Properties

Label 44T48
Degree $44$
Order $1936$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

Degree $n$:  $44$
Transitive number $t$:  $48$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (3,22)(4,21)(5,19)(6,20)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,30)(24,29)(25,28)(26,27)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38), (1,33,8,41)(2,34,7,42)(3,44,5,32)(4,43,6,31)(9,30,22,24)(10,29,21,23)(11,39,19,35)(12,40,20,36)(13,28,17,26)(14,27,18,25)(15,38)(16,37)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $D_{4}$ x 2, $C_4\times C_2$
$16$:  $C_2^2:C_4$
$484$:  22T8

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $D_{4}$

Degree 11: None

Degree 22: 22T8

Low degree siblings

There are no siblings with degree $\leq 29$
Data on whether or not a number field with this Galois group has arithmetically equivalent fields has not been computed.

Conjugacy classes

There are 130 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $1936=2^{4} \cdot 11^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [1936, 116]
Character table: not available.