Properties

Label 46T46
Order \(54215608607986106530529280000\)
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 $t$ :  $46$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,37,3,25,15)(2,38,4,26,16)(5,18,45,10,40,34,11,7,6,17,46,9,39,33,12,8)(13,14)(19,28,36,43)(20,27,35,44)(21,24,22,23)(29,32,30,31), (1,23,6)(2,24,5)(3,38,45,29,9,42,12,35,31,25,14,18,43,7,33,27,40,19,15)(4,37,46,30,10,41,11,36,32,26,13,17,44,8,34,28,39,20,16)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
12926008369442488320000:  $A_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $A_{23}$

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 17,144 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $54215608607986106530529280000=2^{40} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.