Properties

Label 38T49
Order \(9961472\)
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 $t$ :  $49$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,32,24,16,8,38,29,22,14,6,35,28,20,12,3,34,26,17,10,2,31,23,15,7,37,30,21,13,5,36,27,19,11,4,33,25,18,9), (1,17,34,11,28,5,22,37,15,31,10,25,3,19,36,14,30,8,23,2,18,33,12,27,6,21,38,16,32,9,26,4,20,35,13,29,7,24)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
19:  $C_{19}$
38:  $C_{38}$
4980736:  38T48

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $C_{19}$

Low degree siblings

38T49 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 27,632 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $9961472=2^{19} \cdot 19$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.