Properties

Label 44T50
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 $t$:  $50$
Parity:  $1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,32,15,27,8,23,22,41,14,37,5,34,20,29,12,26,3,44,17,39,10,35)(2,31,16,28,7,24,21,42,13,38,6,33,19,30,11,25,4,43,18,40,9,36), (1,21)(2,22)(3,19)(4,20)(5,18)(6,17)(7,15)(8,16)(9,14)(10,13)(11,12)(23,25)(24,26)(27,43)(28,44)(29,42)(30,41)(31,39)(32,40)(33,37)(34,38)(35,36), (1,25,14,31)(2,26,13,32)(3,38,12,42)(4,37,11,41)(5,28,10,30)(6,27,9,29)(7,39)(8,40)(15,43,22,36)(16,44,21,35)(17,33,20,24)(18,34,19,23)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$8$:  $D_{4}$ x 2, $C_2^3$
$16$:  $D_4\times C_2$
$968$:  22T10

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

Degree 11: None

Degree 22: 22T10

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 70 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, 161]
Character table: not available.