Properties

Label 46T28
Degree $46$
Order $96468992$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

Learn more about

Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$23$:  $C_{23}$
$47104$:  46T19 x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T28 x 182182

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 182,384 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $96468992=2^{22} \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.