Properties

Label 46T45
Degree $46$
Order $5.170\times 10^{22}$
Cyclic no
Abelian no
Solvable no
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 23: $S_{23}$

Low degree siblings

46T45

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 2,510 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $51704033477769953280000=2^{20} \cdot 3^{9} \cdot 5^{4} \cdot 7^{3} \cdot 11^{2} \cdot 13 \cdot 17 \cdot 19 \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  no
GAP id:  not available
Character table: not available.