Properties

Label 33T27
Order \(7986\)
n \(33\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

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

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
11:  $C_{11}$
22:  22T1
66:  33T2
726:  33T13

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T27 x 9

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 418 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.