Properties

Label 38T12
Degree $38$
Order $1444$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$4$:  $C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T12 x 9

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 94 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1444=2^{2} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1444, 8]
Character table: not available.