Properties

Label 46T47
Degree $46$
Order $1.084\times 10^{29}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $46$
Transitive number $t$:  $47$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,7,14,23,5,18,19,31,26,15,12,34,2,8,13,24,6,17,20,32,25,16,11,33)(3,38,44,9)(4,37,43,10)(21,40,46,30,22,39,45,29)(27,35,28,36), (1,45,11,41,37,22,26,39,16,36,28,34,32,30,20,6,17)(2,46,12,42,38,21,25,40,15,35,27,33,31,29,19,5,18)(3,44,14,9,23)(4,43,13,10,24)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$12926008369442488320000$:  $A_{23}$
$25852016738884976640000$:  46T43
$54215608607986106530529280000$:  46T46

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 34,288 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $108431217215972213061058560000=2^{41} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.