Properties

Label 46T48
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 $t$:  $48$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,15,45,32,29,19,9,18,42,7,35,37)(2,16,46,31,30,20,10,17,41,8,36,38)(3,43,40,5,12)(4,44,39,6,11)(13,21,34)(14,22,33)(23,27,26,24,28,25), (1,45,6,27,23,41,35,15,20,30,4,11,14,9,34,37,43,7,2,46,5,28,24,42,36,16,19,29,3,12,13,10,33,38,44,8)(17,31,21,26,18,32,22,25)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$25852016738884976640000$:  $S_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $S_{23}$

Low degree siblings

46T49

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 34,075 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.