Properties

Label 21T127
Order \(2939328\)
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 $t$ :  $127$
Parity:  $1$
Primitive:  No
Nilpotency class:  $-1$ (not nilpotent)
Generators:  (1,15,16)(2,14,18)(3,13,17)(4,21,7)(5,20,8,6,19,9)(11,12), (1,20,17,14,10,7,4,3,21,18,13,11,9,5,2,19,16,15,12,8,6)
$|\Aut(F/K)|$:  $1$

Low degree resolvents

|G/N|Galois groups for stem field(s)
3:  $C_3$
21:  $C_7:C_3$
168:  $C_2^3:(C_7: C_3)$ x 2
1344:  14T35

Resolvents shown for degrees $\leq 47$

Subfields

Degree 3: None

Degree 7: $C_7:C_3$

Low degree siblings

42T2239 x 2, 42T2240, 42T2244

Siblings are shown with degree $\leq 47$

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

Conjugacy Classes

There are 99 conjugacy classes of elements. Data not shown.

Group invariants

Order:  $2939328=2^{6} \cdot 3^{8} \cdot 7$
Cyclic:  No
Abelian:  No
Solvable:  Yes
GAP id:  Data not available
Character table: Data not available.