Properties

Label 46T44
Degree $46$
Order $2.585\times 10^{22}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $S_{23}$

Low degree siblings

23T7

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 1,255 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $25852016738884976640000=2^{19} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.