Properties

Label 38T37
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 $t$:  $37$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,20,9,21,17,22,6,23,14,24,3,25,11,26,19,27,8,28,16,29,5,30,13,31,2,32,10,33,18,34,7,35,15,36,4,37,12,38), (1,22,16,25,10,20)(2,26,8,31,17,29)(3,30,19,37,5,38)(4,34,11,24,12,28)(6,23,14,36,7,27)(9,35)(13,32,15,21,18,33)

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
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $D_{9}$
$36$:  $C_6\times S_3$, $D_{18}$
$54$:  18T19
$108$:  36T69

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 51 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.