Properties

Label 38T45
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 $t$:  $45$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $1$
Generators:  (1,33,10,21,13,36,14,22,8,30,6,20,18,23,3,24,17,37,9,35,19,28,16,32,15,27,2,38,4,29,11,26,7,25,12,31)(5,34), (1,29,6,34,16,25,17,26,19,28,4,32,12,21,9,37,3,31,10,38,5,33,14,23,13,22,11,20,7,35,18,27,2,30,8,36)(15,24)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$3$:  $C_3$
$4$:  $C_4$
$6$:  $S_3$, $C_6$
$9$:  $C_9$
$12$:  $C_{12}$, $C_3 : C_4$
$18$:  $S_3\times C_3$, $D_{9}$, $C_{18}$
$36$:  $C_3\times (C_3 : C_4)$, $C_{36}$, 36T9
$54$:  $C_9\times S_3$, 18T19
$108$:  36T62, 36T68
$162$:  18T74
$324$:  36T462

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 118 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.