Properties

Label 38T21
Order \(6498\)
n \(38\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $S_3$, $C_6$
18:  $S_3\times C_3$

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 54 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $6498=2 \cdot 3^{2} \cdot 19^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.