Properties

Label 33T28
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 $t$ :  $28$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,17,6,19,11,21,5,12,10,14,4,16,9,18,3,20,8,22,2,13,7,15)(23,24)(25,33)(26,32)(27,31)(28,30), (1,28,21,8,30,16,4,32,22,11,23,17,7,25,12,3,27,18,10,29,13,6,31,19,2,33,14,9,24,20,5,26,15)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

33T28 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 253 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.