Properties

Label 38T20
Order \(6498\)
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 $t$ :  $20$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,18,19,9,14,2,8,5,16)(3,17,10,4,7,15,11,13,12)(20,25,34,35,33,37,29,26,32)(21,23,38,27,30,24,36,31,22), (1,25,5,32,9,20,13,27,17,34,2,22,6,29,10,36,14,24,18,31,3,38,7,26,11,33,15,21,19,28,4,35,8,23,12,30,16,37)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
18:  $D_{9}$

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 53 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.