Properties

Label 38T47
Degree $38$
Order $233928$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $38$
Transitive number $t$:  $47$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,24,9,23,19,36,3,38,2,31,15,27,17,22,10,30,6,21)(4,26,8,35,13,32,5,33,14,20,11,37,12,25,18,29,16,34)(7,28), (1,37,14,28)(2,29,13,36)(3,21,12,25)(4,32,11,33)(5,24,10,22)(6,35,9,30)(7,27,8,38)(15,20,19,26)(16,31,18,34)(17,23)

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
$8$:  $D_{4}$
$9$:  $C_9$
$12$:  $D_{6}$, $C_6\times C_2$
$18$:  $S_3\times C_3$, $D_{9}$, $C_{18}$ x 3
$24$:  $(C_6\times C_2):C_2$, $D_4 \times C_3$
$36$:  $C_6\times S_3$, $D_{18}$, 36T2
$54$:  $C_9\times S_3$, 18T19
$72$:  12T42, 36T15, 36T24
$108$:  36T63, 36T69
$162$:  18T74
$216$:  36T181, 36T189
$324$:  36T461
$648$:  36T966

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 209 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $233928=2^{3} \cdot 3^{4} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.