Properties

Label 46T50
Order \(216862434431944426122117120000\)
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 $t$ :  $50$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,29,39,14,46,36,7,11)(2,30,40,13,45,35,8,12)(3,32,16,18,27,44,21,25,5,37,24,20,41,4,31,15,17,28,43,22,26,6,38,23,19,42)(9,34)(10,33), (3,35,22,30,45,8,44,27,17,40,19,14,42,23,5,33,10,25,15,11,37,32)(4,36,21,29,46,7,43,28,18,39,20,13,41,24,6,34,9,26,16,12,38,31)
$|\Aut(F/K)|$:  $2$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
25852016738884976640000:  $S_{23}$
51704033477769953280000:  46T45
108431217215972213061058560000:  46T48

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $S_{23}$

Low degree siblings

46T50

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 68,150 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $216862434431944426122117120000=2^{42} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.