Properties

Label 44T26
Order \(484\)
n \(44\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{11}\times C_{11}:C_4$

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Group action invariants

Degree $n$ :  $44$
Transitive number $t$ :  $26$
Group :  $C_{11}\times C_{11}:C_4$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,3,5,7,9,12,14,15,18,19,21,2,4,6,8,10,11,13,16,17,20,22)(23,33,44,31,42,30,39,28,38,25,35,24,34,43,32,41,29,40,27,37,26,36), (1,38,6,43,9,27,13,33,18,39,22,24,4,29,7,36,11,42,15,25,20,32,2,37,5,44,10,28,14,34,17,40,21,23,3,30,8,35,12,41,16,26,19,31)
$|\Aut(F/K)|$:  $22$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
4:  $C_4$
11:  $C_{11}$
22:  $D_{11}$, 22T1
242:  22T7

Resolvents shown for degrees $\leq 29$

Subfields

Degree 2: $C_2$

Degree 4: $C_4$

Degree 11: None

Degree 22: 22T7

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 154 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $484=2^{2} \cdot 11^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [484, 5]
Character table: Data not available.