Properties

Label 38T46
Order \(116964\)
n \(38\)
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)
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)
$|\Aut(F/K)|$:  $1$

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:  Data not available
Character table: Data not available.