Properties

Label 38T19
Order \(4332\)
n \(38\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
3:  $C_3$
4:  $C_2^2$
6:  $C_6$ x 3
12:  $C_6\times C_2$
114:  $C_{19}:C_{6}$ x 2
228:  38T6 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T19 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 51 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4332=2^{2} \cdot 3 \cdot 19^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.