Properties

Label 46T20
Order \(94208\)
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 $t$ :  $20$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,6,7,10,12,13,15,18,20,22,23,26,28,30,31,34,36,38,39,42,44,45)(2,4,5,8,9,11,14,16,17,19,21,24,25,27,29,32,33,35,37,40,41,43,46), (1,29,12,40,22,3,31,14,42,23,5,34,16,43,25,8,35,18,46,28,9,37,20,2,30,11,39,21,4,32,13,41,24,6,33,15,44,26,7,36,17,45,27,10,38,19)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
23:  $C_{23}$
46:  $C_{46}$
47104:  46T19

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $C_{23}$

Low degree siblings

46T20 x 88

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 224 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $94208=2^{12} \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.