Properties

Label 38T50
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 $t$ :  $50$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.