Properties

Label 38T21
Degree $38$
Order $6498$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$18$:  $S_3\times C_3$

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 54 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:  not available
Character table: not available.