Properties

Label 38T14
Degree $38$
Order $2166$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $C_6$
$57$:  $C_{19}:C_{3}$
$114$:  $C_{19}:C_{6}$, 38T4

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T14 x 8

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 75 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2166=2 \cdot 3 \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.