Properties

Label 46T31
Degree $46$
Order $192937984$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$
$46$:  $D_{23}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: None

Degree 23: $D_{23}$

Low degree siblings

46T30 x 2047, 46T31 x 2046

Siblings are shown with degree $\leq 47$

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

Conjugacy classes

There are 94,264 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $192937984=2^{23} \cdot 23$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  not available
Character table: not available.