Properties

Label 21T51
Order \(10206\)
n \(21\)
Cyclic No
Abelian No
Solvable Yes
Primitive No
$p$-group No

Related objects

Learn more about

Group action invariants

Degree $n$ :  $21$
Transitive number $t$ :  $51$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,14,6,16,9,20,10)(2,15,4,17,7,19,11)(3,13,5,18,8,21,12), (1,13,2,15,3,14)(4,12,6,10,5,11)(7,8)(16,19)(17,20)(18,21)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

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

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $D_{7}$

Low degree siblings

21T51 x 12, 21T52 x 13, 42T555 x 13, 42T556 x 13, 42T557 x 13

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 96 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.