Properties

Label 46T26
Order \(1036288\)
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 $t$ :  $26$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,44,29,38,40,5,31,3,19,23)(2,7,43,30,37,39,6,32,4,20,24)(11,22,36,28,26,14,34,15,45,42,17,12,21,35,27,25,13,33,16,46,41,18), (1,27,40,41,4,35,25,32,10,13,29,2,28,39,42,3,36,26,31,9,14,30)(5,43,12,21,16,37,34,18,45,19,7)(6,44,11,22,15,38,33,17,46,20,8)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
11:  $C_{11}$
22:  22T1
253:  $C_{23}:C_{11}$
506:  46T4
518144:  46T25

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}:C_{11}$

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 64 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1036288=2^{12} \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.