Properties

Label 38T46
Degree $38$
Order $116964$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $46$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,7,15,13,4,11,14,18,17,3,16,8,10,19,12,9,5,6)(21,28,27,38,31,32)(22,36,34,37,23,25)(24,33,29,35,26,30), (1,27,9,34,19,38,3,24,2,35,15,25,17,22,10,23,6,29)(4,32,8,26,13,28,5,21,14,36,11,31,12,20,18,30,16,33)(7,37)

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
$9$:  $C_9$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3
$36$:  $C_6\times S_3$, $D_{18}$, 36T2
$54$:  $C_9\times S_3$, 18T19
$108$:  36T63, 36T69
$162$:  18T74
$324$:  36T461

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 121 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $116964=2^{2} \cdot 3^{4} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.