Properties

Label 33T39
Order \(31944\)
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 $t$ :  $39$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,19,25,3,22,24,5,14,23,7,17,33,9,20,32,11,12,31,2,15,30,4,18,29,6,21,28,8,13,27,10,16,26), (1,30,11,24)(2,25,10,29)(3,31,9,23)(4,26,8,28)(5,32,7,33)(6,27)(12,17,22,16,21,15,20,14,19,13,18)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
6:  $S_3$
24:  $S_4$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $S_3$

Degree 11: None

Low degree siblings

44T230

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 100 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $31944=2^{3} \cdot 3 \cdot 11^{3}$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.