Properties

Label 46T7
Order \(1058\)
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 $t$ :  $7$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,43,10,32,19,44,5,33,14,45,23,34,9,46,18,35,4,24,13,36,22,25,8,37,17,26,3,38,12,27,21,39,7,28,16,40,2,29,11,41,20,30,6,42,15,31), (1,5,9,13,17,21,2,6,10,14,18,22,3,7,11,15,19,23,4,8,12,16,20)(24,35,46,34,45,33,44,32,43,31,42,30,41,29,40,28,39,27,38,26,37,25,36)
$|\Aut(F/K)|$:  $23$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
23:  $C_{23}$
46:  $D_{23}$, $C_{46}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: None

Low degree siblings

46T7 x 10

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 299 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1058=2 \cdot 23^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [1058, 3]
Character table: Data not available.