Properties

Label 39T21
Degree $39$
Order $507$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{13}\times C_{13}:C_3$

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T21 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 91 conjugacy classes of elements. Data not shown.

Group invariants

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