Properties

Label 46T36
Order \(2122317824\)
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 $t$ :  $36$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,25,28,32,40,10,42,14,3,29,36)(2,26,27,31,39,9,41,13,4,30,35)(5,34,44,18,11,45,21,20,15,8,38,6,33,43,17,12,46,22,19,16,7,37)(23,24), (1,26,23,28,20,36,4,22,31,11,6,18,40,41,37,45,29,16,43,34,8,14)(2,25,24,27,19,35,3,21,32,12,5,17,39,42,38,46,30,15,44,33,7,13)(9,10)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $F_{23}$

Low degree siblings

46T35

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 8,624 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2122317824=2^{23} \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.