Properties

Label 46T49
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 $t$:  $49$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,37,18)(2,38,17)(3,35,10,8)(4,36,9,7)(5,43,20,30,27,40,25,42,22,23,46,31,15,11,6,44,19,29,28,39,26,41,21,24,45,32,16,12)(13,33,14,34), (1,23,20,46,40,31,10,15,27,22,18,12,25,7,38,2,24,19,45,39,32,9,16,28,21,17,11,26,8,37)(3,44,6,33,30,35,42,13,4,43,5,34,29,36,41,14)

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

46T48

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.