Properties

Label 33T37
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 $t$ :  $37$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,24,18,2,29,14,3,23,21,4,28,17,5,33,13,6,27,20,7,32,16,8,26,12,9,31,19,10,25,15,11,30,22), (1,23,16,2,28,12)(3,33,19,11,29,20)(4,27,15,10,24,13)(5,32,22,9,30,17)(6,26,18,8,25,21)(7,31,14)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
3:  $C_3$
6:  $C_6$
12:  $A_4$
24:  $A_4\times C_2$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 11: None

Low degree siblings

44T229

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 133 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.