Properties

Label 38T16
Degree $38$
Order $4332$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_2^2$
$6$:  $S_3$
$12$:  $D_{6}$

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 63 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4332=2^{2} \cdot 3 \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.