Properties

Label 38T42
Degree $38$
Order $58482$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $42$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,30,14,29,16,23,9,25,5,37,19,33,8,28,18,36,2,27)(3,24,7,31,12,35,4,21,13,32,10,22,11,38,17,20,15,26)(6,34), (1,27,11,23,4,22,7,36,3,30,2,38,16,21,10,31,18,24)(5,33,12,34,9,20,13,26,14,37,19,35,6,25,17,32,15,29)(8,28)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$6$:  $S_3$, $C_6$
$9$:  $C_9$
$18$:  $S_3\times C_3$, $D_{9}$, $C_{18}$
$54$:  $C_9\times S_3$, 18T19
$162$:  18T74

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 77 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $58482=2 \cdot 3^{4} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.