Properties

Label 39T25
Degree $39$
Order $1014$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$26$:  $D_{13}$
$78$:  $C_{13}:C_6$, 39T5

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 13: None

Low degree siblings

39T25 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 50 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1014=2 \cdot 3 \cdot 13^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1014, 13]
Character table: not available.