Properties

Label 33T37
Degree $33$
Order $31944$
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)
$|\Aut(F/K)|$:  $1$
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)

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:  not available
Character table: not available.