Properties

Label 38T48
Degree $38$
Order $4980736$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Learn more about

Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $48$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,15,29,6,20,34,9,23,38,13,28,4,17,32,7,21,35,11,26)(2,16,30,5,19,33,10,24,37,14,27,3,18,31,8,22,36,12,25), (1,38,36,33,31,29,27,25,24,22,20,18,15,13,12,9,7,5,3)(2,37,35,34,32,30,28,26,23,21,19,17,16,14,11,10,8,6,4)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$19$:  $C_{19}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $C_{19}$

Low degree siblings

38T48 x 13796

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 13,816 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4980736=2^{18} \cdot 19$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.