Properties

Label 38T15
Degree $38$
Order $2888$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $15$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
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

|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

There are 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2888=2^{3} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.