Properties

Label 44T36
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 $t$:  $36$
Parity:  $-1$
Primitive:  no
Nilpotency class:  $-1$ (not nilpotent)
$|\Aut(F/K)|$:  $2$
Generators:  (1,26,12,41,21,35,9,29,19,24,7,40,17,34,6,28,15,44,4,37,14,32,2,25,11,42,22,36,10,30,20,23,8,39,18,33,5,27,16,43,3,38,13,31), (1,14)(2,13)(3,11)(4,12)(5,10)(6,9)(15,21)(16,22)(17,19)(18,20)(23,25)(24,26)(27,44)(28,43)(29,41)(30,42)(31,40)(32,39)(33,37)(34,38)

Low degree resolvents

|G/N|Galois groups for stem field(s)
$2$:  $C_2$ x 3
$4$:  $C_4$ x 2, $C_2^2$
$8$:  $C_4\times C_2$
$22$:  $D_{11}$ x 2
$44$:  $D_{22}$ x 2
$484$:  22T9

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: None

Degree 22: 22T9

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 98 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, 18]
Character table: not available.