Galois group: 38T15

• Label: 38T15
• Degree: $38$
• Order: $2888$
• Cyclic: no
• Abelian: no
• Solvable: yes
• Primitive: no
• $p$-group: no
• Group: $D_{19}\wr C_2$

Group invariants

Abstract group:		$D_{19}\wr C_2$
Order:		$2888=2^{3} \cdot 19^{2}$
Cyclic:		no
Abelian:		no
Solvable:		yes
Nilpotency class:		not nilpotent

Group action invariants

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

Low degree resolvents

$\card{(G/N)}$	Galois groups for stem field(s)
$2$:	$C_2$ x 3
$4$:	$C_2^2$
$8$:	$D_{4}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T15

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

77 x 77 character table

Regular extensions

Data not computed