Properties

Label 38T50
Degree $38$
Order $9961472$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $50$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,30,2,29)(3,28,4,27)(5,25,6,26)(7,23)(8,24)(9,21,10,22)(11,20)(12,19)(13,18,14,17)(15,16)(31,38)(32,37)(33,35)(34,36), (1,37,2,38)(3,36)(4,35)(5,33)(6,34)(7,32,8,31)(9,29,10,30)(11,28,12,27)(13,26)(14,25)(15,23,16,24)(17,21,18,22)

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $D_{19}$

Low degree siblings

38T50 x 510, 38T51 x 511

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 7,676 conjugacy classes of elements. Data not shown.

Group invariants

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