Label 38T11
Degree $38$
Order $1444$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$38$:  $D_{19}$ x 2
$76$:  $D_{38}$ x 2

Resolvents shown for degrees $\leq 47$


Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T11 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 121 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1444=2^{2} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1444, 9]
Character table: not available.