Properties

Label 46T21
Order \(128018\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $46$
Transitive number $t$ :  $21$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,40,4,24,20,46,21,33,11,25,19,36,8,41,3,37,7,31,13,45,22,43)(2,27,17,39,5,34,10,38,6,44,23,30,14,32,12,35,9,28,16,29,15,42)(18,26), (1,29,19,25,5,46,21,45,6,33,10,27,12,24,13,34,2,39,8,30,11,37)(3,26,20,35,17,28,4,36,9,40,23,42,7,43,22,32,18,38,16,41,15,31)(14,44)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
11:  $C_{11}$
22:  $D_{11}$, 22T1
242:  22T7

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: 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 104 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $128018=2 \cdot 11^{2} \cdot 23^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.