Properties

Label 46T30
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 $t$:  $30$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,17)(2,18)(3,15,4,16)(5,13)(6,14)(7,11,8,12)(9,10)(19,45,20,46)(21,43,22,44)(23,42)(24,41)(25,40)(26,39)(27,38,28,37)(29,36)(30,35)(31,33,32,34), (1,29,12,40,22,3,32,14,42,24,6,34,15,44,26,8,36,17,45,28,10,38,19)(2,30,11,39,21,4,31,13,41,23,5,33,16,43,25,7,35,18,46,27,9,37,20)

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 2046, 46T31 x 2047

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.