Properties

Label 39T49
Order \(9477\)
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 $t$ :  $49$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,36,30,22,16,12,4,38,32,26,19,15,8)(2,34,28,23,17,10,5,39,33,27,20,13,9)(3,35,29,24,18,11,6,37,31,25,21,14,7), (1,29,18,6,31,21,7,36,24,10,39,27,14)(2,30,16,4,32,19,8,34,22,11,37,25,15)(3,28,17,5,33,20,9,35,23,12,38,26,13)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
13:  $C_{13}$
351:  27T134 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 13: $C_{13}$

Low degree siblings

39T49 x 25

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 69 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $9477=3^{6} \cdot 13$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [9477, 4041]
Character table: Data not available.