Properties

Label 39T48
Order \(6591\)
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 $t$ :  $48$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,27,22,2,30,20,12,39,24,5,28,19,6,34,25,9,37,23,10,35,16,4,36,18,3,33,21,11,31,15,13,29,14,7,32,26,8,38,17), (1,36,19,2,33,25,12,31,23,5,29,16,6,32,18,9,38,21,10,27,15,4,30,14,3,39,26,11,28,17,13,34,22,7,37,20,8,35,24)
$|\Aut(F/K)|$:  $13$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
13:  $C_{13}$
39:  $C_{13}:C_3$ x 2, $C_{39}$
507:  39T20, 39T21 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T48 x 47

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 767 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $6591=3 \cdot 13^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.