Properties

Label 21T52
Order \(10206\)
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 $t$ :  $52$
Parity:  $-1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,6,3,5,2,4)(7,19,8,21,9,20)(10,18,12,17,11,16)(13,14,15), (1,16,10,4,19,13,9)(2,17,11,5,21,14,7)(3,18,12,6,20,15,8)
$|\Aut(F/K)|$:  $3$

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 13, 21T52 x 12, 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.