Properties

Label 21T50
Order \(10206\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $50$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,7,14,21,4,11,18,3,8,13,20,6,12,17)(2,9,15,19,5,10,16), (1,13,6,17,9,19,10)(2,14,4,18,7,21,11)(3,15,5,16,8,20,12)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
2:  $C_2$
7:  $C_7$
14:  $C_{14}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $C_7$

Low degree siblings

21T50 x 51, 42T554 x 52

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 66 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $10206=2 \cdot 3^{6} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.