Properties

Label 39T20
Order \(507\)
n \(39\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{13}:(C_{13}:C_3)$

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Group action invariants

Degree $n$ :  $39$
Transitive number $t$ :  $20$
Group :  $C_{13}:(C_{13}:C_3)$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,23,38)(2,20,39)(3,17,29)(4,19,36)(5,16,33)(6,24,32)(7,22,35)(8,15,31)(9,26,30)(10,18,34)(11,21,27)(12,14,37)(13,25,28), (1,22,32)(2,15,30)(3,18,31)(4,26,35)(5,20,36)(6,14,29)(7,21,37)(8,25,33)(9,16,27)(10,24,28)(11,19,38)(12,23,34)(13,17,39)
$|\Aut(F/K)|$:  $13$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T20 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 59 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $507=3 \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [507, 5]
Character table: Data not available.