Properties

Label 39T1
Order \(39\)
n \(39\)
Cyclic Yes
Abelian Yes
Solvable Yes
Primitive No
$p$-group No
Group: $C_{39}$

Related objects

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Group action invariants

Degree $n$ :  $39$
Transitive number $t$ :  $1$
Group :  $C_{39}$
Parity:  $1$
Primitive:  No
Nilpotency class:  $1$
Generators:  (1,35,28,23,16,10,6,39,33,26,21,15,9,3,34,30,22,18,12,5,38,32,25,20,14,8,2,36,29,24,17,11,4,37,31,27,19,13,7)
$|\Aut(F/K)|$:  $39$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: $C_{13}$

Low degree siblings

There are no siblings 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, 3, 3, 3, 3 $ $1$ $3$ $( 1, 2, 3)( 4, 5, 6)( 7, 8, 9)(10,11,12)(13,14,15)(16,17,18)(19,20,21) (22,23,24)(25,26,27)(28,29,30)(31,32,33)(34,35,36)(37,38,39)$
$ 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 $ $1$ $39$ $( 1, 4, 8,12,15,16,19,24,25,30,33,35,37, 2, 5, 9,10,13,17,20,22,26,28,31,36, 38, 3, 6, 7,11,14,18,21,23,27,29,32,34,39)$
$ 39 $ $1$ $39$ $( 1, 5, 7,12,13,18,19,22,27,30,31,34,37, 3, 4, 9,11,15,17,21,24,26,29,33,36, 39, 2, 6, 8,10,14,16,20,23,25,28,32,35,38)$
$ 13, 13, 13 $ $1$ $13$ $( 1, 6, 9,12,14,17,19,23,26,30,32,36,37)( 2, 4, 7,10,15,18,20,24,27,28,33,34, 38)( 3, 5, 8,11,13,16,21,22,25,29,31,35,39)$
$ 39 $ $1$ $39$ $( 1, 7,13,19,27,31,37, 4,11,17,24,29,36, 2, 8,14,20,25,32,38, 5,12,18,22,30, 34, 3, 9,15,21,26,33,39, 6,10,16,23,28,35)$
$ 39 $ $1$ $39$ $( 1, 8,15,19,25,33,37, 5,10,17,22,28,36, 3, 7,14,21,27,32,39, 4,12,16,24,30, 35, 2, 9,13,20,26,31,38, 6,11,18,23,29,34)$
$ 13, 13, 13 $ $1$ $13$ $( 1, 9,14,19,26,32,37, 6,12,17,23,30,36)( 2, 7,15,20,27,33,38, 4,10,18,24,28, 34)( 3, 8,13,21,25,31,39, 5,11,16,22,29,35)$
$ 39 $ $1$ $39$ $( 1,10,21,30,38, 8,17,27,35, 6,15,22,32, 2,11,19,28,39, 9,18,25,36, 4,13,23, 33, 3,12,20,29,37, 7,16,26,34, 5,14,24,31)$
$ 39 $ $1$ $39$ $( 1,11,20,30,39, 7,17,25,34, 6,13,24,32, 3,10,19,29,38, 9,16,27,36, 5,15,23, 31, 2,12,21,28,37, 8,18,26,35, 4,14,22,33)$
$ 13, 13, 13 $ $1$ $13$ $( 1,12,19,30,37, 9,17,26,36, 6,14,23,32)( 2,10,20,28,38, 7,18,27,34, 4,15,24, 33)( 3,11,21,29,39, 8,16,25,35, 5,13,22,31)$
$ 39 $ $1$ $39$ $( 1,13,27,37,11,24,36, 8,20,32, 5,18,30, 3,15,26,39,10,23,35, 7,19,31, 4,17, 29, 2,14,25,38,12,22,34, 9,21,33, 6,16,28)$
$ 13, 13, 13 $ $1$ $13$ $( 1,14,26,37,12,23,36, 9,19,32, 6,17,30)( 2,15,27,38,10,24,34, 7,20,33, 4,18, 28)( 3,13,25,39,11,22,35, 8,21,31, 5,16,29)$
$ 39 $ $1$ $39$ $( 1,15,25,37,10,22,36, 7,21,32, 4,16,30, 2,13,26,38,11,23,34, 8,19,33, 5,17, 28, 3,14,27,39,12,24,35, 9,20,31, 6,18,29)$
$ 39 $ $1$ $39$ $( 1,16,33, 9,22,38,14,29, 4,19,35,10,26, 3,18,32, 8,24,37,13,28, 6,21,34,12, 25, 2,17,31, 7,23,39,15,30, 5,20,36,11,27)$
$ 13, 13, 13 $ $1$ $13$ $( 1,17,32, 9,23,37,14,30, 6,19,36,12,26)( 2,18,33, 7,24,38,15,28, 4,20,34,10, 27)( 3,16,31, 8,22,39,13,29, 5,21,35,11,25)$
$ 39 $ $1$ $39$ $( 1,18,31, 9,24,39,14,28, 5,19,34,11,26, 2,16,32, 7,22,37,15,29, 6,20,35,12, 27, 3,17,33, 8,23,38,13,30, 4,21,36,10,25)$
$ 13, 13, 13 $ $1$ $13$ $( 1,19,37,17,36,14,32,12,30, 9,26, 6,23)( 2,20,38,18,34,15,33,10,28, 7,27, 4, 24)( 3,21,39,16,35,13,31,11,29, 8,25, 5,22)$
$ 39 $ $1$ $39$ $( 1,20,39,17,34,13,32,10,29, 9,27, 5,23, 2,21,37,18,35,14,33,11,30, 7,25, 6, 24, 3,19,38,16,36,15,31,12,28, 8,26, 4,22)$
$ 39 $ $1$ $39$ $( 1,21,38,17,35,15,32,11,28, 9,25, 4,23, 3,20,37,16,34,14,31,10,30, 8,27, 6, 22, 2,19,39,18,36,13,33,12,29, 7,26, 5,24)$
$ 39 $ $1$ $39$ $( 1,22, 4,26, 8,28,12,31,15,36,16,38,19, 3,24, 6,25, 7,30,11,33,14,35,18,37, 21, 2,23, 5,27, 9,29,10,32,13,34,17,39,20)$
$ 13, 13, 13 $ $1$ $13$ $( 1,23, 6,26, 9,30,12,32,14,36,17,37,19)( 2,24, 4,27, 7,28,10,33,15,34,18,38, 20)( 3,22, 5,25, 8,29,11,31,13,35,16,39,21)$
$ 39 $ $1$ $39$ $( 1,24, 5,26, 7,29,12,33,13,36,18,39,19, 2,22, 6,27, 8,30,10,31,14,34,16,37, 20, 3,23, 4,25, 9,28,11,32,15,35,17,38,21)$
$ 39 $ $1$ $39$ $( 1,25,10,36,21, 4,30,13,38,23, 8,33,17, 3,27,12,35,20, 6,29,15,37,22, 7,32, 16, 2,26,11,34,19, 5,28,14,39,24, 9,31,18)$
$ 13, 13, 13 $ $1$ $13$ $( 1,26,12,36,19, 6,30,14,37,23, 9,32,17)( 2,27,10,34,20, 4,28,15,38,24, 7,33, 18)( 3,25,11,35,21, 5,29,13,39,22, 8,31,16)$
$ 39 $ $1$ $39$ $( 1,27,11,36,20, 5,30,15,39,23, 7,31,17, 2,25,12,34,21, 6,28,13,37,24, 8,32, 18, 3,26,10,35,19, 4,29,14,38,22, 9,33,16)$
$ 39 $ $1$ $39$ $( 1,28,16, 6,33,21, 9,34,22,12,38,25,14, 2,29,17, 4,31,19, 7,35,23,10,39,26, 15, 3,30,18, 5,32,20, 8,36,24,11,37,27,13)$
$ 39 $ $1$ $39$ $( 1,29,18, 6,31,20, 9,35,24,12,39,27,14, 3,28,17, 5,33,19, 8,34,23,11,38,26, 13, 2,30,16, 4,32,21, 7,36,22,10,37,25,15)$
$ 13, 13, 13 $ $1$ $13$ $( 1,30,17, 6,32,19, 9,36,23,12,37,26,14)( 2,28,18, 4,33,20, 7,34,24,10,38,27, 15)( 3,29,16, 5,31,21, 8,35,22,11,39,25,13)$
$ 39 $ $1$ $39$ $( 1,31,24,14, 5,34,26,16, 7,37,29,20,12, 3,33,23,13, 4,36,25,18, 9,39,28,19, 11, 2,32,22,15, 6,35,27,17, 8,38,30,21,10)$
$ 13, 13, 13 $ $1$ $13$ $( 1,32,23,14, 6,36,26,17, 9,37,30,19,12)( 2,33,24,15, 4,34,27,18, 7,38,28,20, 10)( 3,31,22,13, 5,35,25,16, 8,39,29,21,11)$
$ 39 $ $1$ $39$ $( 1,33,22,14, 4,35,26,18, 8,37,28,21,12, 2,31,23,15, 5,36,27,16, 9,38,29,19, 10, 3,32,24,13, 6,34,25,17, 7,39,30,20,11)$
$ 39 $ $1$ $39$ $( 1,34,29,23,18,11, 6,38,31,26,20,13, 9, 2,35,30,24,16,12, 4,39,32,27,21,14, 7, 3,36,28,22,17,10, 5,37,33,25,19,15, 8)$
$ 39 $ $1$ $39$ $( 1,35,28,23,16,10, 6,39,33,26,21,15, 9, 3,34,30,22,18,12, 5,38,32,25,20,14, 8, 2,36,29,24,17,11, 4,37,31,27,19,13, 7)$
$ 13, 13, 13 $ $1$ $13$ $( 1,36,30,23,17,12, 6,37,32,26,19,14, 9)( 2,34,28,24,18,10, 4,38,33,27,20,15, 7)( 3,35,29,22,16,11, 5,39,31,25,21,13, 8)$
$ 13, 13, 13 $ $1$ $13$ $( 1,37,36,32,30,26,23,19,17,14,12, 9, 6)( 2,38,34,33,28,27,24,20,18,15,10, 7, 4)( 3,39,35,31,29,25,22,21,16,13,11, 8, 5)$
$ 39 $ $1$ $39$ $( 1,38,35,32,28,25,23,20,16,14,10, 8, 6, 2,39,36,33,29,26,24,21,17,15,11, 9, 4, 3,37,34,31,30,27,22,19,18,13,12, 7, 5)$
$ 39 $ $1$ $39$ $( 1,39,34,32,29,27,23,21,18,14,11, 7, 6, 3,38,36,31,28,26,22,20,17,13,10, 9, 5, 2,37,35,33,30,25,24,19,16,15,12, 8, 4)$

Group invariants

Order:  $39=3 \cdot 13$
Cyclic:  Yes
Abelian:  Yes
Solvable:  Yes
GAP id:  [39, 2]
Character table: Data not available.