Properties

Label 39T25
Order \(1014\)
n \(39\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$
26:  $D_{13}$
78:  $C_{13}:C_6$, 39T5

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T25 x 3

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 50 conjugacy classes of elements. Data not shown.

Group invariants

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