Sym( [ 1 .. 4 ] )
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S4
[ (), (3,4), (2,3), (2,3,4), (2,4,3), (2,4), (1,2), (1,2)(3,4), (1,2,3), (1,2,3,4), (1,2,4,3), (1,2,4), (1,3,2), (1,3,4,2), (1,3), (1,3,4), (1,3)(2,4), (1,3,2,4), (1,4,3,2), (1,4,2), (1,4,3), (1,4), (1,4,2,3), (1,4)(2,3) ] S4 as permutation of points
1
[ 1 .. 24 ] Group( () ) [ 1, 1 ]
2
[ 1, 2, 3, 4, 5, 6, -2, -1, -5, -6, -3, -4, 13, 14, 15, 16, 17, 18, -15, -16, -13, -14, -18, -17 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, -4, -3, -6, -5, -1, -2, -10, -9, -12, -11, -7, -8 ] Group( [ ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1 ] Group( [ ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(25,26) ] ) [ 2, 1 ]
3
[ 1, 2, 3, 4, 5, 6, 2, 1, 5, 6, 3, 4, 13, 14, 15, 16, 17, 18, 15, 16, 13, 14, 18, 17 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 3, 6, 5, 1, 2, 10, 9, 12, 11, 7, 8 ] Group( [ ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13) ] ) [ 2, 1 ]
4
[ 1, -1, 3, 4, -3, -4, 7, -7, 9, 10, -9, -10, 13, 14, 15, 16, 17, 18, -13, -14, -15, -16, -17, -18 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, -3, -2, -1, 7, 8, 9, 10, 11, 12, 13, -13, 15, 16, -15, -16, -8, -7, -11, -12, -9, -10 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)(15,17)(16,18)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, -9, -8, -7, 13, 14, 15, -15, -14, -13, -5, -6, -2, -1, -4, -3 ] Group( [ ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)(14,17)(15,16)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, -7, -8, 11, -11, -3, -4, -1, -2, -6, -5, 19, 20, 21, -21, -20, -19 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22)(25,26) ] ) [ 2, 1 ]
[ 1, 2, -1, -2, 5, -5, 7, 8, 9, 10, 11, 12, -7, -8, -9, -10, -11, -12, 19, -19, 21, 22, -21, -22 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24)(25,26) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, -1, -2, -3, -4, -5, -6, 13, 14, -13, -14, 17, -17, 19, 20, -19, -20, 23, -23 ] Group( [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,24)(25,26) ] ) [ 2, 1 ]
5
[ 1, 1, 3, 4, 3, 4, 7, 7, 9, 10, 9, 10, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24) ] ) [ 2, 1 ]
[ 1, 2, 3, 3, 2, 1, 7, 8, 9, 10, 11, 12, 13, 13, 15, 16, 15, 16, 8, 7, 11, 12, 9, 10 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)(15,17)(16,18) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 13, 14, 15, 15, 14, 13, 5, 6, 2, 1, 4, 3 ] Group( [ ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)(14,17)(15,16) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 7, 8, 11, 11, 3, 4, 1, 2, 6, 5, 19, 20, 21, 21, 20, 19 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22) ] ) [ 2, 1 ]
[ 1, 2, 1, 2, 5, 5, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11, 12, 19, 19, 21, 22, 21, 22 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24) ] ) [ 2, 1 ]
[ 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 13, 14, 13, 14, 17, 17, 19, 20, 19, 20, 23, 23 ] Group( [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,24) ] ) [ 2, 1 ]
6
[ 1, 2, 2, 1, 1, 2, 7, 8, 9, 10, 11, 12, 8, 7, 11, 12, 9, 10, 7, 8, 9, 10, 11, 12 ] Group( [ ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24) ] ) [ 3, 1 ]
[ 1, 2, 3, 4, 5, 6, 7, 8, 8, 7, 7, 8, 5, 6, 2, 1, 4, 3, 3, 4, 1, 2, 6, 5 ] Group( [ ( 1,21,16)( 2,22,15)( 3,19,18)( 4,20,17)( 5,24,13)( 6,23,14)( 7,11,10)( 8,12, 9) ] ) [ 3, 1 ]
[ 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 13, 14, 14, 13, 13, 14, 2, 1, 5, 6, 3, 4 ] Group( [ ( 1,12,20)( 2,11,19)( 3,10,23)( 4, 9,24)( 5, 8,21)( 6, 7,22)(13,16,17)(14,15,18) ] ) [ 3, 1 ]
[ 1, 2, 3, 4, 5, 6, 3, 4, 1, 2, 6, 5, 1, 2, 3, 4, 5, 6, 19, 20, 20, 19, 19, 20 ] Group( [ ( 1,13, 9)( 2,14,10)( 3,15, 7)( 4,16, 8)( 5,17,12)( 6,18,11)(19,23,22)(20,24,21) ] ) [ 3, 1 ]
7
[ 1, 2, 3, 4, 5, 6, 2, 1, 5, 6, 3, 4, 4, 3, 6, 5, 1, 2, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)
(12,21) ] ) [ 4, 2 ]
8
[ 1, -1, 3, 4, -3, -4, -1, 1, -3, -4, 3, 4, 13, 14, -13, -14, 17, -17, -13, -14, 13, 14, -17, 17 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,26), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)
(14,16)(17,18)(19,21)(20,22)(23,24)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 3, -3, -2, -1, 7, 8, -7, -8, 11, -11, -3, 3, -1, -2, 1, 2, -8, -7, -11, 11, 7, 8 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22)(25,26), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)
(12,22)(13,14)(15,17)(16,18)(25,26) ] ) [ 4, 2 ]
[ 1, 2, -1, -2, 5, -5, 7, 8, 9, -9, -8, -7, -7, -8, -9, 9, 8, 7, -5, 5, -2, -1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24)(25,26), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)
(13,18)(14,17)(15,16)(25,26) ] ) [ 4, 2 ]
9
[ 1, 1, 3, 4, 3, 4, 1, 1, 3, 4, 3, 4, 13, 14, 13, 14, 17, 17, 13, 14, 13, 14, 17, 17 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)
(20,22)(23,24) ] ) [ 4, 2 ]
[ 1, 2, 3, 3, 2, 1, 7, 8, 7, 8, 11, 11, 3, 3, 1, 2, 1, 2, 8, 7, 11, 11, 7, 8 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)(15,17)
(16,18) ] ) [ 4, 2 ]
[ 1, 2, 1, 2, 5, 5, 7, 8, 9, 9, 8, 7, 7, 8, 9, 9, 8, 7, 5, 5, 2, 1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)(14,17)
(15,16) ] ) [ 4, 2 ]
10
[ 1, 2, 3, 4, 5, 6, 2, 1, 5, 6, 3, 4, -4, -3, -6, -5, -1, -2, -6, -5, -4, -3, -2, -1 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)
(11,22)(12,21)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 3, 4, 5, 6, -2, -1, -5, -6, -3, -4, 4, 3, 6, 5, 1, 2, -6, -5, -4, -3, -2, -1 ] Group( [ ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21), ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)
(11,14)(12,13)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 3, 4, 5, 6, -2, -1, -5, -6, -3, -4, -4, -3, -6, -5, -1, -2, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13), ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)
(17,24)(18,23)(25,26) ] ) [ 4, 2 ]
11
[ 1, 2, 3, 4, 5, 6, 2, 1, 5, 6, 3, 4, 6, 5, 4, 3, 2, 1, 4, 3, 6, 5, 1, 2 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,18, 8,23)( 2,17, 7,24)( 3,16,11,20)( 4,15,12,19)( 5,14, 9,22)( 6,13,10,21) ] )
[ 4, 1 ]
[ 1, 2, 3, 4, 5, 6, 5, 6, 2, 1, 4, 3, 4, 3, 6, 5, 1, 2, 1, 2, 3, 4, 5, 6 ] Group( [ ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21), ( 1,10,17,19)( 2, 9,18,20)( 3,12,14,21)( 4,11,13,22)( 5, 7,16,23)( 6, 8,15,24) ] )
[ 4, 1 ]
[ 1, 2, 3, 4, 5, 6, 4, 3, 6, 5, 1, 2, 2, 1, 5, 6, 3, 4, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13), ( 1,11,24,14)( 2,12,23,13)( 3, 8,22,17)( 4, 7,21,18)( 5,10,20,15)( 6, 9,19,16) ] )
[ 4, 1 ]
12
[ 1, 2, 3, 4, 5, 6, 2, 1, 5, 6, 3, 4, -6, -5, -4, -3, -2, -1, -4, -3, -6, -5, -1, -2 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,18, 8,23)( 2,17, 7,24)( 3,16,11,20)( 4,15,12,19)( 5,14, 9,22)
( 6,13,10,21)(25,26) ] ) [ 4, 1 ]
[ 1, 2, 3, 4, 5, 6, -5, -6, -2, -1, -4, -3, 4, 3, 6, 5, 1, 2, -1, -2, -3, -4, -5, -6 ] Group( [ ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21), ( 1,10,17,19)( 2, 9,18,20)( 3,12,14,21)( 4,11,13,22)( 5, 7,16,23)
( 6, 8,15,24)(25,26) ] ) [ 4, 1 ]
[ 1, 2, 3, 4, 5, 6, -4, -3, -6, -5, -1, -2, -2, -1, -5, -6, -3, -4, 6, 5, 4, 3, 2, 1 ] Group( [ ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13), ( 1,11,24,14)( 2,12,23,13)( 3, 8,22,17)( 4, 7,21,18)( 5,10,20,15)
( 6, 9,19,16)(25,26) ] ) [ 4, 1 ]
13
[ 1, 1, 3, 4, 3, 4, -1, -1, -3, -4, -3, -4, 13, 14, -13, -14, 17, -17, 13, 14, -13, -14, 17, -17 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)
(17,18)(19,21)(20,22)(23,24)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 3, 3, 2, 1, 7, 8, -7, -8, 11, -11, -3, -3, -1, -2, -1, -2, 8, 7, 11, -11, -7, -8 ] Group( [ ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)(15,17)(16,18), ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)
(19,24)(20,23)(21,22)(25,26) ] ) [ 4, 2 ]
[ 1, 2, -1, -2, 5, -5, 7, 8, 9, 9, 8, 7, -7, -8, -9, -9, -8, -7, 5, -5, 2, 1, -2, -1 ] Group( [ ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)(14,17)(15,16), ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)
(21,23)(22,24)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 3, -3, -2, -1, 7, 8, 7, 8, 11, 11, 3, -3, 1, 2, -1, -2, -8, -7, -11, -11, -7, -8 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)
(13,14)(15,17)(16,18)(25,26) ] ) [ 4, 2 ]
[ 1, 2, 1, 2, 5, 5, 7, 8, 9, -9, -8, -7, 7, 8, 9, -9, -8, -7, -5, -5, -2, -1, -2, -1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)
(14,17)(15,16)(25,26) ] ) [ 4, 2 ]
[ 1, -1, 3, 4, -3, -4, 1, -1, 3, 4, -3, -4, 13, 14, 13, 14, 17, 17, -13, -14, -13, -14, -17, -17 ] Group( [ ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,24), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)
(15,21)(16,22)(17,23)(18,24)(25,26) ] ) [ 4, 2 ]
14
[ 1, 1, 1, 1, 1, 1, 7, 7, 9, 10, 9, 10, 7, 7, 9, 10, 9, 10, 7, 7, 9, 10, 9, 10 ] Group( [ ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)
(18,24) ] ) [ 6, 1 ]
[ 1, 1, 3, 4, 3, 4, 7, 7, 7, 7, 7, 7, 3, 4, 1, 1, 4, 3, 3, 4, 1, 1, 4, 3 ] Group( [ ( 1,21,16)( 2,22,15)( 3,19,18)( 4,20,17)( 5,24,13)( 6,23,14)( 7,11,10)( 8,12, 9), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)
] ) [ 6, 1 ]
[ 1, 2, 3, 3, 2, 1, 1, 2, 3, 3, 2, 1, 13, 13, 13, 13, 13, 13, 2, 1, 2, 1, 3, 3 ] Group( [ ( 1,12,20)( 2,11,19)( 3,10,23)( 4, 9,24)( 5, 8,21)( 6, 7,22)(13,16,17)(14,15,18), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)
(23,24) ] ) [ 6, 1 ]
[ 1, 2, 1, 2, 5, 5, 1, 2, 1, 2, 5, 5, 1, 2, 1, 2, 5, 5, 19, 19, 19, 19, 19, 19 ] Group( [ ( 1,13, 9)( 2,14,10)( 3,15, 7)( 4,16, 8)( 5,17,12)( 6,18,11)(19,23,22)(20,24,21), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)
(23,24) ] ) [ 6, 1 ]
15
[ 1, -1, -1, 1, 1, -1, 7, -7, 9, 10, -9, -10, -7, 7, -9, -10, 9, 10, 7, -7, 9, 10, -9, -10 ] Group( [ ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)
(17,23)(18,24)(25,26) ] ) [ 6, 1 ]
[ 1, -1, 3, 4, -3, -4, 7, -7, -7, 7, 7, -7, -3, -4, -1, 1, 4, 3, 3, 4, 1, -1, -4, -3 ] Group( [ ( 1,21,16)( 2,22,15)( 3,19,18)( 4,20,17)( 5,24,13)( 6,23,14)( 7,11,10)( 8,12, 9), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)
(17,23)(18,24)(25,26) ] ) [ 6, 1 ]
[ 1, 2, 3, -3, -2, -1, -1, -2, -3, 3, 2, 1, 13, -13, -13, 13, 13, -13, 2, 1, -2, -1, 3, -3 ] Group( [ ( 1,12,20)( 2,11,19)( 3,10,23)( 4, 9,24)( 5, 8,21)( 6, 7,22)(13,16,17)(14,15,18), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)
(20,22)(23,24)(25,26) ] ) [ 6, 1 ]
[ 1, 2, -1, -2, 5, -5, -1, -2, 1, 2, -5, 5, 1, 2, -1, -2, 5, -5, 19, -19, -19, 19, 19, -19 ] Group( [ ( 1,13, 9)( 2,14,10)( 3,15, 7)( 4,16, 8)( 5,17,12)( 6,18,11)(19,23,22)(20,24,21), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)
(20,22)(23,24)(25,26) ] ) [ 6, 1 ]
16
[ 1, 1, 3, 4, 3, 4, 1, 1, 3, 4, 3, 4, -4, -3, -4, -3, -1, -1, -4, -3, -4, -3, -1, -1 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)
(20,22)(23,24), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21)(25,26) ] ) [ 8, 3 ]
[ 1, 2, 3, 3, 2, 1, -2, -1, -2, -1, -3, -3, 3, 3, 1, 2, 1, 2, -1, -2, -3, -3, -2, -1 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)
(15,17)(16,18), ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(25,26) ] ) [ 8, 3 ]
[ 1, 2, 1, 2, 5, 5, -2, -1, -5, -5, -1, -2, -2, -1, -5, -5, -1, -2, 5, 5, 2, 1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)
(14,17)(15,16), ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23)(25,26) ] ) [ 8, 3 ]
17
[ 1, 1, 3, 4, 3, 4, 1, 1, 3, 4, 3, 4, 4, 3, 4, 3, 1, 1, 4, 3, 4, 3, 1, 1 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,24)
, ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21) ] ) [ 8, 3 ]
[ 1, 2, 3, 3, 2, 1, 2, 1, 2, 1, 3, 3, 3, 3, 1, 2, 1, 2, 1, 2, 3, 3, 2, 1 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)(13,14)(15,17)(16,18)
, ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13) ] ) [ 8, 3 ]
[ 1, 2, 1, 2, 5, 5, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 5, 5, 2, 1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)(13,18)(14,17)(15,16)
, ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23) ] ) [ 8, 3 ]
18
[ 1, -1, 3, 4, -3, -4, -1, 1, -3, -4, 3, 4, 4, 3, -4, -3, 1, -1, -4, -3, 4, 3, -1, 1 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,26), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)
(19,21)(20,22)(23,24)(25,26), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21) ] ) [ 8, 3 ]
[ 1, 2, 3, -3, -2, -1, 2, 1, -2, -1, 3, -3, -3, 3, -1, -2, 1, 2, -1, -2, -3, 3, 2, 1 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22)(25,26), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)
(13,14)(15,17)(16,18)(25,26), ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13) ] ) [ 8, 3 ]
[ 1, 2, -1, -2, 5, -5, 2, 1, 5, -5, -1, -2, -2, -1, -5, 5, 1, 2, -5, 5, -2, -1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24)(25,26), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)
(13,18)(14,17)(15,16)(25,26), ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23) ] ) [ 8, 3 ]
19
[ 1, -1, 3, 4, -3, -4, -1, 1, -3, -4, 3, 4, -4, -3, 4, 3, -1, 1, 4, 3, -4, -3, 1, -1 ] Group( [ ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,26), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)
(19,21)(20,22)(23,24)(25,26), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21)(25,26) ] ) [ 8, 3 ]
[ 1, 2, 3, -3, -2, -1, -2, -1, 2, 1, -3, 3, -3, 3, -1, -2, 1, 2, 1, 2, 3, -3, -2, -1 ] Group( [ ( 1,15)( 2,16)( 3,13)( 4,14)( 5,18)( 6,17)( 7, 9)( 8,10)(11,12)(19,24)(20,23)(21,22)(25,26), ( 1, 6)( 2, 5)( 3, 4)( 7,20)( 8,19)( 9,23)(10,24)(11,21)(12,22)
(13,14)(15,17)(16,18)(25,26), ( 1,24)( 2,23)( 3,22)( 4,21)( 5,20)( 6,19)( 7,18)( 8,17)( 9,16)(10,15)(11,14)(12,13)(25,26) ] ) [ 8, 3 ]
[ 1, 2, -1, -2, 5, -5, -2, -1, -5, 5, 1, 2, 2, 1, 5, -5, -1, -2, -5, 5, -2, -1, 2, 1 ] Group( [ ( 1, 3)( 2, 4)( 5, 6)( 7,13)( 8,14)( 9,15)(10,16)(11,17)(12,18)(19,20)(21,23)(22,24)(25,26), ( 1,22)( 2,21)( 3,24)( 4,23)( 5,19)( 6,20)( 7,12)( 8,11)( 9,10)
(13,18)(14,17)(15,16)(25,26), ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23)(25,26) ] ) [ 8, 3 ]
20
[ 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21)
, ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24) ] ) [ 12, 3 ]
21
[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)(11,22)(12,21)
, ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24) ] ) [ 24, 12 ]
22
[ 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1 ] Group( [ ( 1, 8)( 2, 7)( 3,11)( 4,12)( 5, 9)( 6,10)(13,21)(14,22)(15,19)(16,20)(17,24)(18,23), ( 1,17)( 2,18)( 3,14)( 4,13)( 5,16)( 6,15)( 7,23)( 8,24)( 9,20)(10,19)
(11,22)(12,21), ( 1, 4, 5)( 2, 3, 6)( 7,14,19)( 8,13,20)( 9,17,21)(10,18,22)(11,15,23)(12,16,24), ( 1, 2)( 3, 5)( 4, 6)( 7, 8)( 9,11)(10,12)(13,19)(14,20)(15,21)(16,22)(17,23)(18,24)(25,26) ] ) [ 24, 12 ]
23
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] Group( [ ( 1,10,17,19)( 2, 9,18,20)( 3,12,14,21)( 4,11,13,22)( 5, 7,16,23)( 6, 8,15,24), ( 1, 7)( 2, 8)( 3, 9)( 4,10)( 5,11)( 6,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,24),
(25,26) ] ) [ 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, 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, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 3, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 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, 0, 1, 1 ],
[ 5, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1 ],
[ 6, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1 ],
[ 7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1 ],
[ 8, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1 ],
[ 9, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1 ],
[ 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1 ],
[ 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1 ],
[ 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1 ],
[ 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 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, 0, 1, 0, 1 ],
[ 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1 ],
[ 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 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, 0, 1, 0, 1 ],
[ 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 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, 1, 1, 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 = 24, 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 = 12, 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 = 12, 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 = 12, 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 = 12, 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 = 12, 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 = 12, 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 = 12, 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 = 12, 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 = 8, 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 = 8, 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 = 8, 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 = 6, 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 = 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 [ 3, 7 ], maximals 3
Representation 3, dimension of U_i = 1
3, 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 [ 3, 7 ], maximals 3
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 ]
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 = 6, 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 = 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 [ 4, 8 ], maximals 4
Representation 3, dimension of U_i = 1
4, 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 [ 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 6, 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 = 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 [ 4, 13 ], maximals 4
Representation 4, dimension of U_i = 1
2, 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 [ 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 = 4, 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 = 4, 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 = 16, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
5, dim Fix_P(U) K = 8, 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 = 4, 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 = 4, 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 = 16, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
4, dim Fix_P(U) K = 8, 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 = 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 [ 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 = 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 [ 12, 16 ], maximals 12
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 12, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
5, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
2, dim Fix_P(U) K = 6, 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 = 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 [ 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 = 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 [ 11, 17 ], maximals 11
Representation 5, dimension of U_i = 2
1, dim Fix_P(U) K = 12, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
5, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
3, dim Fix_P(U) K = 6, 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 = 3, 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 = 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 [ 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 = 12, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
3, dim Fix_P(U) K = 6, 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 = 3, 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 = 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 [ 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 = 12, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
2, dim Fix_P(U) K = 6, 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 [ 12, 3 ]
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 2, dimension of U_i = 1
NON-REAL projection
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7, 20 ], maximals 7
Representation 3, dimension of U_i = 1
NON-REAL projection
7, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 3, 1 ]
20, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 7, 20 ], maximals 7
Representation 4, dimension of U_i = 3
1, dim Fix_P(U) K = 18, dim Fix_U_i K = 3, N_H(K)/K [ 12, 3 ]
3, dim Fix_P(U) K = 6, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 6, 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, 3, 6, 20 ], maximals 3 6
Possible jumps from S20 [ 3, 6, 7, 7 ]
Symmetry type S21 [ 24, 12 ]
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
20, 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 [ 20, 21 ], maximals 20
Representation 3, dimension of U_i = 2
7, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
17, 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 [ 7, 17, 21 ], maximals 17
Representation 4, 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 = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
6, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
11, 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, 5, 6, 11, 21 ], 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 ]
21, dim Fix_P(U) K = 0, dim Fix_U_i K = 0, N_H(K)/K [ 1, 1 ]
isotropy subgroups [ 1, 5, 9, 14, 21 ], maximals 9 14
Possible jumps from S21 [ 5, 6, 9, 11, 14, 17, 20 ]
Symmetry type S22 [ 24, 12 ]
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
20, 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 [ 20, 22 ], maximals 20
Representation 3, dimension of U_i = 2
7, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 6, 1 ]
18, 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 [ 7, 18, 22 ], maximals 18
Representation 4, dimension of U_i = 3
1, dim Fix_P(U) K = 9, dim Fix_U_i K = 3, N_H(K)/K [ 24, 12 ]
4, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 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 = 3, 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, 4, 6, 12, 22 ], maximals 4 6 12
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 ]
4, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 2, 1 ]
8, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
15, dim Fix_P(U) K = 3, 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 [ 1, 4, 8, 15, 22 ], maximals 8 15
Possible jumps from S22 [ 4, 6, 8, 12, 15, 18, 20 ]
Symmetry type S23 [ 48, 48 ]
Representation 3, 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 4, 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 6, dimension of U_i = 2
7, dim Fix_P(U) K = 4, dim Fix_U_i K = 2, N_H(K)/K [ 12, 4 ]
17, dim Fix_P(U) K = 2, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
18, 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 [ 7, 17, 18, 23 ], maximals 17 18
Representation 7, dimension of U_i = 3
1, dim Fix_P(U) K = 9, dim Fix_U_i K = 3, N_H(K)/K [ 48, 48 ]
2, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 8, 3 ]
4, dim Fix_P(U) K = 6, dim Fix_U_i K = 2, N_H(K)/K [ 4, 2 ]
13, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
15, dim Fix_P(U) K = 3, dim Fix_U_i K = 1, N_H(K)/K [ 2, 1 ]
19, dim Fix_P(U) K = 3, 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 [ 1, 2, 4, 13, 15, 19, 23 ], 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 ]
23, 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, 23 ], maximals 13 14 16
Possible jumps from S23 [ 13, 13, 14, 15, 16, 17, 18, 19, 21, 22 ]