Properties

Label 38T48
Order \(4980736\)
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 $t$ :  $48$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.