Properties

Label 46T41
Degree $46$
Order $8.557\times 10^{13}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$10200960$:  $M_{23}$
$20401920$:  46T27
$42785927331840$:  46T40

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 736 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $85571854663680=2^{30} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.