Properties

Label 39T50
Degree $39$
Order $9477$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $39$
Transitive number $t$:  $50$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $3$
Generators:  (1,31,24,15,4,35,27,18,8,38,30,19,10)(2,32,22,13,5,36,25,16,9,39,28,20,11)(3,33,23,14,6,34,26,17,7,37,29,21,12), (1,37,36,33,29,25,23,20,17,15,12,8,5)(2,38,34,31,30,26,24,21,18,13,10,9,6)(3,39,35,32,28,27,22,19,16,14,11,7,4)

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

39T50 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, 4043]
Character table: not available.