Properties

Label 38T39
Degree $38$
Order $38988$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $39$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,7,12,13,17,14,2,11,9)(3,15,6,8,16,10,5,4,19)(20,35,37,36,27,22,34,28,31)(21,25,23,24,33,38,26,32,29), (1,24,7,20,2,36,3,29,18,38,15,21,8,32,17,26,19,31,11,30,5,34,10,37,9,25,13,35,16,33,4,22,14,28,12,23)(6,27)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$4$:  $C_4$
$6$:  $S_3$, $C_6$
$9$:  $C_9$
$12$:  $C_{12}$, $C_3 : C_4$
$18$:  $S_3\times C_3$, $C_{18}$
$36$:  $C_3\times (C_3 : C_4)$, $C_{36}$
$54$:  $C_9\times S_3$
$108$:  36T62

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 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $38988=2^{2} \cdot 3^{3} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.