Properties

Label 44T35
Degree $44$
Order $968$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no

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Group action invariants

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

Low degree resolvents

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

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$

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 68 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $968=2^{3} \cdot 11^{2}$
Cyclic:  no
Abelian:  no
Solvable:  yes
GAP id:  [968, 38]
Character table: not available.