Properties

Label 39T32
Order \(2028\)
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 $t$ :  $32$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,35,23,3,38,15,6,36,16,4,33,24)(2,30,19,11,37,22,5,28,20,9,34,17)(7,31,25,12,32,18,13,27,14,8,39,21)(10,29,26), (1,7,11,5)(2,12,10,13)(3,4,9,8)(14,23,16,20)(17,25,26,18)(19,22,24,21)(27,33,37,31)(28,38,36,39)(29,30,35,34)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
4:  $C_4$
6:  $C_6$
12:  $C_{12}$
156:  $F_{13}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T32 x 3

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 $ $1$ $1$ $()$
$ 13, 13, 13 $ $12$ $13$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,15,16,17,18,19,20,21,22,23,24,25, 26)(27,31,35,39,30,34,38,29,33,37,28,32,36)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,16,18,20,22,24,26,15,17,19,21,23, 25)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,18,22,26,17,21,25,16,20,24,15,19, 23)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $12$ $13$ $(14,16,18,20,22,24,26,15,17,19,21,23,25)(27,34,28,35,29,36,30,37,31,38,32,39, 33)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,18,22,26,17,21,25,16,20,24,15,19, 23)(27,29,31,33,35,37,39,28,30,32,34,36,38)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,20,26,19,25,18,24,17,23,16,22,15, 21)(27,37,34,31,28,38,35,32,29,39,36,33,30)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,19,24,16,21,26,18,23,15,20,25,17, 22)(27,33,39,32,38,31,37,30,36,29,35,28,34)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,15,16,17,18,19,20,21,22,23,24,25, 26)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $12$ $13$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(27,39,38,37,36,35,34,33,32,31,30,29, 28)$
$ 13, 13, 13 $ $12$ $13$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,21,15,22,16,23,17,24,18,25,19,26, 20)(27,28,29,30,31,32,33,34,35,36,37,38,39)$
$ 13, 13, 13 $ $12$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,23,19,15,24,20,16,25,21,17,26,22, 18)(27,36,32,28,37,33,29,38,34,30,39,35,31)$
$ 13, 13, 13 $ $12$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,26,25,24,23,22,21,20,19,18,17,16, 15)(27,34,28,35,29,36,30,37,31,38,32,39,33)$
$ 13, 13, 13 $ $12$ $13$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,16,18,20,22,24,26,15,17,19,21,23, 25)(27,33,39,32,38,31,37,30,36,29,35,28,34)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $12$ $13$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(27,38,36,34,32,30,28,39,37,35,33,31, 29)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $169$ $3$ $( 1,38,16)( 2,37,20)( 3,36,24)( 4,35,15)( 5,34,19)( 6,33,23)( 7,32,14) ( 8,31,18)( 9,30,22)(10,29,26)(11,28,17)(12,27,21)(13,39,25)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $169$ $3$ $( 1,16,38)( 2,20,37)( 3,24,36)( 4,15,35)( 5,19,34)( 6,23,33)( 7,14,32) ( 8,18,31)( 9,22,30)(10,26,29)(11,17,28)(12,21,27)(13,25,39)$
$ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1 $ $169$ $2$ $( 2,13)( 3,12)( 4,11)( 5,10)( 6, 9)( 7, 8)(15,26)(16,25)(17,24)(18,23)(19,22) (20,21)(27,33)(28,32)(29,31)(34,39)(35,38)(36,37)$
$ 6, 6, 6, 6, 6, 6, 3 $ $169$ $6$ $( 1,38,15,10,34,25)( 2,39,19, 9,33,21)( 3,27,23, 8,32,17)( 4,28,14, 7,31,26) ( 5,29,18, 6,30,22)(11,35,16,13,37,24)(12,36,20)$
$ 6, 6, 6, 6, 6, 6, 3 $ $169$ $6$ $( 1,16,39, 5,26,35)( 2,25,38, 4,17,36)( 3,21,37)( 6,22,34,13,20,27) ( 7,18,33,12,24,28)( 8,14,32,11,15,29)( 9,23,31,10,19,30)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1 $ $169$ $4$ $( 2, 6,13, 9)( 3,11,12, 4)( 5, 8,10, 7)(15,19,26,22)(16,24,25,17)(18,21,23,20) (27,28,33,32)(29,38,31,35)(34,37,39,36)$
$ 12, 12, 12, 3 $ $169$ $12$ $( 1,38,18,12,35,26, 9,37,25,11,27,17)( 2,33,14, 7,34,20, 8,29,16, 3,28,23) ( 4,36,19,10,32,21, 6,39,24,13,30,22)( 5,31,15)$
$ 12, 12, 12, 3 $ $169$ $12$ $( 1,16,36, 5,18,27,11,21,33, 7,19,29)( 2,23,37,13,22,35,10,14,32,12,15,34) ( 3,17,38, 8,26,30, 9,20,31, 4,24,39)( 6,25,28)$
$ 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1 $ $169$ $4$ $( 2, 9,13, 6)( 3, 4,12,11)( 5, 7,10, 8)(15,22,26,19)(16,17,25,24)(18,20,23,21) (27,32,33,28)(29,35,31,38)(34,36,39,37)$
$ 12, 12, 12, 3 $ $169$ $12$ $( 1,38,26, 5,32,23,12,28,21, 8,34,24)( 2,30,22,10,31,16,11,36,25, 3,35,18) ( 4,27,14, 7,29,15, 9,39,20, 6,37,19)(13,33,17)$
$ 12, 12, 12, 3 $ $169$ $12$ $( 1,16,28,12,17,39, 2,22,29, 4,21,31)( 3,15,30, 9,25,36,13,23,27, 7,26,34) ( 5,14,32, 6,20,33,11,24,38,10,18,37)( 8,19,35)$

Group invariants

Order:  $2028=2^{2} \cdot 3 \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.