Properties

Label 38T40
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 $t$:  $40$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,16,4,6,12,11,8,18,10,5,9,2,19,13,14,17,7,15)(20,31,33,23,35,32,28,29,24,30,38,36,27,34,37,22,21,26), (1,27,16,20,15,23,10,38,4,37,12,32,14,26,5,34,17,36)(2,24)(3,21,7,28,8,25,13,29,19,30,11,35,9,22,18,33,6,31)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$3$:  $C_3$
$4$:  $C_2^2$
$6$:  $S_3$, $C_6$ x 3
$9$:  $C_9$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $C_{18}$ x 3
$36$:  $C_6\times S_3$, 36T2
$54$:  $C_9\times S_3$
$108$:  36T63

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