Properties

Label 44T50
Order \(1936\)
n \(44\)
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)
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)
$|\Aut(F/K)|$:  $2$

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: Data not available.