Properties

Label 38T10
Degree $38$
Order $722$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$19$:  $C_{19}$
$38$:  $D_{19}$, $C_{38}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T10 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 209 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $722=2 \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [722, 3]
Character table: not available.