Properties

Label 46T48
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 $t$ :  $48$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
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)
$|\Aut(F/K)|$:  $2$

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

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:  Data not available
Character table: Data not available.