Properties

Label 26T13
Order \(676\)
n \(26\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$ x 3
4:  $C_2^2$
26:  $D_{13}$ x 2
52:  $D_{26}$ x 2

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$

Degree 13: None

Low degree siblings

26T13 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 64 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $676=2^{2} \cdot 13^{2}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  [676, 13]
Character table: Data not available.