Properties

Label 38T40
Order \(38988\)
n \(38\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.