Properties

Label 46T49
Order \(108431217215972213061058560000\)
n \(46\)
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)
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)
$|\Aut(F/K)|$:  $2$

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:  Data not available
Character table: Data not available.