Properties

Label 44T17
Order \(264\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{11}\times S_4$

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Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $17$
Group :  $C_{11}\times S_4$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,41,37,33,32,27,24,18,14,9,6,3,44,38,35,29,28,22,19,13,11,7,4,42,39,36,31,25,21,17,16,12,5)(2,43,40,34,30,26,23,20,15,10,8), (1,26,5,32,9,34,14,38,19,43,22,4,25,8,31,12,33,15,37,18,44,23,3,28,7,30,11,36,16,40,17,41,24,2,27,6,29,10,35,13,39,20,42,21)
$|\Aut(F/K)|$:  $11$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
11:  $C_{11}$
22:  22T1
24:  $S_4$

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: None

Degree 4: $S_4$

Degree 11: $C_{11}$

Degree 22: None

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 55 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $264=2^{3} \cdot 3 \cdot 11$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [264, 31]
Character table: Data not available.