Properties

Label 46T38
Order \(20891566080\)
n \(46\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
10200960:  $M_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $M_{23}$

Low degree siblings

There are no siblings with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 60 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $20891566080=2^{18} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.