Properties

Label 33T38
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 $t$ :  $38$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,16,2,12)(3,19,11,20)(4,15,10,13)(5,22,9,17)(6,18,8,21)(7,14)(24,33)(25,32)(26,31)(27,30)(28,29), (1,23)(2,29,11,28)(3,24,10,33)(4,30,9,27)(5,25,8,32)(6,31,7,26)(13,22)(14,21)(15,20)(16,19)(17,18)
$|\Aut(F/K)|$:  $1$

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

44T231

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 175 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.