Properties

Label 38T13
Order \(2166\)
n \(38\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 90 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2166=2 \cdot 3 \cdot 19^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.