Properties

Label 46T37
Order \(4244635648\)
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 $t$ :  $37$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,17,19,25,43,6,30,10,42,45,11,2,18,20,26,44,5,29,9,41,46,12)(3,24,37,33,21,31,16,13,7,35,27)(4,23,38,34,22,32,15,14,8,36,28), (1,10,2,9)(3,7,4,8)(5,6)(11,46)(12,45)(13,43)(14,44)(15,41)(16,42)(17,40)(18,39)(19,37)(20,38)(21,36,22,35)(23,34,24,33)(25,32,26,31)(27,29,28,30)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
11:  $C_{11}$
22:  22T1 x 3
44:  44T2
506:  $F_{23}$
1012:  46T6
2122317824:  46T35

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $F_{23}$

Low degree siblings

46T37

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 17,248 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $4244635648=2^{24} \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.