Properties

Label 46T50
Degree $46$
Order $2.169\times 10^{29}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $46$
Transitive number $t$:  $50$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
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)

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:  not available
Character table: not available.