Properties

Label 39T28
Order \(1053\)
n \(39\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $39$
Transitive number $t$ :  $28$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,35,28,24,17,11,4,39,31,26,19,13,9,2,36,29,22,18,12,5,37,32,27,20,14,7,3,34,30,23,16,10,6,38,33,25,21,15,8), (1,8,13,19,25,32,39,5,11,16,23,30,36,3,7,15,21,27,31,38,4,10,18,22,29,35,2,9,14,20,26,33,37,6,12,17,24,28,34)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
13:  $C_{13}$
39:  $C_{39}$
351:  27T134

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 13: $C_{13}$

Low degree siblings

39T28

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

Cycle TypeSizeOrderRepresentative
$ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $1$ $1$ $()$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $( 4, 5, 6)(10,11,12)(13,14,15)(16,17,18)(19,21,20)(22,24,23)(28,29,30) (31,33,32)(34,35,36)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $( 4, 6, 5)(10,12,11)(13,15,14)(16,18,17)(19,20,21)(22,23,24)(28,30,29) (31,32,33)(34,36,35)$
$ 13, 13, 13 $ $27$ $13$ $( 1,24, 4,26, 9,29,12,32,14,34,16,38,21)( 2,22, 5,27, 7,30,10,33,15,35,17,39, 19)( 3,23, 6,25, 8,28,11,31,13,36,18,37,20)$
$ 13, 13, 13 $ $27$ $13$ $( 1, 4, 9,12,14,16,21,24,26,29,32,34,38)( 2, 5, 7,10,15,17,19,22,27,30,33,35, 39)( 3, 6, 8,11,13,18,20,23,25,28,31,36,37)$
$ 13, 13, 13 $ $27$ $13$ $( 1, 9,14,21,26,32,38, 4,12,16,24,29,34)( 2, 7,15,19,27,33,39, 5,10,17,22,30, 35)( 3, 8,13,20,25,31,37, 6,11,18,23,28,36)$
$ 13, 13, 13 $ $27$ $13$ $( 1,14,26,38,12,24,34, 9,21,32, 4,16,29)( 2,15,27,39,10,22,35, 7,19,33, 5,17, 30)( 3,13,25,37,11,23,36, 8,20,31, 6,18,28)$
$ 13, 13, 13 $ $27$ $13$ $( 1,26,12,34,21, 4,29,14,38,24, 9,32,16)( 2,27,10,35,19, 5,30,15,39,22, 7,33, 17)( 3,25,11,36,20, 6,28,13,37,23, 8,31,18)$
$ 13, 13, 13 $ $27$ $13$ $( 1,12,21,29,38, 9,16,26,34, 4,14,24,32)( 2,10,19,30,39, 7,17,27,35, 5,15,22, 33)( 3,11,20,28,37, 8,18,25,36, 6,13,23,31)$
$ 13, 13, 13 $ $27$ $13$ $( 1,21,38,16,34,14,32,12,29, 9,26, 4,24)( 2,19,39,17,35,15,33,10,30, 7,27, 5, 22)( 3,20,37,18,36,13,31,11,28, 8,25, 6,23)$
$ 13, 13, 13 $ $27$ $13$ $( 1,38,34,32,29,26,24,21,16,14,12, 9, 4)( 2,39,35,33,30,27,22,19,17,15,10, 7, 5)( 3,37,36,31,28,25,23,20,18,13,11, 8, 6)$
$ 13, 13, 13 $ $27$ $13$ $( 1,34,29,24,16,12, 4,38,32,26,21,14, 9)( 2,35,30,22,17,10, 5,39,33,27,19,15, 7)( 3,36,28,23,18,11, 6,37,31,25,20,13, 8)$
$ 13, 13, 13 $ $27$ $13$ $( 1,29,16, 4,32,21, 9,34,24,12,38,26,14)( 2,30,17, 5,33,19, 7,35,22,10,39,27, 15)( 3,28,18, 6,31,20, 8,36,23,11,37,25,13)$
$ 13, 13, 13 $ $27$ $13$ $( 1,16,32, 9,24,38,14,29, 4,21,34,12,26)( 2,17,33, 7,22,39,15,30, 5,19,35,10, 27)( 3,18,31, 8,23,37,13,28, 6,20,36,11,25)$
$ 13, 13, 13 $ $27$ $13$ $( 1,32,24,14, 4,34,26,16, 9,38,29,21,12)( 2,33,22,15, 5,35,27,17, 7,39,30,19, 10)( 3,31,23,13, 6,36,25,18, 8,37,28,20,11)$
$ 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $(10,12,11)(13,15,14)(16,17,18)(22,24,23)(28,29,30)(31,32,33)(37,38,39)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $( 7, 8, 9)(10,12,11)(16,18,17)(19,20,21)(22,23,24)(25,27,26)(28,29,30) (31,33,32)(34,36,35)(37,39,38)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)$
$ 39 $ $27$ $39$ $( 1,24, 6,25, 8,28,12,31,14,36,18,38,19, 2,22, 4,26, 9,29,10,32,15,34,16,39, 20, 3,23, 5,27, 7,30,11,33,13,35,17,37,21)$
$ 39 $ $27$ $39$ $( 1, 4, 9,12,13,17,20,23,27,30,31,34,38, 2, 5, 7,10,14,18,21,24,25,28,32,35, 39, 3, 6, 8,11,15,16,19,22,26,29,33,36,37)$
$ 39 $ $27$ $39$ $( 1, 9,14,20,25,31,38, 5,10,16,22,29,35, 2, 7,15,21,26,32,39, 6,11,17,23,30, 36, 3, 8,13,19,27,33,37, 4,12,18,24,28,34)$
$ 39 $ $27$ $39$ $( 1,14,25,37,12,23,35, 7,19,33, 6,18,29, 2,15,26,38,10,24,36, 8,20,31, 4,16, 30, 3,13,27,39,11,22,34, 9,21,32, 5,17,28)$
$ 39 $ $27$ $39$ $( 1,26,12,36,20, 6,28,14,37,24, 8,31,16, 2,27,10,34,21, 4,29,15,38,22, 9,32, 17, 3,25,11,35,19, 5,30,13,39,23, 7,33,18)$
$ 39 $ $27$ $39$ $( 1,12,20,28,38, 7,17,25,36, 6,13,22,32, 2,10,21,29,39, 8,18,26,34, 4,14,23, 33, 3,11,19,30,37, 9,16,27,35, 5,15,24,31)$
$ 39 $ $27$ $39$ $( 1,21,38,17,36,13,33,11,30, 8,25, 6,23, 2,19,39,18,34,14,31,12,28, 9,26, 4, 24, 3,20,37,16,35,15,32,10,29, 7,27, 5,22)$
$ 39 $ $27$ $39$ $( 1,38,35,33,28,26,24,20,18,14,11, 7, 5, 2,39,36,31,29,27,22,21,16,15,12, 8, 6, 3,37,34,32,30,25,23,19,17,13,10, 9, 4)$
$ 39 $ $27$ $39$ $( 1,34,29,22,16,10, 4,38,33,25,20,13, 7, 2,35,30,23,17,11, 5,39,31,26,21,14, 8, 3,36,28,24,18,12, 6,37,32,27,19,15, 9)$
$ 39 $ $27$ $39$ $( 1,29,17, 6,31,21, 9,34,24,11,39,25,13, 2,30,18, 4,32,19, 7,35,22,12,37,26, 14, 3,28,16, 5,33,20, 8,36,23,10,38,27,15)$
$ 39 $ $27$ $39$ $( 1,16,33, 8,23,39,13,30, 6,20,36,11,27, 2,17,31, 9,24,37,14,28, 4,21,34,12, 25, 3,18,32, 7,22,38,15,29, 5,19,35,10,26)$
$ 39 $ $27$ $39$ $( 1,32,22,14, 6,36,25,18, 9,38,30,20,11, 2,33,23,15, 4,34,26,16, 7,39,28,21, 12, 3,31,24,13, 5,35,27,17, 8,37,29,19,10)$
$ 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $(10,11,12)(13,14,15)(16,18,17)(22,23,24)(28,30,29)(31,33,32)(37,39,38)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $13$ $3$ $( 4, 6, 5)( 7, 8, 9)(13,14,15)(16,18,17)(19,21,20)(22,23,24)(25,27,26) (28,29,30)(31,32,33)(34,35,36)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $1$ $3$ $( 1, 3, 2)( 4, 6, 5)( 7, 9, 8)(10,12,11)(13,15,14)(16,18,17)(19,21,20) (22,24,23)(25,27,26)(28,30,29)(31,33,32)(34,36,35)(37,39,38)$
$ 39 $ $27$ $39$ $( 1,24, 5,27, 7,30,12,33,14,35,17,38,20, 3,23, 4,26, 9,29,11,32,13,34,16,37, 19, 2,22, 6,25, 8,28,10,31,15,36,18,39,21)$
$ 39 $ $27$ $39$ $( 1, 4, 9,12,15,18,19,22,25,28,33,34,38, 3, 6, 8,11,14,17,21,24,27,30,32,36, 37, 2, 5, 7,10,13,16,20,23,26,29,31,35,39)$
$ 39 $ $27$ $39$ $( 1, 9,14,19,27,33,38, 6,11,16,23,29,36, 3, 8,13,21,26,32,37, 5,10,18,22,28, 35, 2, 7,15,20,25,31,39, 4,12,17,24,30,34)$
$ 39 $ $27$ $39$ $( 1,14,27,39,12,22,36, 8,20,31, 5,17,29, 3,13,26,38,11,24,35, 7,19,33, 4,16, 28, 2,15,25,37,10,23,34, 9,21,32, 6,18,30)$
$ 39 $ $27$ $39$ $( 1,26,12,35,19, 5,30,14,39,24, 7,33,16, 3,25,11,34,21, 4,29,13,38,23, 9,32, 18, 2,27,10,36,20, 6,28,15,37,22, 8,31,17)$
$ 39 $ $27$ $39$ $( 1,12,19,30,38, 8,18,27,35, 5,15,23,32, 3,11,21,29,37, 7,17,26,34, 4,14,22, 31, 2,10,20,28,39, 9,16,25,36, 6,13,24,33)$
$ 39 $ $27$ $39$ $( 1,21,38,18,35,15,31,10,28, 7,27, 5,22, 3,20,37,17,34,14,33,12,30, 9,26, 4, 24, 2,19,39,16,36,13,32,11,29, 8,25, 6,23)$
$ 39 $ $27$ $39$ $( 1,38,36,31,30,26,24,19,17,14,10, 8, 6, 3,37,35,33,29,25,23,21,16,13,12, 7, 5, 2,39,34,32,28,27,22,20,18,15,11, 9, 4)$
$ 39 $ $27$ $39$ $( 1,34,29,23,16,11, 4,38,31,27,19,15, 8, 3,36,28,22,18,10, 6,37,33,26,21,14, 7, 2,35,30,24,17,12, 5,39,32,25,20,13, 9)$
$ 39 $ $27$ $39$ $( 1,29,18, 5,33,21, 9,34,24,10,37,27,15, 3,28,17, 4,32,20, 8,36,23,12,39,26, 14, 2,30,16, 6,31,19, 7,35,22,11,38,25,13)$
$ 39 $ $27$ $39$ $( 1,16,31, 7,22,37,15,28, 5,19,35,10,25, 3,18,33, 9,24,39,14,30, 4,21,34,12, 27, 2,17,32, 8,23,38,13,29, 6,20,36,11,26)$
$ 39 $ $27$ $39$ $( 1,32,23,14, 5,35,27,17, 9,38,28,19,10, 3,31,22,13, 4,34,26,16, 8,37,30,21, 12, 2,33,24,15, 6,36,25,18, 7,39,29,20,11)$

Group invariants

Order:  $1053=3^{4} \cdot 13$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1053, 50]
Character table: Data not available.