Properties

Label 46T43
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 $t$:  $43$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,36,14,39)(2,35,13,40)(3,24,27,12,15,38,42,5,19,8,34,44)(4,23,28,11,16,37,41,6,20,7,33,43)(9,30,31,21,18,26,46)(10,29,32,22,17,25,45), (1,19,33,13,45,18,36,44,16,12,23,5,7,38,25,3,10,27,39,2,20,34,14,46,17,35,43,15,11,24,6,8,37,26,4,9,28,40)(21,41)(22,42)(29,31)(30,32)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$12926008369442488320000$:  $A_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

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 1,282 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.