Properties

Label 38T10
Order \(722\)
n \(38\)
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)
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)
$|\Aut(F/K)|$:  $19$

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: Data not available.