Properties

Label 39T24
Order \(1014\)
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 $t$ :  $24$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,27,21)(2,39,25)(3,38,16)(4,37,20)(5,36,24)(6,35,15)(7,34,19)(8,33,23)(9,32,14)(10,31,18)(11,30,22)(12,29,26)(13,28,17), (1,30,26,8,37,15)(2,31,17,7,36,24)(3,32,21,6,35,20)(4,33,25,5,34,16)(9,38,19,13,29,22)(10,39,23,12,28,18)(11,27,14)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T24 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 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,16,18,20,22,24,26,15,17,19,21,23, 25)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,18,22,26,17,21,25,16,20,24,15,19, 23)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,22,17,25,20,15,23,18,26,21,16,24, 19)(27,33,39,32,38,31,37,30,36,29,35,28,34)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,17,20,23,26,16,19,22,25,15,18,21, 24)(27,39,38,37,36,35,34,33,32,31,30,29,28)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,20,26,19,25,18,24,17,23,16,22,15, 21)(27,38,36,34,32,30,28,39,37,35,33,31,29)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(14,26,25,24,23,22,21,20,19,18,17,16, 15)(27,36,32,28,37,33,29,38,34,30,39,35,31)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $(14,21,15,22,16,23,17,24,18,25,19,26,20)(27,32,37,29,34,39,31,36,28,33,38,30, 35)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,23,19,15,24,20,16,25,21,17,26,22, 18)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,25,23,21,19,17,15,26,24,22,20,18, 16)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,16,18,20,22,24,26,15,17,19,21,23, 25)(27,38,36,34,32,30,28,39,37,35,33,31,29)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,24,21,18,15,25,22,19,16,26,23,20, 17)(27,31,35,39,30,34,38,29,33,37,28,32,36)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(27,30,33,36,39,29,32,35,38,28,31,34, 37)$
$ 13, 13, 13 $ $6$ $13$ $( 1,13,12,11,10, 9, 8, 7, 6, 5, 4, 3, 2)(14,19,24,16,21,26,18,23,15,20,25,17, 22)(27,37,34,31,28,38,35,32,29,39,36,33,30)$
$ 13, 13, 13 $ $6$ $13$ $( 1,12,10, 8, 6, 4, 2,13,11, 9, 7, 5, 3)(14,17,20,23,26,16,19,22,25,15,18,21, 24)(27,29,31,33,35,37,39,28,30,32,34,36,38)$
$ 13, 13, 13 $ $6$ $13$ $( 1,10, 6, 2,11, 7, 3,12, 8, 4,13, 9, 5)(14,26,25,24,23,22,21,20,19,18,17,16, 15)(27,39,38,37,36,35,34,33,32,31,30,29,28)$
$ 13, 13, 13 $ $6$ $13$ $( 1,11, 8, 5, 2,12, 9, 6, 3,13,10, 7, 4)(14,15,16,17,18,19,20,21,22,23,24,25, 26)(27,34,28,35,29,36,30,37,31,38,32,39,33)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,17,20,23,26,16,19,22,25,15,18,21, 24)(27,32,37,29,34,39,31,36,28,33,38,30,35)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,19,24,16,21,26,18,23,15,20,25,17, 22)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,23,19,15,24,20,16,25,21,17,26,22, 18)(27,30,33,36,39,29,32,35,38,28,31,34,37)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 4, 7,10,13, 3, 6, 9,12, 2, 5, 8,11)(14,21,15,22,16,23,17,24,18,25,19,26, 20)(27,35,30,38,33,28,36,31,39,34,29,37,32)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 7,13, 6,12, 5,11, 4,10, 3, 9, 2, 8)(27,33,39,32,38,31,37,30,36,29,35,28, 34)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 6,11, 3, 8,13, 5,10, 2, 7,12, 4, 9)(14,25,23,21,19,17,15,26,24,22,20,18, 16)(27,38,36,34,32,30,28,39,37,35,33,31,29)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 8, 2, 9, 3,10, 4,11, 5,12, 6,13, 7)(14,16,18,20,22,24,26,15,17,19,21,23, 25)(27,28,29,30,31,32,33,34,35,36,37,38,39)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11,12,13)(14,18,22,26,17,21,25,16,20,24,15,19, 23)(27,29,31,33,35,37,39,28,30,32,34,36,38)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 3, 5, 7, 9,11,13, 2, 4, 6, 8,10,12)(14,20,26,19,25,18,24,17,23,16,22,15, 21)(27,37,34,31,28,38,35,32,29,39,36,33,30)$
$ 13, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,24,21,18,15,25,22,19,16,26,23,20, 17)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 5, 9,13, 4, 8,12, 3, 7,11, 2, 6,10)(14,26,25,24,23,22,21,20,19,18,17,16, 15)(27,34,28,35,29,36,30,37,31,38,32,39,33)$
$ 13, 13, 13 $ $6$ $13$ $( 1, 9, 4,12, 7, 2,10, 5,13, 8, 3,11, 6)(14,25,23,21,19,17,15,26,24,22,20,18, 16)(27,28,29,30,31,32,33,34,35,36,37,38,39)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $169$ $3$ $( 1,27,21)( 2,39,25)( 3,38,16)( 4,37,20)( 5,36,24)( 6,35,15)( 7,34,19) ( 8,33,23)( 9,32,14)(10,31,18)(11,30,22)(12,29,26)(13,28,17)$
$ 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 $ $169$ $3$ $( 1,21,27)( 2,25,39)( 3,16,38)( 4,20,37)( 5,24,36)( 6,15,35)( 7,19,34) ( 8,23,33)( 9,14,32)(10,18,31)(11,22,30)(12,26,29)(13,17,28)$
$ 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 $ $169$ $6$ $( 1,27,23,10,36,20)( 2,28,14, 9,35,16)( 3,29,18, 8,34,25)( 4,30,22, 7,33,21) ( 5,31,26, 6,32,17)(11,37,24,13,39,19)(12,38,15)$
$ 6, 6, 6, 6, 6, 6, 3 $ $169$ $6$ $( 1,21,37, 5,18,33)( 2,17,36, 4,22,34)( 3,26,35)( 6,14,32,13,25,38) ( 7,23,31,12,16,39)( 8,19,30,11,20,27)( 9,15,29,10,24,28)$

Group invariants

Order:  $1014=2 \cdot 3 \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1014, 10]
Character table: Data not available.