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K4_2_subdiv
1
[ 1 .. 16 ] Group( () ) [ 1, 1 ]
2
[ 1, -1, 3, -3, 5, 6, 7, 8, -5, -8, -7, -6, 13, -13, 15, -15 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16)(17,18) ] ) [ 2, 1 ]
[ 1, 2, -1, -2, 5, 6, -5, -6, 9, 10, -9, -10, 13, 14, -13, -14 ] Group( [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,18) ] ) [ 2, 1 ]
[ 1, 2, -2, -1, 5, 6, 7, 8, -7, -6, -5, -8, 13, 14, -14, -13 ] Group( [ ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15)(17,18) ] ) [ 2, 1 ]
3
[ 1, 1, 3, 3, 5, 6, 7, 8, 5, 8, 7, 6, 13, 13, 15, 15 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16) ] ) [ 2, 1 ]
[ 1, 2, 1, 2, 5, 6, 5, 6, 9, 10, 9, 10, 13, 14, 13, 14 ] Group( [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16) ] ) [ 2, 1 ]
[ 1, 2, 2, 1, 5, 6, 7, 8, 7, 6, 5, 8, 13, 14, 14, 13 ] Group( [ ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15) ] ) [ 2, 1 ]
4
[ 0, 0, 3, -3, 0, 6, 7, 8, 0, 10, -7, 12, -12, -6, -8, -10 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18) ] ) [ 2, 1 ]
[ 0, 2, 0, -2, 5, 6, 7, 8, -8, -7, -6, -5, 0, 14, 0, -14 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,18) ] ) [ 2, 1 ]
[ 0, 2, -2, 0, 5, 6, 7, 0, 9, -6, 11, 0, -5, -7, -9, -11 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16)(17,18) ] ) [ 2, 1 ]
[ 1, 0, -1, 0, 5, 6, 7, 8, -6, -5, -8, -7, 13, 0, -13, 0 ] Group( [ ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15)(17,18) ] ) [ 2, 1 ]
[ 1, 0, 0, -1, 5, 0, 7, 8, 9, 0, 11, -8, -11, -9, -7, -5 ] Group( [ ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13)(17,18) ] ) [ 2, 1 ]
[ 1, -1, 0, 0, 5, 6, 0, 8, -5, 10, 0, 12, -6, -12, -10, -8 ] Group( [ ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18) ] ) [ 2, 1 ]
5
[ 1, 2, 3, 3, 5, 6, 7, 8, 9, 10, 7, 12, 12, 6, 8, 10 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13) ] ) [ 2, 1 ]
[ 1, 2, 3, 2, 5, 6, 7, 8, 8, 7, 6, 5, 13, 14, 15, 14 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16) ] ) [ 2, 1 ]
[ 1, 2, 2, 4, 5, 6, 7, 8, 9, 6, 11, 12, 5, 7, 9, 11 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16) ] ) [ 2, 1 ]
[ 1, 2, 1, 4, 5, 6, 7, 8, 6, 5, 8, 7, 13, 14, 13, 16 ] Group( [ ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15) ] ) [ 2, 1 ]
[ 1, 2, 3, 1, 5, 6, 7, 8, 9, 10, 11, 8, 11, 9, 7, 5 ] Group( [ ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13) ] ) [ 2, 1 ]
[ 1, 1, 3, 4, 5, 6, 7, 8, 5, 10, 11, 12, 6, 12, 10, 8 ] Group( [ ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14) ] ) [ 2, 1 ]
6
[ 1, 2, 2, 2, 5, 6, 6, 8, 8, 10, 10, 5, 5, 10, 8, 6 ] Group( [ ( 2, 3, 4)( 5,13,12)( 6, 7,16)( 8, 9,15)(10,11,14) ] ) [ 3, 1 ]
[ 1, 2, 1, 1, 5, 6, 7, 7, 6, 5, 11, 11, 7, 6, 11, 5 ] Group( [ ( 1, 4, 3)( 5,16,10)( 6, 9,14)( 7,13, 8)(11,15,12) ] ) [ 3, 1 ]
[ 1, 1, 3, 1, 5, 6, 7, 5, 9, 7, 6, 9, 6, 5, 7, 9 ] Group( [ ( 1, 2, 4)( 5,14, 8)( 6,11,13)( 7,15,10)( 9,16,12) ] ) [ 3, 1 ]
[ 1, 1, 1, 4, 5, 5, 7, 8, 9, 9, 8, 7, 9, 7, 5, 8 ] Group( [ ( 1, 3, 2)( 5,15, 6)( 7,14,12)( 8,11,16)( 9,13,10) ] ) [ 3, 1 ]
7
[ 1, 1, 1, 1, 5, 6, 5, 6, 5, 6, 5, 6, 13, 13, 13, 13 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16) ] ) [ 4, 2 ]
8
[ 0, 0, 0, 0, 0, 6, 0, 8, 0, 8, 0, 6, -6, -6, -8, -8 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18) ] ) [ 4, 2 ]
[ 0, 0, 0, 0, 5, 6, 5, 6, -6, -5, -6, -5, 0, 0, 0, 0 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,18), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15)(17,18) ] ) [ 4, 2 ]
[ 0, 0, 0, 0, 5, 0, 7, 0, 7, 0, 5, 0, -5, -7, -7, -5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16)(17,18), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13)(17,18) ] ) [ 4, 2 ]
9
[ 1, 1, 3, 3, 5, 6, 7, 8, 5, 8, 7, 6, 6, 6, 8, 8 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14) ] ) [ 4, 2 ]
[ 1, 2, 1, 2, 5, 6, 5, 6, 6, 5, 6, 5, 13, 14, 13, 14 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15) ] ) [ 4, 2 ]
[ 1, 2, 2, 1, 5, 6, 7, 8, 7, 6, 5, 8, 5, 7, 7, 5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13) ] ) [ 4, 2 ]
10
[ 1, 1, -1, -1, 5, 6, -5, -6, 5, -6, -5, 6, 13, 13, -13, -13 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,18) ] ) [ 4, 2 ]
[ 1, -1, 1, -1, 5, 6, 5, 6, -5, -6, -5, -6, 13, -13, 13, -13 ] Group( [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16), ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15)(17,18) ] ) [ 4, 2 ]
[ 1, -1, -1, 1, 5, 6, -5, -6, -5, 6, 5, -6, 13, -13, -13, 13 ] Group( [ ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15), ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16)(17,18) ] ) [ 4, 2 ]
11
[ 1, 1, 1, 1, 5, 6, 5, 8, 5, 8, 5, 6, 8, 8, 6, 6 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16), ( 1, 4, 2, 3)( 5,11, 9, 7)( 6,15,12,16)( 8,14,10,13) ] ) [ 4, 1 ]
[ 1, 1, 1, 1, 5, 5, 5, 5, 9, 9, 9, 9, 13, 13, 13, 13 ] Group( [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16), ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16) ] ) [ 4, 1 ]
[ 1, 1, 1, 1, 5, 6, 7, 6, 7, 6, 5, 6, 7, 5, 5, 7 ] Group( [ ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15), ( 1, 3, 4, 2)( 5,15,11,14)( 6,12,10, 8)( 7,16, 9,13) ] ) [ 4, 1 ]
12
[ 1, 1, -1, -1, 5, 6, -5, 8, 5, 8, -5, 6, -8, -8, -6, -6 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16), ( 1, 4, 2, 3)( 5,11, 9, 7)( 6,15,12,16)( 8,14,10,13)(17,18) ] ) [ 4, 1 ]
[ 1, -1, 1, -1, 5, -5, 5, -5, 9, -9, 9, -9, 13, -13, 13, -13 ] Group( [ ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16), ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16)(17,18) ] ) [ 4, 1 ]
[ 1, -1, -1, 1, 5, 6, 7, -6, 7, 6, 5, -6, -7, -5, -5, -7 ] Group( [ ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15), ( 1, 3, 4, 2)( 5,15,11,14)( 6,12,10, 8)( 7,16, 9,13)(17,18) ] ) [ 4, 1 ]
13
[ 1, -1, 0, 0, 5, 6, 0, 8, -5, -8, 0, -6, -6, 6, 8, -8 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18) ] ) [ 4, 2 ]
[ 1, 0, -1, 0, 5, 6, -5, -6, -6, -5, 6, 5, 13, 0, -13, 0 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15)(17,18) ] ) [ 4, 2 ]
[ 1, 0, 0, -1, 5, 0, 7, 8, -7, 0, -5, -8, 5, 7, -7, -5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13)(17,18) ] ) [ 4, 2 ]
[ 0, 2, 0, -2, 5, 6, -5, -6, 6, 5, -6, -5, 0, 14, 0, -14 ] Group( [ ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15), ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,18) ] ) [ 4, 2 ]
[ 0, 2, -2, 0, 5, 6, 7, 0, -7, -6, -5, 0, -5, -7, 7, 5 ] Group( [ ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13), ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16)(17,18) ] ) [ 4, 2 ]
[ 0, 0, 3, -3, 0, 6, 7, 8, 0, -8, -7, -6, 6, -6, -8, 8 ] Group( [ ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14), ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18) ] ) [ 4, 2 ]
14
[ 1, 2, 2, 2, 5, 6, 6, 8, 8, 6, 6, 5, 5, 6, 8, 6 ] Group( [ ( 2, 3, 4)( 5,13,12)( 6, 7,16)( 8, 9,15)(10,11,14), ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13) ] ) [ 6, 1 ]
[ 1, 2, 1, 1, 5, 6, 7, 7, 6, 5, 7, 7, 7, 6, 7, 5 ] Group( [ ( 1, 4, 3)( 5,16,10)( 6, 9,14)( 7,13, 8)(11,15,12), ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13) ] ) [ 6, 1 ]
[ 1, 1, 3, 1, 5, 6, 7, 5, 5, 7, 6, 5, 6, 5, 7, 5 ] Group( [ ( 1, 2, 4)( 5,14, 8)( 6,11,13)( 7,15,10)( 9,16,12), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14) ] ) [ 6, 1 ]
[ 1, 1, 1, 4, 5, 5, 7, 8, 5, 5, 8, 7, 5, 7, 5, 8 ] Group( [ ( 1, 3, 2)( 5,15, 6)( 7,14,12)( 8,11,16)( 9,13,10), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14) ] ) [ 6, 1 ]
15
[ 0, 0, 0, 0, 0, 6, 6, 0, 0, -6, -6, 0, 0, -6, 0, 6 ] Group( [ ( 2, 3, 4)( 5,13,12)( 6, 7,16)( 8, 9,15)(10,11,14), ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18) ] ) [ 6, 1 ]
[ 0, 0, 0, 0, 0, 0, 7, 7, 0, 0, -7, -7, 7, 0, -7, 0 ] Group( [ ( 1, 4, 3)( 5,16,10)( 6, 9,14)( 7,13, 8)(11,15,12), ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18) ] ) [ 6, 1 ]
[ 0, 0, 0, 0, 5, 0, 0, 5, -5, 0, 0, -5, 0, 5, 0, -5 ] Group( [ ( 1, 2, 4)( 5,14, 8)( 6,11,13)( 7,15,10)( 9,16,12), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18) ] ) [ 6, 1 ]
[ 0, 0, 0, 0, 5, 5, 0, 0, -5, -5, 0, 0, -5, 0, 5, 0 ] Group( [ ( 1, 3, 2)( 5,15, 6)( 7,14,12)( 8,11,16)( 9,13,10), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18) ] ) [ 6, 1 ]
16
[ 1, 1, -1, -1, 5, 6, -5, -6, 5, -6, -5, 6, 6, 6, -6, -6 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,18) ] ) [ 8, 3 ]
[ 1, -1, 1, -1, 5, -5, 5, -5, -5, 5, -5, 5, 13, -13, 13, -13 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15), ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15)(17,18) ] ) [ 8, 3 ]
[ 1, -1, -1, 1, 5, 6, -5, -6, -5, 6, 5, -6, 5, -5, -5, 5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13), ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16)(17,18) ] ) [ 8, 3 ]
17
[ 1, 1, 1, 1, 5, 6, 5, 6, 5, 6, 5, 6, 6, 6, 6, 6 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16) ] ) [ 8, 3 ]
[ 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 13, 13, 13, 13 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15), ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15) ] ) [ 8, 3 ]
[ 1, 1, 1, 1, 5, 6, 5, 6, 5, 6, 5, 6, 5, 5, 5, 5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13), ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16) ] ) [ 8, 3 ]
18
[ 0, 0, 0, 0, 0, 6, 0, 6, 0, 6, 0, 6, -6, -6, -6, -6 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16) ] ) [ 8, 3 ]
[ 0, 0, 0, 0, 5, -5, 5, -5, 5, -5, 5, -5, 0, 0, 0, 0 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,18), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15)(17,18), ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15) ] ) [ 8, 3 ]
[ 0, 0, 0, 0, 5, 0, 5, 0, 5, 0, 5, 0, -5, -5, -5, -5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16)(17,18), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13)(17,18), ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16) ] ) [ 8, 3 ]
19
[ 0, 0, 0, 0, 0, 6, 0, -6, 0, -6, 0, 6, -6, -6, 6, 6 ] Group( [ ( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13)(17,18), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14)(17,18), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16)(17,18) ] ) [ 8, 3 ]
[ 0, 0, 0, 0, 5, 5, 5, 5, -5, -5, -5, -5, 0, 0, 0, 0 ] Group( [ ( 2, 4)( 5,12)( 6,11)( 7,10)( 8, 9)(14,16)(17,18), ( 1, 3)( 5,10)( 6, 9)( 7,12)( 8,11)(13,15)(17,18), ( 1, 4)( 2, 3)( 5,11)( 6,10)( 7, 9)( 8,12)(13,16)(14,15)(17,18) ] ) [ 8, 3 ]
[ 0, 0, 0, 0, 5, 0, -5, 0, -5, 0, 5, 0, -5, 5, 5, -5 ] Group( [ ( 2, 3)( 5,13)( 6,10)( 7,14)( 9,15)(11,16)(17,18), ( 1, 4)( 5,16)( 7,15)( 8,12)( 9,14)(11,13)(17,18), ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16)(17,18) ] ) [ 8, 3 ]
20
[ 1, 1, 1, 1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 ] Group( [ ( 1, 2)( 3, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(13,14)(15,16), ( 1, 3)( 2, 4)( 5, 7)( 6, 8)( 9,11)(10,12)(13,15)(14,16), ( 2, 3, 4)( 5,13,12)( 6, 7,16)( 8, 9,15)(10,11,14),
( 3, 4)( 6,14)( 7,11)( 8,15)(10,16)(12,13) ] ) [ 24, 12 ]
21
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Group( [ ( 1, 2, 3, 4)( 5, 6, 7, 8)( 9,10,11,12)(13,14,15,16), ( 1, 2)( 5, 9)( 6,13)( 8,16)(10,15)(12,14), (17,18) ] ) [ 48, 48 ]
Subgroup structure
[ [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 ],
[ 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, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 3, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1 ],
[ 4, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1 ],
[ 5, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1 ],
[ 6, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1 ],
[ 7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1 ],
[ 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1 ],
[ 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1 ],
[ 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1 ],
[ 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1 ],
[ 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1 ],
[ 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ],
[ 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1 ],
[ 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1 ],
[ 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 ],
[ 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 1 ],
[ 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ],
[ 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 21, 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 = 16, 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 = 8, 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 = 8, 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 = 8, 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 = 8, 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 = 10, 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 = 10, 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 [ 3, 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
NON-REAL projection
1, dim Fix_P(U) K = 5, dim Fix_U_i K = 1, N_H(K)/K [ 3, 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
Representation 3, dimension of U_i = 1
NON-REAL projection
1, dim Fix_P(U) K = 5, dim Fix_U_i K = 1, N_H(K)/K [ 3, 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, 1 ]
Symmetry type S7 [ 4, 2 ]
Representation 1, dimension of U_i = 1
7, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7 ], maximals
Representation 2, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 [ 3, 7 ], maximals 3
Representation 3, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 [ 3, 7 ], maximals 3
Representation 4, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 [ 3, 7 ], maximals 3
Possible jumps from S7 [ 3, 3, 3 ]
Symmetry type S8 [ 4, 2 ]
Representation 1, dimension of U_i = 1
8, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 8 ], maximals
Representation 2, dimension of U_i = 1
4, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 4, 8 ], maximals 4
Representation 3, dimension of U_i = 1
4, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 4, 8 ], maximals 4
Representation 4, dimension of U_i = 1
3, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
8, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 3, 8 ], maximals 3
Possible jumps from S8 [ 3, 4, 4 ]
Symmetry type S9 [ 4, 2 ]
Representation 1, dimension of U_i = 1
9, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 9 ], maximals
Representation 2, dimension of U_i = 1
5, dim Fix_P(U) K = 4, 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
Representation 3, dimension of U_i = 1
5, dim Fix_P(U) K = 4, 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
Representation 4, dimension of U_i = 1
3, dim Fix_P(U) K = 2, 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 [ 3, 9 ], maximals 3
Possible jumps from S9 [ 3, 5, 5 ]
Symmetry type S10 [ 4, 2 ]
Representation 1, dimension of U_i = 1
10, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 10 ], maximals
Representation 2, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 [ 3, 10 ], maximals 3
Representation 3, dimension of U_i = 1
2, dim Fix_P(U) K = 4, 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
2, dim Fix_P(U) K = 4, 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
Possible jumps from S10 [ 2, 2, 3 ]
Symmetry type S11 [ 4, 1 ]
Representation 1, dimension of U_i = 1
11, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 11 ], maximals
Representation 2, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 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 [ 4, 1 ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 11 ], maximals 1
Representation 4, 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 [ 4, 1 ]
11, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 11 ], maximals 1
Possible jumps from S11 [ 1, 1, 3 ]
Symmetry type S12 [ 4, 1 ]
Representation 1, dimension of U_i = 1
12, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 12 ], maximals
Representation 2, dimension of U_i = 1
3, dim Fix_P(U) K = 4, 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 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 [ 4, 1 ]
12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 12 ], maximals 1
Representation 4, 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 [ 4, 1 ]
12, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 12 ], maximals 1
Possible jumps from S12 [ 1, 1, 3 ]
Symmetry type S13 [ 4, 2 ]
Representation 1, dimension of U_i = 1
13, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 13 ], maximals
Representation 2, dimension of U_i = 1
5, dim Fix_P(U) K = 6, 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 [ 5, 13 ], maximals 5
Representation 3, dimension of U_i = 1
4, 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 [ 4, 13 ], maximals 4
Representation 4, dimension of U_i = 1
2, dim Fix_P(U) K = 4, 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 [ 2, 13 ], maximals 2
Possible jumps from S13 [ 2, 4, 5 ]
Symmetry type S14 [ 6, 1 ]
Representation 1, dimension of U_i = 1
14, dim Fix_P(U) K = 5, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 14 ], maximals
Representation 2, dimension of U_i = 1
6, dim Fix_P(U) K = 1, 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 [ 6, 14 ], maximals 6
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 10, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
5, dim Fix_P(U) K = 5, 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, 5, 14 ], maximals 5
Possible jumps from S14 [ 5, 6 ]
Symmetry type S15 [ 6, 1 ]
Representation 1, dimension of U_i = 1
15, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 15 ], maximals
Representation 2, dimension of U_i = 1
6, dim Fix_P(U) K = 5, 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 [ 6, 15 ], maximals 6
Representation 3, dimension of U_i = 2
1, dim Fix_P(U) K = 10, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
4, dim Fix_P(U) K = 5, 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, 4, 15 ], maximals 4
Possible jumps from S15 [ 4, 6 ]
Symmetry type S16 [ 8, 3 ]
Representation 1, dimension of U_i = 1
16, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 16 ], maximals
Representation 2, dimension of U_i = 1
10, dim Fix_P(U) K = 1, 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 [ 10, 16 ], maximals 10
Representation 3, dimension of U_i = 1
9, dim Fix_P(U) K = 3, 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 [ 9, 16 ], maximals 9
Representation 4, dimension of U_i = 1
12, dim Fix_P(U) K = 1, 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 [ 12, 16 ], maximals 12
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
5, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
2, dim Fix_P(U) K = 4, 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 [ 1, 2, 5, 16 ], maximals 2 5
Possible jumps from S16 [ 2, 5, 9, 10, 12 ]
Symmetry type S17 [ 8, 3 ]
Representation 1, dimension of U_i = 1
17, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 17 ], maximals
Representation 2, dimension of U_i = 1
7, dim Fix_P(U) K = 1, 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 [ 7, 17 ], maximals 7
Representation 3, dimension of U_i = 1
9, dim Fix_P(U) K = 3, 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 [ 9, 17 ], maximals 9
Representation 4, dimension of U_i = 1
11, dim Fix_P(U) K = 1, 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 [ 11, 17 ], maximals 11
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
5, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
3, dim Fix_P(U) K = 4, 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 [ 1, 3, 5, 17 ], maximals 3 5
Possible jumps from S17 [ 3, 5, 7, 9, 11 ]
Symmetry type S18 [ 8, 3 ]
Representation 1, dimension of U_i = 1
18, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 18 ], maximals
Representation 2, dimension of U_i = 1
7, dim Fix_P(U) K = 3, 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 [ 7, 18 ], maximals 7
Representation 3, dimension of U_i = 1
8, dim Fix_P(U) K = 1, 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 4, dimension of U_i = 1
12, dim Fix_P(U) K = 3, 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 [ 12, 18 ], maximals 12
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
3, dim Fix_P(U) K = 4, 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 [ 1, 3, 4, 18 ], maximals 3 4
Possible jumps from S18 [ 3, 4, 7, 8, 12 ]
Symmetry type S19 [ 8, 3 ]
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
10, dim Fix_P(U) K = 3, 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 [ 10, 19 ], maximals 10
Representation 3, dimension of U_i = 1
8, 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 [ 8, 19 ], maximals 8
Representation 4, dimension of U_i = 1
11, dim Fix_P(U) K = 3, 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 [ 11, 19 ], maximals 11
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 8, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 4, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
2, dim Fix_P(U) K = 4, 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, 2, 4, 19 ], maximals 2 4
Possible jumps from S19 [ 2, 4, 8, 10, 11 ]
Symmetry type S20 [ 24, 12 ]
Representation 1, dimension of U_i = 1
20, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 20 ], maximals
Representation 3, dimension of U_i = 2
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
17, dim Fix_P(U) K = 1, 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 [ 7, 17, 20 ], maximals 17
Representation 4, dimension of U_i = 3
1, dim Fix_P(U) K = 3, dim Fix_U_i K = 3, N_H(K)/K [ 24, 12 ]
5, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
11, 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 [ 1, 5, 6, 11, 20 ], maximals 5 6 11
Representation 5, dimension of U_i = 3
1, dim Fix_P(U) K = 9, dim Fix_U_i K = 3, N_H(K)/K [ 24, 12 ]
5, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 2, 1 ]
9, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
14, dim Fix_P(U) K = 3, 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 [ 1, 5, 9, 14, 20 ], maximals 9 14
Possible jumps from S20 [ 5, 6, 9, 11, 14, 17 ]
Symmetry type S21 [ 48, 48 ]
Representation 3, dimension of U_i = 1
20, 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 [ 20, 21 ], maximals 20
Representation 6, dimension of U_i = 2
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
17, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 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 [ 7, 17, 18, 21 ], maximals 17 18
Representation 7, dimension of U_i = 3
1, dim Fix_P(U) K = 3, dim Fix_U_i K = 3, N_H(K)/K [ 48, 48 ]
2, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 2, dim Fix_U_i K = 2, N_H(K)/K [ 4, 2 ]
13, dim Fix_P(U) K = 1, dim Fix_U_i K = 1, N_H(K)/K [ 2, 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 = 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 [ 1, 2, 4, 13, 15, 19, 21 ], maximals 13 15 19
Representation 8, dimension of U_i = 3
1, dim Fix_P(U) K = 9, dim Fix_U_i K = 3, N_H(K)/K [ 48, 48 ]
5, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 4, 2 ]
2, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
13, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
14, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
16, dim Fix_P(U) K = 3, 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, 2, 5, 13, 14, 16, 21 ], maximals 13 14 16
Possible jumps from S21 [ 13, 13, 14, 15, 16, 17, 18, 19, 20 ]
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, 1 ]
Possible jumps from S7 [ 3, 3, 3 ]
Possible jumps from S8 [ 3, 4, 4 ]
Possible jumps from S9 [ 3, 5, 5 ]
Possible jumps from S10 [ 2, 2, 3 ]
Possible jumps from S11 [ 1, 1, 3 ]
Possible jumps from S12 [ 1, 1, 3 ]
Possible jumps from S13 [ 2, 4, 5 ]
Possible jumps from S14 [ 5, 6 ]
Possible jumps from S15 [ 4, 6 ]
Possible jumps from S16 [ 2, 5, 9, 10, 12 ]
Possible jumps from S17 [ 3, 5, 7, 9, 11 ]
Possible jumps from S18 [ 3, 4, 7, 8, 12 ]
Possible jumps from S19 [ 2, 4, 8, 10, 11 ]
Possible jumps from S20 [ 5, 6, 9, 11, 14, 17 ]
Possible jumps from S21 [ 13, 13, 14, 15, 16, 17, 18, 19, 20 ]