Properties

Label 38T49
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 $t$:  $49$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,32,24,16,8,38,29,22,14,6,35,28,20,12,3,34,26,17,10,2,31,23,15,7,37,30,21,13,5,36,27,19,11,4,33,25,18,9), (1,17,34,11,28,5,22,37,15,31,10,25,3,19,36,14,30,8,23,2,18,33,12,27,6,21,38,16,32,9,26,4,20,35,13,29,7,24)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$19$:  $C_{19}$
$38$:  $C_{38}$
$4980736$:  38T48

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 19: $C_{19}$

Low degree siblings

38T49 x 13796

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 27,632 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.