9,10] : A1+A1s : 1045 : 5 : 123213432132343213 : 10 : [{{1, 3, 4}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 62 : 72 : 1107 : [62, 7] : phi[9,10] : phi[9,10] : A1+A1s : 1107 : 7 : 13213432132343213234 : 10 : [{{1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}, {2, 3, 4}}] 63 : 72 : 1118 : [63, 7] : phi[9,10] : phi[9,10] : A1+A1s : 1118 : 7 : 12132134321323432132 : 10 : [{{1, 2, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}, {2, 3, 4}}] 64 : 72 : 1139 : [64, 8] : phi[9,10] : phi[9,10] : A1+A1s : 1139 : 8 : 2132132432132343213234 : 10 : [{{2, 4}}, {{2, 3}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 65 : 72 : 1143 : [65, 8] : phi[9,10] : phi[9,10] : A1+A1s : 1143 : 8 : 1232132343213234321323 : 10 : [{{1, 3}}, {{2, 3}, {1, 2, 4}}, {{1, 3}, {2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}] 66 : 72 : 1140 : [66, 8] : phi[9,10] : phi[9,10] : A1+A1s : 1140 : 8 : 2132132343213234321323 : 10 : [{{2, 3}}, {{1, 3}, {2, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}}, {{1, 3}, {2, 4}, {1, 2, 4}, {1, 3, 4}}, {{2, 3}, {1, 2, 4}, {1, 3, 4}, {1, 2, 3}, {2, 3, 4}}] 67 : 72 : 1065 : [67, 0] : phi[2,16,2]+phi[4,13] : phi[4,13] : A1s : 1065 : 0 : 2323432132343213234 : 13 : [{{2, 3, 4}}, {{1, 3, 4}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 2, 4}, {2, 3, 4}}] 68 : 72 : 1096 : [68, 0] : phi[2,16,1]+phi[4,13] : phi[4,13] : A1s : 1096 : 0 : 1213213234321324321 : 13 : [{{1, 2, 3}}, {{1, 2, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3, 4}, {1, 2, 3}}] 69 : 72 : 1130 : [69, 1] : phi[2,16,2]+phi[4,13] : phi[4,13] : A1s : 1130 : 1 : 123213432132343213234 : 13 : [{{1, 3, 4}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3, 4}, {1, 2, 3}}] 70 : 72 : 1133 : [70, 2] : phi[2,16,1]+phi[4,13] : phi[4,13] : A1s : 1133 : 2 : 121321432132343213234 : 13 : [{{1, 2, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 2, 4}, {2, 3, 4}}, {{1, 3, 4}, {1, 2, 3}}, {{1, 2, 4}, {2, 3, 4}}] 71 : 72 : 1151 : [71, 0] : phi[1,24] : phi[1,24] : 0 : 1151 : 0 : 121321323432132343213234 : 24 : [{{1, 2, 3, 4}}, {}, {}, {}, {}]