Properties

Label 46T9
Order \(2116\)
n \(46\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T9 x 11

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 136 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2116=2^{2} \cdot 23^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.