Properties

Label 38T36
Degree $38$
Order $25992$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$3$:  $C_3$
$4$:  $C_2^2$
$6$:  $C_6$ x 3
$8$:  $D_{4}$
$9$:  $C_9$
$12$:  $C_6\times C_2$
$18$:  $C_{18}$ x 3
$24$:  $D_4 \times C_3$
$36$:  36T2
$72$:  36T15

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 19: None

Low degree siblings

38T36

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

There are 53 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $25992=2^{3} \cdot 3^{2} \cdot 19^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.