Properties

Label 33T26
Order \(7986\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Learn more about

Group action invariants

Degree $n$ :  $33$
Transitive number $t$ :  $26$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,18,32,10,15,33)(2,14,26,9,19,28)(3,21,31,8,12,23)(4,17,25,7,16,29)(5,13,30,6,20,24)(11,22,27), (1,15,31,2,19,25,3,12,30,4,16,24,5,20,29,6,13,23,7,17,28,8,21,33,9,14,27,10,18,32,11,22,26)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$
22:  $D_{11}$
66:  33T4
726:  33T12

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

33T26 x 39

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 241 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $7986=2 \cdot 3 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.