Properties

Label 26T11
Order \(338\)
n \(26\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No
Group: $C_{13}\times D_{13}$

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Group action invariants

Degree $n$ :  $26$
Transitive number $t$ :  $11$
Group :  $C_{13}\times D_{13}$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,23,13,18,12,26,11,21,10,16,9,24,8,19,7,14,6,22,5,17,4,25,3,20,2,15), (1,15,8,24,2,20,9,16,3,25,10,21,4,17,11,26,5,22,12,18,6,14,13,23,7,19)
$|\Aut(F/K)|$:  $13$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
13:  $C_{13}$
26:  $D_{13}$, $C_{26}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

26T11 x 5

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy Classes

There are 104 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $338=2 \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [338, 3]
Character table: Data not available.