Properties

Label 21T143
Order \(14224896\)
n \(21\)
Cyclic No
Abelian No
Solvable No
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $143$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,13,20)(2,10,16)(3,14,19,7,9,15)(4,11,21)(5,8,17,6,12,18), (1,18,10,4,17,8,2,20,14)(3,16,9,5,21,13,6,19,11)(7,15,12)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: $C_3$

Degree 7: None

Low degree siblings

21T143, 24T24055, 42T2782 x 2

Siblings are shown with degree $\leq 47$

A number field with this Galois group has exactly one arithmetically equivalent field.

Conjugacy Classes

There are 88 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $14224896=2^{9} \cdot 3^{4} \cdot 7^{3}$
Cyclic:  No
Abelian:  No
Solvable:  No
GAP id:  Data not available
Character table: Data not available.