Properties

Label 38T20
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 $t$:  $20$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.