Properties

Label 46T40
Degree $46$
Order $4.279\times 10^{13}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

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

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 368 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $42785927331840=2^{29} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.