Properties

Label 21T61
Order \(15309\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

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Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $61$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,8,15,19,5,10,17,3,7,13,20,4,11,18,2,9,14,21,6,12,16), (1,21,17,14,10,9,4,3,19,18,15,11,8,6,2,20,16,13,12,7,5)
$|\Aut(F/K)|$:  $3$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
7:  $C_7$
21:  $C_{21}$
5103:  21T39

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $C_7$

Low degree siblings

21T61 x 103

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 333 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $15309=3^{7} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.