Galois group: 38T19

• Label: 38T19
• Degree: $38$
• Order: $4332$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $D_{19}^2:C_3$

Group invariants

Abstract group:		$D_{19}^2:C_3$
Order:		$4332=2^{2} \cdot 3 \cdot 19^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

Degree $n$:		$38$
Transitive number $t$:		$19$
Parity:		$-1$
Primitive:		no
$\card{\Aut(F/K)}$:		$1$
Generators:		$(1,26,16,34,10,27)(2,24,8,31,17,32)(3,22,19,28,5,37)(4,20,11,25,12,23)(6,35,14,38,7,33)(9,29)(13,21,15,36,18,30)$, $(1,31,13,36,12,34)(2,33,5,20,19,29)(3,35,16,23,7,24)(4,37,8,26,14,38)(6,22,11,32,9,28)(10,30,17,25,18,27)(15,21)$

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$3$:	$C_3$
$4$:	$C_2^2$
$6$:	$C_6$ x 3
$12$:	$C_6\times C_2$
$114$:	$C_{19}:C_{6}$ x 2
$228$:	38T6 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T19 x 8

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

Conjugacy classes not computed

Character table

51 x 51 character table

Regular extensions

Data not computed